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Math Help - Help with hard integral

  1. #1
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    Help with hard integral

    Hello, this is one of my homework problem, and it's pretty difficult, since I have to use arctan, but I can't figure out how to use it here.. And help would be appreciated.

    Find the integral of:

    (sin(x))^2 / ( 1 + (sin(x))^2 )
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  2. #2
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    Quote Originally Posted by hashshashin715 View Post
    Hello, this is one of my homework problem, and it's pretty difficult, since I have to use arctan, but I can't figure out how to use it here.. And help would be appreciated.

    Find the integral of:

    (sin(x))^2 / ( 1 + (sin(x))^2 )

    Consider

     \frac{\sin^2(x) }{1 + \sin^2(x) } = 1  - \frac{1}{ 1 + \sin^2(x)}

    and

     \frac{1}{ 1 + \sin^2(x) } = \frac{ 1}{ \sin^2(x) + \cos^2(x) + \sin^2(x) } = \frac{1}{ \cos^2(x) + 2\sin^2(x)}

     = \frac{\sec^2(x)}{ 1 + 2 \tan^2(x) }
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  3. #3
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    Thanks so much
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  4. #4
    MHF Contributor Drexel28's Avatar
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    Also, the series of substitutions x=\arcsin(y) and then y^2=1-z^2 may be enlightening.
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