int_rules_6_7_9 = @theory begin

    #= ::Subsection::Closed:: =#
    #= 6.7.9*Active*hyperbolic*functions =#
    @apply_utils Antiderivative(((~(e') + ~(f') * ~x) ^ ~(m') * sinh(~(c') + ~(d') * ~x) ^ ~(n')) / (~a + ~(b') * sinh(~(c') + ~(d') * ~x)), ~x) => (1 / ~b) * Antiderivative((~e + ~f * ~x) ^ ~m * sinh(~c + ~d * ~x) ^ (~n - 1), ~x) - (~a / ~b) * Antiderivative(((~e + ~f * ~x) ^ ~m * sinh(~c + ~d * ~x) ^ (~n - 1)) / (~a + ~b * sinh(~c + ~d * ~x)), ~x) <-- FreeQ([~a, ~b, ~c, ~d, ~e, ~f], ~x) && (IGtQ(~m, 0) && IGtQ(~n, 0))
    @apply_utils Antiderivative(((~(e') + ~(f') * ~x) ^ ~(m') * cosh(~(c') + ~(d') * ~x) ^ ~(n')) / (~a + ~(b') * cosh(~(c') + ~(d') * ~x)), ~x) => (1 / ~b) * Antiderivative((~e + ~f * ~x) ^ ~m * cosh(~c + ~d * ~x) ^ (~n - 1), ~x) - (~a / ~b) * Antiderivative(((~e + ~f * ~x) ^ ~m * cosh(~c + ~d * ~x) ^ (~n - 1)) / (~a + ~b * cosh(~c + ~d * ~x)), ~x) <-- FreeQ([~a, ~b, ~c, ~d, ~e, ~f], ~x) && (IGtQ(~m, 0) && IGtQ(~n, 0))
    @apply_utils Antiderivative(((~(e') + ~(f') * ~x) ^ ~(m') * cosh(~(c') + ~(d') * ~x)) / (~a + ~(b') * sinh(~(c') + ~(d') * ~x)), ~x) => -((~e + ~f * ~x) ^ (~m + 1)) / (~b * ~f * (~m + 1)) + 2 * Antiderivative(((~e + ~f * ~x) ^ ~m * ℯ ^ (~c + ~d * ~x)) / (~a + ~b * ℯ ^ (~c + ~d * ~x)), ~x) <-- FreeQ([~a, ~b, ~c, ~d, ~e, ~f], ~x) && (IGtQ(~m, 0) && EqQ((~a) ^ 2 + (~b) ^ 2, 0))
    @apply_utils Antiderivative(((~(e') + ~(f') * ~x) ^ ~(m') * sinh(~(c') + ~(d') * ~x)) / (~a + ~(b') * cosh(~(c') + ~(d') * ~x)), ~x) => -((~e + ~f * ~x) ^ (~m + 1)) / (~b * ~f * (~m + 1)) + 2 * Antiderivative(((~e + ~f * ~x) ^ ~m * ℯ ^ (~c + ~d * ~x)) / (~a + ~b * ℯ ^ (~c + ~d * ~x)), ~x) <-- FreeQ([~a, ~b, ~c, ~d, ~e, ~f], ~x) && (IGtQ(~m, 0) && EqQ((~a) ^ 2 - (~b) ^ 2, 0))
    @apply_utils Antiderivative(((~(e') + ~(f') * ~x) ^ ~(m') * cosh(~(c') + ~(d') * ~x)) / (~a + ~(b') * sinh(~(c') + ~(d') * ~x)), ~x) => -((~e + ~f * ~x) ^ (~m + 1)) / (~b * ~f * (~m + 1)) + Antiderivative(((~e + ~f * ~x) ^ ~m * ℯ ^ (~c + ~d * ~x)) / ((~a - Rt((~a) ^ 2 + (~b) ^ 2, 2)) + ~b * ℯ ^ (~c + ~d * ~x)), ~x) + Antiderivative(((~e + ~f * ~x) ^ ~m * ℯ ^ (~c + ~d * ~x)) / (~a + Rt((~a) ^ 2 + (~b) ^ 2, 2) + ~b * ℯ ^ (~c + ~d * ~x)), ~x) <-- FreeQ([~a, ~b, ~c, ~d, ~e, ~f], ~x) && (IGtQ(~m, 0) && NeQ((~a) ^ 2 + (~b) ^ 2, 0))
    @apply_utils Antiderivative(((~(e') + ~(f') * ~x) ^ ~(m') * sinh(~(c') + ~(d') * ~x)) / (~a + ~(b') * cosh(~(c') + ~(d') * ~x)), ~x) => -((~e + ~f * ~x) ^ (~m + 1)) / (~b * ~f * (~m + 1)) + Antiderivative(((~e + ~f * ~x) ^ ~m * ℯ ^ (~c + ~d * ~x)) / ((~a - Rt((~a) ^ 2 - (~b) ^ 2, 2)) + ~b * ℯ ^ (~c + ~d * ~x)), ~x) + Antiderivative(((~e + ~f * ~x) ^ ~m * ℯ ^ (~c + ~d * ~x)) / (~a + Rt((~a) ^ 2 - (~b) ^ 2, 2) + ~b * ℯ ^ (~c + ~d * ~x)), ~x) <-- FreeQ([~a, ~b, ~c, ~d, ~e, ~f], ~x) && (IGtQ(~m, 0) && NeQ((~a) ^ 2 - (~b) ^ 2, 0))
    @apply_utils Antiderivative(((~(e') + ~(f') * ~x) ^ ~(m') * cosh(~(c') + ~(d') * ~x) ^ ~n) / (~a + ~(b') * sinh(~(c') + ~(d') * ~x)), ~x) => (1 / ~a) * Antiderivative((~e + ~f * ~x) ^ ~m * cosh(~c + ~d * ~x) ^ (~n - 2), ~x) + (1 / ~b) * Antiderivative((~e + ~f * ~x) ^ ~m * cosh(~c + ~d * ~x) ^ (~n - 2) * sinh(~c + ~d * ~x), ~x) <-- FreeQ([~a, ~b, ~c, ~d, ~e, ~f, ~m], ~x) && (IGtQ(~n, 1) && EqQ((~a) ^ 2 + (~b) ^ 2, 0))
    @apply_utils Antiderivative(((~(e') + ~(f') * ~x) ^ ~(m') * sinh(~(c') + ~(d') * ~x) ^ ~n) / (~a + ~(b') * cosh(~(c') + ~(d') * ~x)), ~x) => (-1 / ~a) * Antiderivative((~e + ~f * ~x) ^ ~m * sinh(~c + ~d * ~x) ^ (~n - 2), ~x) + (1 / ~b) * Antiderivative((~e + ~f * ~x) ^ ~m * sinh(~c + ~d * ~x) ^ (~n - 2) * cosh(~c + ~d * ~x), ~x) <-- FreeQ([~a, ~b, ~c, ~d, ~e, ~f, ~m], ~x) && (IGtQ(~n, 1) && EqQ((~a) ^ 2 - (~b) ^ 2, 0))
    @apply_utils Antiderivative(((~(e') + ~(f') * ~x) ^ ~(m') * cosh(~(c') + ~(d') * ~x) ^ ~n) / (~a + ~(b') * sinh(~(c') + ~(d') * ~x)), ~x) => (-(~a) / (~b) ^ 2) * Antiderivative((~e + ~f * ~x) ^ ~m * cosh(~c + ~d * ~x) ^ (~n - 2), ~x) + (1 / ~b) * Antiderivative((~e + ~f * ~x) ^ ~m * cosh(~c + ~d * ~x) ^ (~n - 2) * sinh(~c + ~d * ~x), ~x) + (((~a) ^ 2 + (~b) ^ 2) / (~b) ^ 2) * Antiderivative(((~e + ~f * ~x) ^ ~m * cosh(~c + ~d * ~x) ^ (~n - 2)) / (~a + ~b * sinh(~c + ~d * ~x)), ~x) <-- FreeQ([~a, ~b, ~c, ~d, ~e, ~f], ~x) && (IGtQ(~n, 1) && (NeQ((~a) ^ 2 + (~b) ^ 2, 0) && IGtQ(~m, 0)))
