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Could anyone show me how to find the integral of

$1\over{\sin^2x}$ and $1\over{\sin^4x}$

systematically?

  • 1
    Hint: can you rewrite these as $csc^{2}(x)$ and $csc^{4}(x)$ and then proceed that way? Then. you can use [**Integrals**](http://www.integraltec.com/math/math.php?f=csc_n.html#csc2)2012-12-18

2 Answers 2

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Try the change of variables $u = \cot(x)$.

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Hint:
$d(\cot{x})=-\dfrac{1}{\sin^2{x}}dx \\ 1+\cot^2{x}=\dfrac{1}{\sin^2{x}} $