what is the integral of sin2x/sinx?
825804
First, let's simplify sin(2x) / sin(x)\nRemember that sin(2x) = 2sin(x)cos(x), so\nsin(2x) / sin(x) \n= 2sin(x)cos(x) / sin(x)\n= 2cos(x)\nThe integral of 2cos(x) dx\n= 2sin(x) + C
730722
put sinx=t\ncosxdx=dt\nI=fcos(pi t)dt with limits -1,+1\nI=(sin(pi t))/pi with limits +1,-1\nI=(sin(pi)-sin(-pi))/pi=0\nthanks & good luck
950010
replace [Cos(2x)]^2 with 1 - [Sin(2x)]^2.\n\nnow multiply to get...[Sin(2x)]^3 - [Sin(2x)]^5.\n\nthen separate integral into two parts...\n\nnow use power rule and chain rule and don't forget to add a constant.
878725
antiderivative of:\n20-12cos2pi(x-0.1)\nis:\n\n20x - 12 sin( 2pi(x-0.1)) / 2pi +C\n=20x - 6 sin( 2pi(x-0.1)) / pi +C\nto double check just take the derivative of the function and see that you get:  20-12cos2pi(x-0.1) '
898033
cos2x = 1 - 2 (sin x) ^2 = sin x\n\nthen 2 ( sin x)^2 + sin x  - 1 = 0\n or (2sin x - 1 )(sin x + 1) = 0\nsin x = 1/2 , - 1\nx = 30 deg, or - 90 deg
1182723
sinx+cosecx=2\nsin+(1/sinx)=2\nfrom here try to cross multiply!
281867
Well I assume you are trying to work out x and I also assume that it's not cos [to the power of] (x^3) but Cos [multiptied by] (x^3)\n\nYou need to integrate to remove the d/dx:\n\nCos integrated is Sin and you then have to divide by the differental of what's in the brackets\n\n=> sin(x^3) / 3x^2
159947
What is "CAS"?\n\nAnyway, one way is to know that \n   sin(x) = (e^(ix) - e(-ix))/(2i) \nwhere i is the imaginary number.\n\nSome numerical fidgetry leads to:\n\n   - e^(-2x)(cos(x) + 2sin(x))/5\n\nYou can probably get the same result by integrating by parts twice:\n\n    I = int(sin(x)e^(-2x)dx)\n\nUsing u = sin(x), dv = e^(-2x)dx we get v = -e^(-2x)/2\n\n    I = -sin(x)e^(-2x)/2 + 1/2* int(cos(x)e^(-2x)dx)\n\nNow applying integration by parts on the second term:\n\n    J = int(cos(x)e^(-2x)dx)\n\nwith u = cos(x) and dv = e^(-2x), we get du = -sin(x) dx\nand v = -e^(-2x)/2\n\n   J = -cos(x)e^(-2x)/2 - 1/2 int(sin(x)e^(-2x)dx)\n\nSo:\n   I = -sin(x)e^(-2x)/2 + 1/2 J\n\nand:\n\n  J = -cos(x)e^(-2x)/2 - 1/2 I\n\nSolving for I will give you the same result.  [ The integration by parts steps might not be exactly correct - check them yourself.]
246551
integral of sine squared.\nso theres a conversion thing which says \nsin^2 x = (1-cos 2x)/2\nso if you use that then u have to integrate 1/2 - cos 2x/2\nwhich is just 1/2x - sin 2x / 4
1059709
i think ur question meant sinx = cosecx\nsinx = 1/sinx\nsin^2x = 1\nsinx = 1\nsinx is 1 at 90degree\nthus  x = 90 degree
420145
The antideriative is the same as an integral.  For this, we can use the fact that sin^2(t) + cos^2(t) = 1.  Then,\n\n[int] cos^2(t)/sin(t) dt = [int] (1 - sin^2(t))/sin(t) dt\n= [int] (1/sin(t)) - sin(t) dt\n= [int] csc(t) - sin(t) dt\n= ln(tan(t/2)) + cos(t) + C
748051
The primitive of your integral is:\n\ns*(e^(st))*(1/w)*atan(s/w)\n\nYou have to do a trigonometric substitution to get there. Do not always trust the weird answers you get with complex calculators.
723523
Int tanx ln(cosx)dx\n\nwrite tanx=sinx/cosx\n\nsubstitute y = cos(x)\ndy=-sinx dx\n\n-Int ln(y)/y dy\n\nsub z = ln(y)\ndz=ln(y)/y dy\n\n-Int z dz = -z^2/2 = -(1/2)ln^2(y) = -(1/2)ln^2(cos(x)) + C
350899
coshx\nand the derivative of coshx is sinhx
411302
cos^2 (2x) is equal to 1-sin^2(2x), remember, sin^2(x)+cos^2(x)=1
837567
Interesting...there are actually two solutions. Let's use substitution:\n\nLet u = cos(x). du = -sin(x)dx.\n\nSo Integral[sin(x)cos(x)]dx\n\n= - Integral[udu]\n\n= -u^2/2\n\n= -[cos(x)]^2/2\n\nNow, let u = sin(x). du = cos(x)dx.\n\nSo Integral[sin(x)cos(x)dx]\n\n= Integral[udu]\n\n= u^2/2 = [sin(x)]^2/2\n\nJust to check, I did a definite integral on both results, and got the same value for both.\n\nPretty neat...
880226
it is not what you specified\n\nIt cannot be solved without identities\n\nsin ^5 t = sin^4 t sin t\n= (1-cos^2 t)^2 sin t\n\nnow let cost = x\nso diffentiate to get - sint dt = dx\n\nso we need to integrate\n\n-(1-x^2)^2 dx\n\n= -dx + 2 x^2 dx - x^4 dx\n\nintegrating we get\n\n-x + 2x^3/3 - x^5/5 + C\n= - cos t + 2 cos^3 t/3 - cos^5 t /5 + C\n\nwhere C is constant of integration