    @apply_utils Antiderivative(((~(e') + ~(f') * ~x) ^ ~(m') * sinh(~(c') + ~(d') * ~x) ^ ~n) / (~a + ~(b') * cosh(~(c') + ~(d') * ~x)), ~x) => (-(~a) / (~b) ^ 2) * Antiderivative((~e + ~f * ~x) ^ ~m * sinh(~c + ~d * ~x) ^ (~n - 2), ~x) + (1 / ~b) * Antiderivative((~e + ~f * ~x) ^ ~m * sinh(~c + ~d * ~x) ^ (~n - 2) * cosh(~c + ~d * ~x), ~x) + (((~a) ^ 2 - (~b) ^ 2) / (~b) ^ 2) * Antiderivative(((~e + ~f * ~x) ^ ~m * sinh(~c + ~d * ~x) ^ (~n - 2)) / (~a + ~b * cosh(~c + ~d * ~x)), ~x) <-- FreeQ([~a, ~b, ~c, ~d, ~e, ~f], ~x) && (IGtQ(~n, 1) && (NeQ((~a) ^ 2 - (~b) ^ 2, 0) && IGtQ(~m, 0)))
    @apply_utils Antiderivative(((~(e') + ~(f') * ~x) ^ ~(m') * tanh(~(c') + ~(d') * ~x) ^ ~(n')) / (~a + ~(b') * sinh(~(c') + ~(d') * ~x)), ~x) => (1 / ~b) * Antiderivative((~e + ~f * ~x) ^ ~m * sech(~c + ~d * ~x) * tanh(~c + ~d * ~x) ^ (~n - 1), ~x) - (~a / ~b) * Antiderivative(((~e + ~f * ~x) ^ ~m * sech(~c + ~d * ~x) * tanh(~c + ~d * ~x) ^ (~n - 1)) / (~a + ~b * sinh(~c + ~d * ~x)), ~x) <-- FreeQ([~a, ~b, ~c, ~d, ~e, ~f], ~x) && (IGtQ(~m, 0) && IGtQ(~n, 0))
    @apply_utils Antiderivative(((~(e') + ~(f') * ~x) ^ ~(m') * coth(~(c') + ~(d') * ~x) ^ ~(n')) / (~a + ~(b') * cosh(~(c') + ~(d') * ~x)), ~x) => (1 / ~b) * Antiderivative((~e + ~f * ~x) ^ ~m * csch(~c + ~d * ~x) * coth(~c + ~d * ~x) ^ (~n - 1), ~x) - (~a / ~b) * Antiderivative(((~e + ~f * ~x) ^ ~m * csch(~c + ~d * ~x) * coth(~c + ~d * ~x) ^ (~n - 1)) / (~a + ~b * cosh(~c + ~d * ~x)), ~x) <-- FreeQ([~a, ~b, ~c, ~d, ~e, ~f], ~x) && (IGtQ(~m, 0) && IGtQ(~n, 0))
    @apply_utils Antiderivative(((~(e') + ~(f') * ~x) ^ ~(m') * coth(~(c') + ~(d') * ~x) ^ ~(n')) / (~a + ~(b') * sinh(~(c') + ~(d') * ~x)), ~x) => (1 / ~a) * Antiderivative((~e + ~f * ~x) ^ ~m * coth(~c + ~d * ~x) ^ ~n, ~x) - (~b / ~a) * Antiderivative(((~e + ~f * ~x) ^ ~m * cosh(~c + ~d * ~x) * coth(~c + ~d * ~x) ^ (~n - 1)) / (~a + ~b * sinh(~c + ~d * ~x)), ~x) <-- FreeQ([~a, ~b, ~c, ~d, ~e, ~f], ~x) && (IGtQ(~m, 0) && IGtQ(~n, 0))
    @apply_utils Antiderivative(((~(e') + ~(f') * ~x) ^ ~(m') * tanh(~(c') + ~(d') * ~x) ^ ~(n')) / (~a + ~(b') * cosh(~(c') + ~(d') * ~x)), ~x) => (1 / ~a) * Antiderivative((~e + ~f * ~x) ^ ~m * tanh(~c + ~d * ~x) ^ ~n, ~x) - (~b / ~a) * Antiderivative(((~e + ~f * ~x) ^ ~m * sinh(~c + ~d * ~x) * tanh(~c + ~d * ~x) ^ (~n - 1)) / (~a + ~b * cosh(~c + ~d * ~x)), ~x) <-- FreeQ([~a, ~b, ~c, ~d, ~e, ~f], ~x) && (IGtQ(~m, 0) && IGtQ(~n, 0))
    @apply_utils Antiderivative(((~(e') + ~(f') * ~x) ^ ~(m') * sech(~(c') + ~(d') * ~x) ^ ~(n')) / (~a + ~(b') * sinh(~(c') + ~(d') * ~x)), ~x) => (1 / ~a) * Antiderivative((~e + ~f * ~x) ^ ~m * sech(~c + ~d * ~x) ^ (~n + 2), ~x) + (1 / ~b) * Antiderivative((~e + ~f * ~x) ^ ~m * sech(~c + ~d * ~x) ^ (~n + 1) * tanh(~c + ~d * ~x), ~x) <-- FreeQ([~a, ~b, ~c, ~d, ~e, ~f, ~n], ~x) && (IGtQ(~m, 0) && EqQ((~a) ^ 2 + (~b) ^ 2, 0))
    @apply_utils Antiderivative(((~(e') + ~(f') * ~x) ^ ~(m') * csch(~(c') + ~(d') * ~x) ^ ~(n')) / (~a + ~(b') * cosh(~(c') + ~(d') * ~x)), ~x) => (-1 / ~a) * Antiderivative((~e + ~f * ~x) ^ ~m * csch(~c + ~d * ~x) ^ (~n + 2), ~x) + (1 / ~b) * Antiderivative((~e + ~f * ~x) ^ ~m * csch(~c + ~d * ~x) ^ (~n + 1) * coth(~c + ~d * ~x), ~x) <-- FreeQ([~a, ~b, ~c, ~d, ~e, ~f, ~n], ~x) && (IGtQ(~m, 0) && EqQ((~a) ^ 2 - (~b) ^ 2, 0))
    @apply_utils Antiderivative(((~(e') + ~(f') * ~x) ^ ~(m') * sech(~(c') + ~(d') * ~x) ^ ~(n')) / (~a + ~(b') * sinh(~(c') + ~(d') * ~x)), ~x) => ((~b) ^ 2 / ((~a) ^ 2 + (~b) ^ 2)) * Antiderivative(((~e + ~f * ~x) ^ ~m * sech(~c + ~d * ~x) ^ (~n - 2)) / (~a + ~b * sinh(~c + ~d * ~x)), ~x) + (1 / ((~a) ^ 2 + (~b) ^ 2)) * Antiderivative((~e + ~f * ~x) ^ ~m * sech(~c + ~d * ~x) ^ ~n * (~a - ~b * sinh(~c + ~d * ~x)), ~x) <-- FreeQ([~a, ~b, ~c, ~d, ~e, ~f], ~x) && (IGtQ(~m, 0) && (NeQ((~a) ^ 2 + (~b) ^ 2, 0) && IGtQ(~n, 0)))
    @apply_utils Antiderivative(((~(e') + ~(f') * ~x) ^ ~(m') * csch(~(c') + ~(d') * ~x) ^ ~(n')) / (~a + ~(b') * cosh(~(c') + ~(d') * ~x)), ~x) => ((~b) ^ 2 / ((~a) ^ 2 - (~b) ^ 2)) * Antiderivative(((~e + ~f * ~x) ^ ~m * csch(~c + ~d * ~x) ^ (~n - 2)) / (~a + ~b * cosh(~c + ~d * ~x)), ~x) + (1 / ((~a) ^ 2 - (~b) ^ 2)) * Antiderivative((~e + ~f * ~x) ^ ~m * csch(~c + ~d * ~x) ^ ~n * (~a - ~b * cosh(~c + ~d * ~x)), ~x) <-- FreeQ([~a, ~b, ~c, ~d, ~e, ~f], ~x) && (IGtQ(~m, 0) && (NeQ((~a) ^ 2 - (~b) ^ 2, 0) && IGtQ(~n, 0)))
    @apply_utils Antiderivative(((~(e') + ~(f') * ~x) ^ ~(m') * csch(~(c') + ~(d') * ~x) ^ ~(n')) / (~a + ~(b') * sinh(~(c') + ~(d') * ~x)), ~x) => (1 / ~a) * Antiderivative((~e + ~f * ~x) ^ ~m * csch(~c + ~d * ~x) ^ ~n, ~x) - (~b / ~a) * Antiderivative(((~e + ~f * ~x) ^ ~m * csch(~c + ~d * ~x) ^ (~n - 1)) / (~a + ~b * sinh(~c + ~d * ~x)), ~x) <-- FreeQ([~a, ~b, ~c, ~d, ~e, ~f], ~x) && (IGtQ(~m, 0) && IGtQ(~n, 0))
