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Math Help - Trig Integration

  1. #1
    Senior Member polymerase's Avatar
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    Trig Integration

    How do u integrate:

    <br />
\int \tan^5x\cos^3x dx<br />

    <br />
\int \sin^4x\cot^7x dx<br />

    I can't seem to find the right combinations of identities to sub. in, in order to solve.
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  2. #2
    MHF Contributor red_dog's Avatar
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    \displaystyle\int\tan^5x\cos^3xdx=\int\frac{\sin^5  x}{\cos^2x}dx=\int\frac{\sin^4x}{\cos^2x}\sin xdx=\int\frac{(1-\cos^2x)^2}{\cos^2x}\sin xdx
    and use the substitution \cos x=u

    Do the same way with the other integrale.
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