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Math Help - What should I make u in this integration problem?

  1. #1
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    What should I make u in this integration problem?

    \int \frac{\sin(32x)}{1+\cos(32x)^2} dx

    I tried 32x and sin(32x) but even if those are right I don't know where to go from there.
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  2. #2
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    is the denominator 1+\cos^2(32x) or 1 + \cos(32^2x^2) ?
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  3. #3
    Senior Member DeMath's Avatar
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    Quote Originally Posted by Dana_Scully View Post
    \int \frac{\sin(32x)}{1+\cos(32x)^2} dx

    I tried 32x and sin(32x) but even if those are right I don't know where to go from there.
    \int {\frac{{\sin \left( {32x} \right)}}{{1 + {{\cos }^2}\left( {32x} \right)}}dx}  = \left\{ \begin{gathered}\cos (32x) = u, \hfill \\- 32\sin (32x)dx = du \hfill \\ \end{gathered}  \right\} =  - \frac{1}{{32}} \int {\frac{{du}}{{1 + {u^2}}}}  = - \frac{1}{{32}}\arctan \left( u \right) + C =  - \frac{1}{{32}}\arctan \left( {\cos (32x)} \right) + C.
    Last edited by DeMath; January 19th 2009 at 12:32 PM.
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  4. #4
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    Skeeter, it was the former one. DeMath, thank you again!
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  5. #5
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    Quote Originally Posted by Dana_Scully View Post
    Skeeter, it was the former one. DeMath, thank you again!
    Well, that changes things considerably, doesn't it? I'm going to try and solve the original integral you posted without using a table or program.
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