    @apply_utils Antiderivative(((~(e') + ~(f') * ~x) ^ ~(m') * sech(~(c') + ~(d') * ~x) ^ ~(n')) / (~a + ~(b') * cosh(~(c') + ~(d') * ~x)), ~x) => (1 / ~a) * Antiderivative((~e + ~f * ~x) ^ ~m * sech(~c + ~d * ~x) ^ ~n, ~x) - (~b / ~a) * Antiderivative(((~e + ~f * ~x) ^ ~m * sech(~c + ~d * ~x) ^ (~n - 1)) / (~a + ~b * cosh(~c + ~d * ~x)), ~x) <-- FreeQ([~a, ~b, ~c, ~d, ~e, ~f], ~x) && (IGtQ(~m, 0) && IGtQ(~n, 0))
    @apply_utils Antiderivative(((~(e') + ~(f') * ~x) ^ ~(m') * (~F)(~(c') + ~(d') * ~x) ^ ~(n')) / (~a + ~(b') * sinh(~(c') + ~(d') * ~x)), ~x) => Unintegrable(((~e + ~f * ~x) ^ ~m * (~F)(~c + ~d * ~x) ^ ~n) / (~a + ~b * sinh(~c + ~d * ~x)), ~x) <-- FreeQ([~a, ~b, ~c, ~d, ~e, ~f, ~m, ~n], ~x) && HyperbolicQ(~F)
    @apply_utils Antiderivative(((~(e') + ~(f') * ~x) ^ ~(m') * (~F)(~(c') + ~(d') * ~x) ^ ~(n')) / (~a + ~(b') * cosh(~(c') + ~(d') * ~x)), ~x) => Unintegrable(((~e + ~f * ~x) ^ ~m * (~F)(~c + ~d * ~x) ^ ~n) / (~a + ~b * cosh(~c + ~d * ~x)), ~x) <-- FreeQ([~a, ~b, ~c, ~d, ~e, ~f, ~m, ~n], ~x) && HyperbolicQ(~F)
    @apply_utils Antiderivative(((~(e') + ~(f') * ~x) ^ ~(m') * cosh(~(c') + ~(d') * ~x) ^ ~(p') * sinh(~(c') + ~(d') * ~x) ^ ~(n')) / (~a + ~(b') * sinh(~(c') + ~(d') * ~x)), ~x) => (1 / ~b) * Antiderivative((~e + ~f * ~x) ^ ~m * cosh(~c + ~d * ~x) ^ ~p * sinh(~c + ~d * ~x) ^ (~n - 1), ~x) - (~a / ~b) * Antiderivative(((~e + ~f * ~x) ^ ~m * cosh(~c + ~d * ~x) ^ ~p * sinh(~c + ~d * ~x) ^ (~n - 1)) / (~a + ~b * sinh(~c + ~d * ~x)), ~x) <-- FreeQ([~a, ~b, ~c, ~d, ~e, ~f], ~x) && (IGtQ(~m, 0) && (IGtQ(~n, 0) && IGtQ(~p, 0)))
    @apply_utils Antiderivative(((~(e') + ~(f') * ~x) ^ ~(m') * sinh(~(c') + ~(d') * ~x) ^ ~(p') * cosh(~(c') + ~(d') * ~x) ^ ~(n')) / (~a + ~(b') * cosh(~(c') + ~(d') * ~x)), ~x) => (1 / ~b) * Antiderivative((~e + ~f * ~x) ^ ~m * sinh(~c + ~d * ~x) ^ ~p * cosh(~c + ~d * ~x) ^ (~n - 1), ~x) - (~a / ~b) * Antiderivative(((~e + ~f * ~x) ^ ~m * sinh(~c + ~d * ~x) ^ ~p * cosh(~c + ~d * ~x) ^ (~n - 1)) / (~a + ~b * cosh(~c + ~d * ~x)), ~x) <-- FreeQ([~a, ~b, ~c, ~d, ~e, ~f], ~x) && (IGtQ(~m, 0) && (IGtQ(~n, 0) && IGtQ(~p, 0)))
    @apply_utils Antiderivative(((~(e') + ~(f') * ~x) ^ ~(m') * sinh(~(c') + ~(d') * ~x) ^ ~(p') * tanh(~(c') + ~(d') * ~x) ^ ~(n')) / (~a + ~(b') * sinh(~(c') + ~(d') * ~x)), ~x) => (1 / ~b) * Antiderivative((~e + ~f * ~x) ^ ~m * sinh(~c + ~d * ~x) ^ (~p - 1) * tanh(~c + ~d * ~x) ^ ~n, ~x) - (~a / ~b) * Antiderivative(((~e + ~f * ~x) ^ ~m * sinh(~c + ~d * ~x) ^ (~p - 1) * tanh(~c + ~d * ~x) ^ ~n) / (~a + ~b * sinh(~c + ~d * ~x)), ~x) <-- FreeQ([~a, ~b, ~c, ~d, ~e, ~f], ~x) && (IGtQ(~m, 0) && (IGtQ(~n, 0) && IGtQ(~p, 0)))
    @apply_utils Antiderivative(((~(e') + ~(f') * ~x) ^ ~(m') * cosh(~(c') + ~(d') * ~x) ^ ~(p') * coth(~(c') + ~(d') * ~x) ^ ~(n')) / (~a + ~(b') * cosh(~(c') + ~(d') * ~x)), ~x) => (1 / ~b) * Antiderivative((~e + ~f * ~x) ^ ~m * cosh(~c + ~d * ~x) ^ (~p - 1) * coth(~c + ~d * ~x) ^ ~n, ~x) - (~a / ~b) * Antiderivative(((~e + ~f * ~x) ^ ~m * cosh(~c + ~d * ~x) ^ (~p - 1) * coth(~c + ~d * ~x) ^ ~n) / (~a + ~b * cosh(~c + ~d * ~x)), ~x) <-- FreeQ([~a, ~b, ~c, ~d, ~e, ~f], ~x) && (IGtQ(~m, 0) && (IGtQ(~n, 0) && IGtQ(~p, 0)))
    @apply_utils Antiderivative(((~(e') + ~(f') * ~x) ^ ~(m') * sech(~(c') + ~(d') * ~x) ^ ~(p') * tanh(~(c') + ~(d') * ~x) ^ ~(n')) / (~a + ~(b') * sinh(~(c') + ~(d') * ~x)), ~x) => (1 / ~b) * Antiderivative((~e + ~f * ~x) ^ ~m * sech(~c + ~d * ~x) ^ (~p + 1) * tanh(~c + ~d * ~x) ^ (~n - 1), ~x) - (~a / ~b) * Antiderivative(((~e + ~f * ~x) ^ ~m * sech(~c + ~d * ~x) ^ (~p + 1) * tanh(~c + ~d * ~x) ^ (~n - 1)) / (~a + ~b * sinh(~c + ~d * ~x)), ~x) <-- FreeQ([~a, ~b, ~c, ~d, ~e, ~f], ~x) && (IGtQ(~m, 0) && (IGtQ(~n, 0) && IGtQ(~p, 0)))
    @apply_utils Antiderivative(((~(e') + ~(f') * ~x) ^ ~(m') * csch(~(c') + ~(d') * ~x) ^ ~(p') * coth(~(c') + ~(d') * ~x) ^ ~(n')) / (~a + ~(b') * cosh(~(c') + ~(d') * ~x)), ~x) => (1 / ~b) * Antiderivative((~e + ~f * ~x) ^ ~m * csch(~c + ~d * ~x) ^ (~p + 1) * coth(~c + ~d * ~x) ^ (~n - 1), ~x) - (~a / ~b) * Antiderivative(((~e + ~f * ~x) ^ ~m * csch(~c + ~d * ~x) ^ (~p + 1) * coth(~c + ~d * ~x) ^ (~n - 1)) / (~a + ~b * cosh(~c + ~d * ~x)), ~x) <-- FreeQ([~a, ~b, ~c, ~d, ~e, ~f], ~x) && (IGtQ(~m, 0) && (IGtQ(~n, 0) && IGtQ(~p, 0)))
