How do I integrate Cos x Sin x dx?

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How do I integrate Cos x Sin x dx? I'm working on an engineering problem and having trouble getting up to speed with simple integral calculus. Any help is much appreciated!
Best AnswerAsker's Choice
you can solve in different ways you will get diff answer but they will be right

1) put sinx = t
cosxdx = dt

∫ tdt = t^2/2 +c = 1/2sin^2 X +c

2) sinxcosx = 1/2 sin2x
∫ 1/2sin2x dx = -1/4 cos2x +c

Asker's rating & comment

4 out of 5
Great answer --- thanks! The others were great, too, but this answer listed two approaches.
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  • Mirhossein Jamali answered 6 years ago
    cos(x)*sin(x)=1/2 *sin(2x)=>
    int(cosx*sinx*dx)=int(1/2*sin(2x)dx)
    =-1/4*cos(2x)
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  • yucd answered 4 months ago
    cosx sinx dx = 1/2sin^2 x +c ,meaning half of sinx square
    also cosxsinx = -1/2cos^2 x + c ,means half of cos square negative.
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  • sahsjing answered 6 years ago
    ∫cosx sinx dx
    = ∫sinx dsinx
    = (1/2)sin^2(x) + c
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  • Rashma answered 6 years ago
    since
    dy/dx (cos x) = - sin x

    dy/dx (sin x) = cos x

    then integrating them wld be the opp of it.

    integral of Cos x = sin x

    Integral of Sin x = - cos x



    Integral of Cos x Sin x
    = Integral of Cos x + integral of Sin x
    = Sin x - cos x
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  • cb52211 answered 6 years ago
    CosXSinS is as simplified as it gets.
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