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Math Help - trig intergral

  1. #1
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    trig intergral

    csc^4 2x cot 2x dx
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  2. #2
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    Quote Originally Posted by Bust2000 View Post
    csc^4 2x cot 2x dx
    csc^4 (2x) cot (2x) = \frac{cos(2x)}{sin^4(2x)sin(2x)} \Rightarrow \frac{cos(2x)}{sin^5(2x)}

    Now, sub: u=sin(2x)
    du=2cos(2x)dx
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  3. #3
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    Hello, Bust2000!

    Another approach . ..


    Integrate: . \int \csc^4\!2x\cot2x\,dx

    We have: . \int\csc^3\!2x(\csc2x\cot2x\,dx)

    Let u\:=\:\csc2x\quad\Rightarrow\quad du \:=\:-2\csc2x\cot2x\,dx\quad\Rightarrow\quad \csc2x\cot2x\,dx\:=\:-\frac{1}{2}\,du

    Substitute: . -\frac{1}{2}\int u^3\,du\;\;=\;\;-\frac{1}{8}u^4 + C

    Back-substitute: . -\frac{1}{8}\csc^4\!2x + C

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