    @apply_utils Antiderivative(((~(e') + ~(f') * ~x) ^ ~(m') * cosh(~(c') + ~(d') * ~x) ^ ~(p') * coth(~(c') + ~(d') * ~x) ^ ~(n')) / (~a + ~(b') * sinh(~(c') + ~(d') * ~x)), ~x) => (1 / ~a) * Antiderivative((~e + ~f * ~x) ^ ~m * cosh(~c + ~d * ~x) ^ ~p * coth(~c + ~d * ~x) ^ ~n, ~x) - (~b / ~a) * Antiderivative(((~e + ~f * ~x) ^ ~m * cosh(~c + ~d * ~x) ^ (~p + 1) * coth(~c + ~d * ~x) ^ (~n - 1)) / (~a + ~b * sinh(~c + ~d * ~x)), ~x) <-- FreeQ([~a, ~b, ~c, ~d, ~e, ~f], ~x) && (IGtQ(~m, 0) && (IGtQ(~n, 0) && IGtQ(~p, 0)))
    @apply_utils Antiderivative(((~(e') + ~(f') * ~x) ^ ~(m') * sinh(~(c') + ~(d') * ~x) ^ ~(p') * tanh(~(c') + ~(d') * ~x) ^ ~(n')) / (~a + ~(b') * cosh(~(c') + ~(d') * ~x)), ~x) => (1 / ~a) * Antiderivative((~e + ~f * ~x) ^ ~m * sinh(~c + ~d * ~x) ^ ~p * tanh(~c + ~d * ~x) ^ ~n, ~x) - (~b / ~a) * Antiderivative(((~e + ~f * ~x) ^ ~m * sinh(~c + ~d * ~x) ^ (~p + 1) * tanh(~c + ~d * ~x) ^ (~n - 1)) / (~a + ~b * cosh(~c + ~d * ~x)), ~x) <-- FreeQ([~a, ~b, ~c, ~d, ~e, ~f], ~x) && (IGtQ(~m, 0) && (IGtQ(~n, 0) && IGtQ(~p, 0)))
    @apply_utils Antiderivative(((~(e') + ~(f') * ~x) ^ ~(m') * csch(~(c') + ~(d') * ~x) ^ ~(p') * coth(~(c') + ~(d') * ~x) ^ ~(n')) / (~a + ~(b') * sinh(~(c') + ~(d') * ~x)), ~x) => (1 / ~a) * Antiderivative((~e + ~f * ~x) ^ ~m * csch(~c + ~d * ~x) ^ ~p * coth(~c + ~d * ~x) ^ ~n, ~x) - (~b / ~a) * Antiderivative(((~e + ~f * ~x) ^ ~m * csch(~c + ~d * ~x) ^ (~p - 1) * coth(~c + ~d * ~x) ^ ~n) / (~a + ~b * sinh(~c + ~d * ~x)), ~x) <-- FreeQ([~a, ~b, ~c, ~d, ~e, ~f], ~x) && (IGtQ(~m, 0) && (IGtQ(~n, 0) && IGtQ(~p, 0)))
    @apply_utils Antiderivative(((~(e') + ~(f') * ~x) ^ ~(m') * sech(~(c') + ~(d') * ~x) ^ ~(p') * tanh(~(c') + ~(d') * ~x) ^ ~(n')) / (~a + ~(b') * cosh(~(c') + ~(d') * ~x)), ~x) => (1 / ~a) * Antiderivative((~e + ~f * ~x) ^ ~m * sech(~c + ~d * ~x) ^ ~p * tanh(~c + ~d * ~x) ^ ~n, ~x) - (~b / ~a) * Antiderivative(((~e + ~f * ~x) ^ ~m * sech(~c + ~d * ~x) ^ (~p - 1) * tanh(~c + ~d * ~x) ^ ~n) / (~a + ~b * cosh(~c + ~d * ~x)), ~x) <-- FreeQ([~a, ~b, ~c, ~d, ~e, ~f], ~x) && (IGtQ(~m, 0) && (IGtQ(~n, 0) && IGtQ(~p, 0)))
    @apply_utils Antiderivative(((~(e') + ~(f') * ~x) ^ ~(m') * sech(~(c') + ~(d') * ~x) ^ ~(p') * csch(~(c') + ~(d') * ~x) ^ ~(n')) / (~a + ~(b') * sinh(~(c') + ~(d') * ~x)), ~x) => (1 / ~a) * Antiderivative((~e + ~f * ~x) ^ ~m * sech(~c + ~d * ~x) ^ ~p * csch(~c + ~d * ~x) ^ ~n, ~x) - (~b / ~a) * Antiderivative(((~e + ~f * ~x) ^ ~m * sech(~c + ~d * ~x) ^ ~p * csch(~c + ~d * ~x) ^ (~n - 1)) / (~a + ~b * sinh(~c + ~d * ~x)), ~x) <-- FreeQ([~a, ~b, ~c, ~d, ~e, ~f], ~x) && (IGtQ(~m, 0) && (IGtQ(~n, 0) && IGtQ(~p, 0)))
    @apply_utils Antiderivative(((~(e') + ~(f') * ~x) ^ ~(m') * csch(~(c') + ~(d') * ~x) ^ ~(p') * sech(~(c') + ~(d') * ~x) ^ ~(n')) / (~a + ~(b') * cosh(~(c') + ~(d') * ~x)), ~x) => (1 / ~a) * Antiderivative((~e + ~f * ~x) ^ ~m * csch(~c + ~d * ~x) ^ ~p * sech(~c + ~d * ~x) ^ ~n, ~x) - (~b / ~a) * Antiderivative(((~e + ~f * ~x) ^ ~m * csch(~c + ~d * ~x) ^ ~p * sech(~c + ~d * ~x) ^ (~n - 1)) / (~a + ~b * cosh(~c + ~d * ~x)), ~x) <-- FreeQ([~a, ~b, ~c, ~d, ~e, ~f], ~x) && (IGtQ(~m, 0) && (IGtQ(~n, 0) && IGtQ(~p, 0)))
    @apply_utils Antiderivative(((~(e') + ~(f') * ~x) ^ ~(m') * (~F)(~(c') + ~(d') * ~x) ^ ~(n') * (~G)(~(c') + ~(d') * ~x) ^ ~(p')) / (~a + ~(b') * sinh(~(c') + ~(d') * ~x)), ~x) => Unintegrable(((~e + ~f * ~x) ^ ~m * (~F)(~c + ~d * ~x) ^ ~n * (~G)(~c + ~d * ~x) ^ ~p) / (~a + ~b * sinh(~c + ~d * ~x)), ~x) <-- FreeQ([~a, ~b, ~c, ~d, ~e, ~f, ~m, ~n, ~p], ~x) && (HyperbolicQ(~F) && HyperbolicQ(~G))
    @apply_utils Antiderivative(((~(e') + ~(f') * ~x) ^ ~(m') * (~F)(~(c') + ~(d') * ~x) ^ ~(n') * (~G)(~(c') + ~(d') * ~x) ^ ~(p')) / (~a + ~(b') * cosh(~(c') + ~(d') * ~x)), ~x) => Unintegrable(((~e + ~f * ~x) ^ ~m * (~F)(~c + ~d * ~x) ^ ~n * (~G)(~c + ~d * ~x) ^ ~p) / (~a + ~b * cosh(~c + ~d * ~x)), ~x) <-- FreeQ([~a, ~b, ~c, ~d, ~e, ~f, ~m, ~n, ~p], ~x) && (HyperbolicQ(~F) && HyperbolicQ(~G))
    @apply_utils Antiderivative(((~(e') + ~(f') * ~x) ^ ~(m') * (~F)(~(c') + ~(d') * ~x) ^ ~(n')) / (~a + ~(b') * sech(~(c') + ~(d') * ~x)), ~x) => Antiderivative(((~e + ~f * ~x) ^ ~m * cosh(~c + ~d * ~x) * (~F)(~c + ~d * ~x) ^ ~n) / (~b + ~a * cosh(~c + ~d * ~x)), ~x) <-- FreeQ([~a, ~b, ~c, ~d, ~e, ~f], ~x) && (HyperbolicQ(~F) && IntegersQ(~m, ~n))
    @apply_utils Antiderivative(((~(e') + ~(f') * ~x) ^ ~(m') * (~F)(~(c') + ~(d') * ~x) ^ ~(n')) / (~a + ~(b') * csch(~(c') + ~(d') * ~x)), ~x) => Antiderivative(((~e + ~f * ~x) ^ ~m * sinh(~c + ~d * ~x) * (~F)(~c + ~d * ~x) ^ ~n) / (~b + ~a * sinh(~c + ~d * ~x)), ~x) <-- FreeQ([~a, ~b, ~c, ~d, ~e, ~f], ~x) && (HyperbolicQ(~F) && IntegersQ(~m, ~n))
