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## Homework Statement

Evaluate [tex]\int{\frac{x^2}{(1-x^2)^\frac{5}{2}}}dx[/tex] via

*trigonometric substitution.*

You can do this via normal u-substitution but I'm unsure of how to evaluate via trigonometric substitution.

## Homework Equations

## The Attempt at a Solution

Letting [tex]x=sinθ[/tex],

[tex]\int{\frac{sin^{2}θ}{(1-sin^{2}θ)^\frac{5}{2}}}dθ=\int{\frac{sin^{2}θ}{(cos^{2}θ)^\frac{5}{2}}}dθ[/tex]

but I'm not sure how the working in the answers gets up to [tex]\int{\frac{x^2}{(1-x^2)^\frac{5}{2}}}dx=\int{\frac{sin^{2}θ}{cos^{4}θ}}dθ[/tex].

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