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Math Help - Integration problem with trig functions and u-substitution

  1. #1
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    Integration problem with trig functions and u-substitution

    Hey, I'm having trouble figuring out where to go with this problem:

    \int \frac{\cos(x)}{\sin(x)^8} dx

    What would u be? I'm really bad with trig functions.
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  2. #2
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    Quote Originally Posted by Dana_Scully View Post
    Hey, I'm having trouble figuring out where to go with this problem:

    \int \frac{\cos(x)}{\sin(x)^8} dx

    What would u be? I'm really bad with trig functions.
    \int {\frac{{\cos x}}{{{{\sin }^8}x}}} dx = \left\{ \begin{gathered}\sin x = u, \hfill \\\cos xdx = du \hfill \\ \end{gathered}  \right\} = \int {\frac{1}{{{u^8}}}} du = \int {{u^{ - 8}}} du =  - \frac{{{u^{ - 7}}}}{7} + C =  - \frac{1}{{7{u^7}}} + C =  - \frac{1}{{7{{\sin }^7}x}} + C.
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    Ah, I see. Thank you so much!
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