    @apply_utils Antiderivative(((~(e') + ~(f') * ~x) ^ ~(m') * (~F)(~(c') + ~(d') * ~x) ^ ~(n') * (~G)(~(c') + ~(d') * ~x) ^ ~(p')) / (~a + ~(b') * sech(~(c') + ~(d') * ~x)), ~x) => Antiderivative(((~e + ~f * ~x) ^ ~m * cosh(~c + ~d * ~x) * (~F)(~c + ~d * ~x) ^ ~n * (~G)(~c + ~d * ~x) ^ ~p) / (~b + ~a * cosh(~c + ~d * ~x)), ~x) <-- FreeQ([~a, ~b, ~c, ~d, ~e, ~f], ~x) && (HyperbolicQ(~F) && (HyperbolicQ(~G) && IntegersQ(~m, ~n, ~p)))
    @apply_utils Antiderivative(((~(e') + ~(f') * ~x) ^ ~(m') * (~F)(~(c') + ~(d') * ~x) ^ ~(n') * (~G)(~(c') + ~(d') * ~x) ^ ~(p')) / (~a + ~(b') * csch(~(c') + ~(d') * ~x)), ~x) => Antiderivative(((~e + ~f * ~x) ^ ~m * sinh(~c + ~d * ~x) * (~F)(~c + ~d * ~x) ^ ~n * (~G)(~c + ~d * ~x) ^ ~p) / (~b + ~a * sinh(~c + ~d * ~x)), ~x) <-- FreeQ([~a, ~b, ~c, ~d, ~e, ~f], ~x) && (HyperbolicQ(~F) && (HyperbolicQ(~G) && IntegersQ(~m, ~n, ~p)))
    @apply_utils Antiderivative(sinh(~(a') + ~(b') * ~x) ^ ~(p') * sinh(~(c') + ~(d') * ~x) ^ ~(q'), ~x) => (1 / 2 ^ (~p + ~q)) * Antiderivative(ExpandIntegrand((-(ℯ ^ (-(~c) - ~d * ~x)) + ℯ ^ (~c + ~d * ~x)) ^ ~q, (-(ℯ ^ (-(~a) - ~b * ~x)) + ℯ ^ (~a + ~b * ~x)) ^ ~p, ~x), ~x) <-- FreeQ([~a, ~b, ~c, ~d, ~q], ~x) && (IGtQ(~p, 0) && Not(IntegerQ(~q)))
    @apply_utils Antiderivative(cosh(~(a') + ~(b') * ~x) ^ ~(p') * cosh(~(c') + ~(d') * ~x) ^ ~(q'), ~x) => (1 / 2 ^ (~p + ~q)) * Antiderivative(ExpandIntegrand((ℯ ^ (-(~c) - ~d * ~x) + ℯ ^ (~c + ~d * ~x)) ^ ~q, (ℯ ^ (-(~a) - ~b * ~x) + ℯ ^ (~a + ~b * ~x)) ^ ~p, ~x), ~x) <-- FreeQ([~a, ~b, ~c, ~d, ~q], ~x) && (IGtQ(~p, 0) && Not(IntegerQ(~q)))
    @apply_utils Antiderivative(sinh(~(a') + ~(b') * ~x) ^ ~(p') * cosh(~(c') + ~(d') * ~x) ^ ~(q'), ~x) => (1 / 2 ^ (~p + ~q)) * Antiderivative(ExpandIntegrand((ℯ ^ (-(~c) - ~d * ~x) + ℯ ^ (~c + ~d * ~x)) ^ ~q, (-(ℯ ^ (-(~a) - ~b * ~x)) + ℯ ^ (~a + ~b * ~x)) ^ ~p, ~x), ~x) <-- FreeQ([~a, ~b, ~c, ~d, ~q], ~x) && (IGtQ(~p, 0) && Not(IntegerQ(~q)))
    @apply_utils Antiderivative(cosh(~(a') + ~(b') * ~x) ^ ~(p') * sinh(~(c') + ~(d') * ~x) ^ ~(q'), ~x) => (1 / 2 ^ (~p + ~q)) * Antiderivative(ExpandIntegrand((-(ℯ ^ (-(~c) - ~d * ~x)) + ℯ ^ (~c + ~d * ~x)) ^ ~q, (ℯ ^ (-(~a) - ~b * ~x) + ℯ ^ (~a + ~b * ~x)) ^ ~p, ~x), ~x) <-- FreeQ([~a, ~b, ~c, ~d, ~q], ~x) && (IGtQ(~p, 0) && Not(IntegerQ(~q)))
    @apply_utils Antiderivative(sinh(~(a') + ~(b') * ~x) * tanh(~(c') + ~(d') * ~x), ~x) => Antiderivative((-(ℯ ^ -((~a + ~b * ~x))) / 2 + ℯ ^ (~a + ~b * ~x) / 2 + ℯ ^ -((~a + ~b * ~x)) / (1 + ℯ ^ (2 * (~c + ~d * ~x)))) - ℯ ^ (~a + ~b * ~x) / (1 + ℯ ^ (2 * (~c + ~d * ~x))), ~x) <-- FreeQ([~a, ~b, ~c, ~d], ~x) && NeQ((~b) ^ 2 - (~d) ^ 2, 0)
    @apply_utils Antiderivative(cosh(~(a') + ~(b') * ~x) * coth(~(c') + ~(d') * ~x), ~x) => Antiderivative(((ℯ ^ -((~a + ~b * ~x)) / 2 + ℯ ^ (~a + ~b * ~x) / 2) - ℯ ^ -((~a + ~b * ~x)) / (1 - ℯ ^ (2 * (~c + ~d * ~x)))) - ℯ ^ (~a + ~b * ~x) / (1 - ℯ ^ (2 * (~c + ~d * ~x))), ~x) <-- FreeQ([~a, ~b, ~c, ~d], ~x) && NeQ((~b) ^ 2 - (~d) ^ 2, 0)
    @apply_utils Antiderivative(sinh(~(a') + ~(b') * ~x) * coth(~(c') + ~(d') * ~x), ~x) => Antiderivative((-(ℯ ^ -((~a + ~b * ~x))) / 2 + ℯ ^ (~a + ~b * ~x) / 2 + ℯ ^ -((~a + ~b * ~x)) / (1 - ℯ ^ (2 * (~c + ~d * ~x)))) - ℯ ^ (~a + ~b * ~x) / (1 - ℯ ^ (2 * (~c + ~d * ~x))), ~x) <-- FreeQ([~a, ~b, ~c, ~d], ~x) && NeQ((~b) ^ 2 - (~d) ^ 2, 0)
    @apply_utils Antiderivative(cosh(~(a') + ~(b') * ~x) * tanh(~(c') + ~(d') * ~x), ~x) => Antiderivative(((ℯ ^ -((~a + ~b * ~x)) / 2 + ℯ ^ (~a + ~b * ~x) / 2) - ℯ ^ -((~a + ~b * ~x)) / (1 + ℯ ^ (2 * (~c + ~d * ~x)))) - ℯ ^ (~a + ~b * ~x) / (1 + ℯ ^ (2 * (~c + ~d * ~x))), ~x) <-- FreeQ([~a, ~b, ~c, ~d], ~x) && NeQ((~b) ^ 2 - (~d) ^ 2, 0)
    @apply_utils Antiderivative(sinh(~(a') / (~(c') + ~(d') * ~x)) ^ ~(n'), ~x) => (-1 / ~d) * Subst(Antiderivative(sinh(~a * ~x) ^ ~n / (~x) ^ 2, ~x), ~x, 1 / (~c + ~d * ~x)) <-- FreeQ([~a, ~c, ~d], ~x) && IGtQ(~n, 0)
    @apply_utils Antiderivative(cosh(~(a') / (~(c') + ~(d') * ~x)) ^ ~(n'), ~x) => (-1 / ~d) * Subst(Antiderivative(cosh(~a * ~x) ^ ~n / (~x) ^ 2, ~x), ~x, 1 / (~c + ~d * ~x)) <-- FreeQ([~a, ~c, ~d], ~x) && IGtQ(~n, 0)
    @apply_utils Antiderivative(sinh((~(e') * (~(a') + ~(b') * ~x)) / (~(c') + ~(d') * ~x)) ^ ~(n'), ~x) => (-1 / ~d) * Subst(Antiderivative(sinh((~b * ~e) / ~d - (~e * (~b * ~c - ~a * ~d) * ~x) / ~d) ^ ~n / (~x) ^ 2, ~x), ~x, 1 / (~c + ~d * ~x)) <-- FreeQ([~a, ~b, ~c, ~d], ~x) && (IGtQ(~n, 0) && NeQ(~b * ~c - ~a * ~d, 0))
    @apply_utils Antiderivative(cosh((~(e') * (~(a') + ~(b') * ~x)) / (~(c') + ~(d') * ~x)) ^ ~(n'), ~x) => (-1 / ~d) * Subst(Antiderivative(cosh((~b * ~e) / ~d - (~e * (~b * ~c - ~a * ~d) * ~x) / ~d) ^ ~n / (~x) ^ 2, ~x), ~x, 1 / (~c + ~d * ~x)) <-- FreeQ([~a, ~b, ~c, ~d], ~x) && (IGtQ(~n, 0) && NeQ(~b * ~c - ~a * ~d, 0))
    @apply_utils Antiderivative(sinh(~u) ^ ~(n'), ~x) => With([lst = QuotientOfLinearsParts(~u, ~x)], Antiderivative(sinh((lst(1) + lst(2) * ~x) / (lst(3) + lst(4) * ~x)) ^ ~n, ~x)) <-- IGtQ(~n, 0) && QuotientOfLinearsQ(~u, ~x)
    @apply_utils Antiderivative(cosh(~u) ^ ~(n'), ~x) => With([lst = QuotientOfLinearsParts(~u, ~x)], Antiderivative(cosh((lst(1) + lst(2) * ~x) / (lst(3) + lst(4) * ~x)) ^ ~n, ~x)) <-- IGtQ(~n, 0) && QuotientOfLinearsQ(~u, ~x)
    @apply_utils Antiderivative(~(u') * sinh(~v) ^ ~(p') * sinh(~w) ^ ~(q'), ~x) => Antiderivative(~u * sinh(~v) ^ (~p + ~q), ~x) <-- EqQ(~w, ~v)
    @apply_utils Antiderivative(~(u') * cosh(~v) ^ ~(p') * cosh(~w) ^ ~(q'), ~x) => Antiderivative(~u * cosh(~v) ^ (~p + ~q), ~x) <-- EqQ(~w, ~v)
    @apply_utils Antiderivative(sinh(~v) ^ ~(p') * sinh(~w) ^ ~(q'), ~x) => Antiderivative(ExpandTrigReduce(sinh(~v) ^ ~p * sinh(~w) ^ ~q, ~x), ~x) <-- IGtQ(~p, 0) && (IGtQ(~q, 0) && (PolynomialQ(~v, ~x) && PolynomialQ(~w, ~x) || BinomialQ([~v, ~w], ~x) && IndependentQ(Cancel(~v / ~w), ~x)))
    @apply_utils Antiderivative(cosh(~v) ^ ~(p') * cosh(~w) ^ ~(q'), ~x) => Antiderivative(ExpandTrigReduce(cosh(~v) ^ ~p * cosh(~w) ^ ~q, ~x), ~x) <-- IGtQ(~p, 0) && (IGtQ(~q, 0) && (PolynomialQ(~v, ~x) && PolynomialQ(~w, ~x) || BinomialQ([~v, ~w], ~x) && IndependentQ(Cancel(~v / ~w), ~x)))
    @apply_utils Antiderivative((~x) ^ ~(m') * sinh(~v) ^ ~(p') * sinh(~w) ^ ~(q'), ~x) => Antiderivative(ExpandTrigReduce((~x) ^ ~m, sinh(~v) ^ ~p * sinh(~w) ^ ~q, ~x), ~x) <-- IGtQ(~m, 0) && (IGtQ(~p, 0) && (IGtQ(~q, 0) && (PolynomialQ(~v, ~x) && PolynomialQ(~w, ~x) || BinomialQ([~v, ~w], ~x) && IndependentQ(Cancel(~v / ~w), ~x))))
    @apply_utils Antiderivative((~x) ^ ~(m') * cosh(~v) ^ ~(p') * cosh(~w) ^ ~(q'), ~x) => Antiderivative(ExpandTrigReduce((~x) ^ ~m, cosh(~v) ^ ~p * cosh(~w) ^ ~q, ~x), ~x) <-- IGtQ(~m, 0) && (IGtQ(~p, 0) && (IGtQ(~q, 0) && (PolynomialQ(~v, ~x) && PolynomialQ(~w, ~x) || BinomialQ([~v, ~w], ~x) && IndependentQ(Cancel(~v / ~w), ~x))))
    @apply_utils Antiderivative(~(u') * sinh(~v) ^ ~(p') * cosh(~w) ^ ~(p'), ~x) => (1 / 2 ^ ~p) * Antiderivative(~u * sinh(2 * ~v) ^ ~p, ~x) <-- EqQ(~w, ~v) && IntegerQ(~p)
    @apply_utils Antiderivative(sinh(~v) ^ ~(p') * cosh(~w) ^ ~(q'), ~x) => Antiderivative(ExpandTrigReduce(sinh(~v) ^ ~p * cosh(~w) ^ ~q, ~x), ~x) <-- IGtQ(~p, 0) && (IGtQ(~q, 0) && (PolynomialQ(~v, ~x) && PolynomialQ(~w, ~x) || BinomialQ([~v, ~w], ~x) && IndependentQ(Cancel(~v / ~w), ~x)))
    @apply_utils Antiderivative((~x) ^ ~(m') * sinh(~v) ^ ~(p') * cosh(~w) ^ ~(q'), ~x) => Antiderivative(ExpandTrigReduce((~x) ^ ~m, sinh(~v) ^ ~p * cosh(~w) ^ ~q, ~x), ~x) <-- IGtQ(~m, 0) && (IGtQ(~p, 0) && (IGtQ(~q, 0) && (PolynomialQ(~v, ~x) && PolynomialQ(~w, ~x) || BinomialQ([~v, ~w], ~x) && IndependentQ(Cancel(~v / ~w), ~x))))
    @apply_utils Antiderivative(sinh(~v) * tanh(~w) ^ ~(n'), ~x) => Antiderivative(cosh(~v) * tanh(~w) ^ (~n - 1), ~x) - cosh(~v - ~w) * Antiderivative(sech(~w) * tanh(~w) ^ (~n - 1), ~x) <-- GtQ(~n, 0) && (NeQ(~w, ~v) && FreeQ(~v - ~w, ~x))
    @apply_utils Antiderivative(cosh(~v) * coth(~w) ^ ~(n'), ~x) => Antiderivative(sinh(~v) * coth(~w) ^ (~n - 1), ~x) + cosh(~v - ~w) * Antiderivative(csch(~w) * coth(~w) ^ (~n - 1), ~x) <-- GtQ(~n, 0) && (NeQ(~w, ~v) && FreeQ(~v - ~w, ~x))
    @apply_utils Antiderivative(sinh(~v) * coth(~w) ^ ~(n'), ~x) => Antiderivative(cosh(~v) * coth(~w) ^ (~n - 1), ~x) + sinh(~v - ~w) * Antiderivative(csch(~w) * coth(~w) ^ (~n - 1), ~x) <-- GtQ(~n, 0) && (NeQ(~w, ~v) && FreeQ(~v - ~w, ~x))
    @apply_utils Antiderivative(cosh(~v) * tanh(~w) ^ ~(n'), ~x) => Antiderivative(sinh(~v) * tanh(~w) ^ (~n - 1), ~x) - sinh(~v - ~w) * Antiderivative(sech(~w) * tanh(~w) ^ (~n - 1), ~x) <-- GtQ(~n, 0) && (NeQ(~w, ~v) && FreeQ(~v - ~w, ~x))
    @apply_utils Antiderivative(sinh(~v) * sech(~w) ^ ~(n'), ~x) => cosh(~v - ~w) * Antiderivative(tanh(~w) * sech(~w) ^ (~n - 1), ~x) + sinh(~v - ~w) * Antiderivative(sech(~w) ^ (~n - 1), ~x) <-- GtQ(~n, 0) && (NeQ(~w, ~v) && FreeQ(~v - ~w, ~x))
    @apply_utils Antiderivative(cosh(~v) * csch(~w) ^ ~(n'), ~x) => cosh(~v - ~w) * Antiderivative(coth(~w) * csch(~w) ^ (~n - 1), ~x) + sinh(~v - ~w) * Antiderivative(csch(~w) ^ (~n - 1), ~x) <-- GtQ(~n, 0) && (NeQ(~w, ~v) && FreeQ(~v - ~w, ~x))
    @apply_utils Antiderivative(sinh(~v) * csch(~w) ^ ~(n'), ~x) => sinh(~v - ~w) * Antiderivative(coth(~w) * csch(~w) ^ (~n - 1), ~x) + cosh(~v - ~w) * Antiderivative(csch(~w) ^ (~n - 1), ~x) <-- GtQ(~n, 0) && (NeQ(~w, ~v) && FreeQ(~v - ~w, ~x))
    @apply_utils Antiderivative(cosh(~v) * sech(~w) ^ ~(n'), ~x) => sinh(~v - ~w) * Antiderivative(tanh(~w) * sech(~w) ^ (~n - 1), ~x) + cosh(~v - ~w) * Antiderivative(sech(~w) ^ (~n - 1), ~x) <-- GtQ(~n, 0) && (NeQ(~w, ~v) && FreeQ(~v - ~w, ~x))
    @apply_utils Antiderivative((~(e') + ~(f') * ~x) ^ ~(m') * (~a + ~(b') * sinh(~(c') + ~(d') * ~x) * cosh(~(c') + ~(d') * ~x)) ^ ~(n'), ~x) => Antiderivative((~e + ~f * ~x) ^ ~m * (~a + (~b * sinh(2 * ~c + 2 * ~d * ~x)) / 2) ^ ~n, ~x) <-- FreeQ([~a, ~b, ~c, ~d, ~e, ~f, ~m, ~n], ~x)
    @apply_utils Antiderivative((~x) ^ ~(m') * (~a + ~(b') * sinh(~(c') + ~(d') * ~x) ^ 2) ^ ~n, ~x) => (1 / 2 ^ ~n) * Antiderivative((~x) ^ ~m * ((2 * ~a - ~b) + ~b * cosh(2 * ~c + 2 * ~d * ~x)) ^ ~n, ~x) <-- FreeQ([~a, ~b, ~c, ~d], ~x) && (NeQ(~a - ~b, 0) && (IGtQ(~m, 0) && (ILtQ(~n, 0) && (EqQ(~n, -1) || EqQ(~m, 1) && EqQ(~n, -2)))))
    @apply_utils Antiderivative((~x) ^ ~(m') * (~a + ~(b') * cosh(~(c') + ~(d') * ~x) ^ 2) ^ ~n, ~x) => (1 / 2 ^ ~n) * Antiderivative((~x) ^ ~m * (2 * ~a + ~b + ~b * cosh(2 * ~c + 2 * ~d * ~x)) ^ ~n, ~x) <-- FreeQ([~a, ~b, ~c, ~d], ~x) && (NeQ(~a - ~b, 0) && (IGtQ(~m, 0) && (ILtQ(~n, 0) && (EqQ(~n, -1) || EqQ(~m, 1) && EqQ(~n, -2)))))
    @apply_utils Antiderivative((~(f') + ~(g') * ~x) ^ ~(m') / (~(a') + ~(b') * cosh(~(d') + ~(e') * ~x) ^ 2 + ~(c') * sinh(~(d') + ~(e') * ~x) ^ 2), ~x) => 2 * Antiderivative((~f + ~g * ~x) ^ ~m / (((2 * ~a + ~b) - ~c) + (~b + ~c) * cosh(2 * ~d + 2 * ~e * ~x)), ~x) <-- FreeQ([~a, ~b, ~c, ~d, ~e, ~f, ~g], ~x) && (IGtQ(~m, 0) && (NeQ(~a + ~b, 0) && NeQ(~a + ~c, 0)))
    @apply_utils Antiderivative(((~(f') + ~(g') * ~x) ^ ~(m') * sech(~(d') + ~(e') * ~x) ^ 2) / (~b + ~(c') * tanh(~(d') + ~(e') * ~x) ^ 2), ~x) => 2 * Antiderivative((~f + ~g * ~x) ^ ~m / ((~b - ~c) + (~b + ~c) * cosh(2 * ~d + 2 * ~e * ~x)), ~x) <-- FreeQ([~b, ~c, ~d, ~e, ~f, ~g], ~x) && IGtQ(~m, 0)
    @apply_utils Antiderivative(((~(f') + ~(g') * ~x) ^ ~(m') * sech(~(d') + ~(e') * ~x) ^ 2) / (~(b') + ~(a') * sech(~(d') + ~(e') * ~x) ^ 2 + ~(c') * tanh(~(d') + ~(e') * ~x) ^ 2), ~x) => 2 * Antiderivative((~f + ~g * ~x) ^ ~m / (((2 * ~a + ~b) - ~c) + (~b + ~c) * cosh(2 * ~d + 2 * ~e * ~x)), ~x) <-- FreeQ([~a, ~b, ~c, ~d, ~e, ~f, ~g], ~x) && (IGtQ(~m, 0) && (NeQ(~a + ~b, 0) && NeQ(~a + ~c, 0)))
    @apply_utils Antiderivative(((~(f') + ~(g') * ~x) ^ ~(m') * csch(~(d') + ~(e') * ~x) ^ 2) / (~c + ~(b') * coth(~(d') + ~(e') * ~x) ^ 2), ~x) => 2 * Antiderivative((~f + ~g * ~x) ^ ~m / ((~b - ~c) + (~b + ~c) * cosh(2 * ~d + 2 * ~e * ~x)), ~x) <-- FreeQ([~b, ~c, ~d, ~e, ~f, ~g], ~x) && IGtQ(~m, 0)
    @apply_utils Antiderivative(((~(f') + ~(g') * ~x) ^ ~(m') * csch(~(d') + ~(e') * ~x) ^ 2) / (~(c') + ~(b') * coth(~(d') + ~(e') * ~x) ^ 2 + ~(a') * csch(~(d') + ~(e') * ~x) ^ 2), ~x) => 2 * Antiderivative((~f + ~g * ~x) ^ ~m / (((2 * ~a + ~b) - ~c) + (~b + ~c) * cosh(2 * ~d + 2 * ~e * ~x)), ~x) <-- FreeQ([~a, ~b, ~c, ~d, ~e, ~f, ~g], ~x) && (IGtQ(~m, 0) && (NeQ(~a + ~b, 0) && NeQ(~a + ~c, 0)))
    @apply_utils Antiderivative(((~(e') + ~(f') * ~x) * (~A + ~(B') * sinh(~(c') + ~(d') * ~x))) / (~a + ~(b') * sinh(~(c') + ~(d') * ~x)) ^ 2, ~x) => (~B * (~e + ~f * ~x) * cosh(~c + ~d * ~x)) / (~a * ~d * (~a + ~b * sinh(~c + ~d * ~x))) - ((~B * ~f) / (~a * ~d)) * Antiderivative(cosh(~c + ~d * ~x) / (~a + ~b * sinh(~c + ~d * ~x)), ~x) <-- FreeQ([~a, ~b, ~c, ~d, ~e, ~f, ~A, ~B], ~x) && EqQ(~a * ~A + ~b * ~B, 0)
    @apply_utils Antiderivative(((~(e') + ~(f') * ~x) * (~A + ~(B') * cosh(~(c') + ~(d') * ~x))) / (~a + ~(b') * cosh(~(c') + ~(d') * ~x)) ^ 2, ~x) => (~B * (~e + ~f * ~x) * sinh(~c + ~d * ~x)) / (~a * ~d * (~a + ~b * cosh(~c + ~d * ~x))) - ((~B * ~f) / (~a * ~d)) * Antiderivative(sinh(~c + ~d * ~x) / (~a + ~b * cosh(~c + ~d * ~x)), ~x) <-- FreeQ([~a, ~b, ~c, ~d, ~e, ~f, ~A, ~B], ~x) && EqQ(~a * ~A - ~b * ~B, 0)
    @apply_utils Antiderivative((~(e') + ~(f') * ~x) ^ ~(m') * sinh(~(a') + ~(b') * (~c + ~(d') * ~x) ^ ~n) ^ ~(p'), ~x) => (1 / (~d) ^ (~m + 1)) * Subst(Antiderivative(((~d * ~e - ~c * ~f) + ~f * ~x) ^ ~m * sinh(~a + ~b * (~x) ^ ~n) ^ ~p, ~x), ~x, ~c + ~d * ~x) <-- FreeQ([~a, ~b, ~c, ~d, ~e, ~f, ~n], ~x) && (IGtQ(~m, 0) && RationalQ(~p))
    @apply_utils Antiderivative((~(e') + ~(f') * ~x) ^ ~(m') * cosh(~(a') + ~(b') * (~c + ~(d') * ~x) ^ ~n) ^ ~(p'), ~x) => (1 / (~d) ^ (~m + 1)) * Subst(Antiderivative(((~d * ~e - ~c * ~f) + ~f * ~x) ^ ~m * cosh(~a + ~b * (~x) ^ ~n) ^ ~p, ~x), ~x, ~c + ~d * ~x) <-- FreeQ([~a, ~b, ~c, ~d, ~e, ~f, ~n], ~x) && (IGtQ(~m, 0) && RationalQ(~p))
    @apply_utils Antiderivative(sech(~v) ^ ~(m') * (~a + ~(b') * tanh(~v)) ^ ~(n'), ~x) => Antiderivative((~a * cosh(~v) + ~b * sinh(~v)) ^ ~n, ~x) <-- FreeQ([~a, ~b], ~x) && (IntegerQ((~m - 1) / 2) && EqQ(~m + ~n, 0))
    @apply_utils Antiderivative(csch(~v) ^ ~(m') * (~a + ~(b') * coth(~v)) ^ ~(n'), ~x) => Antiderivative((~b * cosh(~v) + ~a * sinh(~v)) ^ ~n, ~x) <-- FreeQ([~a, ~b], ~x) && (IntegerQ((~m - 1) / 2) && EqQ(~m + ~n, 0))
    @apply_utils Antiderivative(~(u') * sinh(~(a') + ~(b') * ~x) ^ ~(m') * sinh(~(c') + ~(d') * ~x) ^ ~(n'), ~x) => Antiderivative(ExpandTrigReduce(~u, sinh(~a + ~b * ~x) ^ ~m * sinh(~c + ~d * ~x) ^ ~n, ~x), ~x) <-- FreeQ([~a, ~b, ~c, ~d], ~x) && (IGtQ(~m, 0) && IGtQ(~n, 0))
    @apply_utils Antiderivative(~(u') * cosh(~(a') + ~(b') * ~x) ^ ~(m') * cosh(~(c') + ~(d') * ~x) ^ ~(n'), ~x) => Antiderivative(ExpandTrigReduce(~u, cosh(~a + ~b * ~x) ^ ~m * cosh(~c + ~d * ~x) ^ ~n, ~x), ~x) <-- FreeQ([~a, ~b, ~c, ~d], ~x) && (IGtQ(~m, 0) && IGtQ(~n, 0))
    @apply_utils Antiderivative(sech(~(a') + ~(b') * ~x) * sech(~c + ~(d') * ~x), ~x) => -(csch((~b * ~c - ~a * ~d) / ~d)) * Antiderivative(tanh(~a + ~b * ~x), ~x) + csch((~b * ~c - ~a * ~d) / ~b) * Antiderivative(tanh(~c + ~d * ~x), ~x) <-- FreeQ([~a, ~b, ~c, ~d], ~x) && (EqQ((~b) ^ 2 - (~d) ^ 2, 0) && NeQ(~b * ~c - ~a * ~d, 0))
    @apply_utils Antiderivative(csch(~(a') + ~(b') * ~x) * csch(~c + ~(d') * ~x), ~x) => csch((~b * ~c - ~a * ~d) / ~b) * Antiderivative(coth(~a + ~b * ~x), ~x) - csch((~b * ~c - ~a * ~d) / ~d) * Antiderivative(coth(~c + ~d * ~x), ~x) <-- FreeQ([~a, ~b, ~c, ~d], ~x) && (EqQ((~b) ^ 2 - (~d) ^ 2, 0) && NeQ(~b * ~c - ~a * ~d, 0))
    @apply_utils Antiderivative(tanh(~(a') + ~(b') * ~x) * tanh(~c + ~(d') * ~x), ~x) => (~b * ~x) / ~d - (~b / ~d) * cosh((~b * ~c - ~a * ~d) / ~d) * Antiderivative(sech(~a + ~b * ~x) * sech(~c + ~d * ~x), ~x) <-- FreeQ([~a, ~b, ~c, ~d], ~x) && (EqQ((~b) ^ 2 - (~d) ^ 2, 0) && NeQ(~b * ~c - ~a * ~d, 0))
    @apply_utils Antiderivative(coth(~(a') + ~(b') * ~x) * coth(~c + ~(d') * ~x), ~x) => (~b * ~x) / ~d + cosh((~b * ~c - ~a * ~d) / ~d) * Antiderivative(csch(~a + ~b * ~x) * csch(~c + ~d * ~x), ~x) <-- FreeQ([~a, ~b, ~c, ~d], ~x) && (EqQ((~b) ^ 2 - (~d) ^ 2, 0) && NeQ(~b * ~c - ~a * ~d, 0))
    @apply_utils Antiderivative(~(u') * (~(a') * cosh(~v) + ~(b') * sinh(~v)) ^ ~(n'), ~x) => Antiderivative(~u * (~a * ℯ ^ ((~a / ~b) * ~v)) ^ ~n, ~x) <-- FreeQ([~a, ~b, ~n], ~x) && EqQ((~a) ^ 2 - (~b) ^ 2, 0)
    @apply_utils Antiderivative(sinh(~(d') * (~(a') + ~(b') * log(~(c') * (~x) ^ ~(n'))) ^ 2), ~x) => (-1 / 2) * Antiderivative(ℯ ^ (-(~d) * (~a + ~b * log(~c * (~x) ^ ~n)) ^ 2), ~x) + (1 / 2) * Antiderivative(ℯ ^ (~d * (~a + ~b * log(~c * (~x) ^ ~n)) ^ 2), ~x) <-- FreeQ([~a, ~b, ~c, ~d, ~n], ~x)
    @apply_utils Antiderivative(cosh(~(d') * (~(a') + ~(b') * log(~(c') * (~x) ^ ~(n'))) ^ 2), ~x) => (1 / 2) * Antiderivative(ℯ ^ (-(~d) * (~a + ~b * log(~c * (~x) ^ ~n)) ^ 2), ~x) + (1 / 2) * Antiderivative(ℯ ^ (~d * (~a + ~b * log(~c * (~x) ^ ~n)) ^ 2), ~x) <-- FreeQ([~a, ~b, ~c, ~d, ~n], ~x)
    @apply_utils Antiderivative((~(e') * ~x) ^ ~(m') * sinh(~(d') * (~(a') + ~(b') * log(~(c') * (~x) ^ ~(n'))) ^ 2), ~x) => (-1 / 2) * Antiderivative((~e * ~x) ^ ~m * ℯ ^ (-(~d) * (~a + ~b * log(~c * (~x) ^ ~n)) ^ 2), ~x) + (1 / 2) * Antiderivative((~e * ~x) ^ ~m * ℯ ^ (~d * (~a + ~b * log(~c * (~x) ^ ~n)) ^ 2), ~x) <-- FreeQ([~a, ~b, ~c, ~d, ~e, ~m, ~n], ~x)
    @apply_utils Antiderivative((~(e') * ~x) ^ ~(m') * cosh(~(d') * (~(a') + ~(b') * log(~(c') * (~x) ^ ~(n'))) ^ 2), ~x) => (1 / 2) * Antiderivative((~e * ~x) ^ ~m * ℯ ^ (-(~d) * (~a + ~b * log(~c * (~x) ^ ~n)) ^ 2), ~x) + (1 / 2) * Antiderivative((~e * ~x) ^ ~m * ℯ ^ (~d * (~a + ~b * log(~c * (~x) ^ ~n)) ^ 2), ~x) <-- FreeQ([~a, ~b, ~c, ~d, ~e, ~m, ~n], ~x)
end
