- #1

- 9

- 0

## Homework Statement

[tex]\int[/tex][tex]^{1}_{0}[/tex] [tex]\frac{3x^2 -1}{\sqrt{x-x^3}}[/tex] dx

## Homework Equations

For case [tex]\sqrt{a^2-x^2}[/tex], use substitution a*sin[tex]\theta[/tex].

## The Attempt at a Solution

[tex]\int[/tex][tex]^{1}_{0}[/tex] [tex]\frac{3x^2 -1}{\sqrt{x-x^3}}[/tex] dx

= [tex]\int[/tex][tex]^{1}_{0}[/tex] [tex]\frac{3x^2 -1}{\sqrt{1-x^2}\sqrt{x}}[/tex] dx

Substitute: x = sin[tex]\theta[/tex], dx = cos[tex]\theta[/tex] d[tex]\theta[/tex], bounds of 0 - 1 remain the same as sin 0 = 0 and sin 1 = 1.

[tex]\int[/tex][tex]^{1}_{0}[/tex] [tex]\frac{3sin^2\theta -1}{\sqrt{cos^2\theta}\sqrt{sin\theta}}[/tex] cos[tex]\theta[/tex] d[tex]\theta[/tex]

= [tex]\int[/tex][tex]^{1}_{0}[/tex] [tex]\frac{3sin^2\theta -1}{cos\theta\sqrt{sin\theta}}[/tex] d[tex]\theta[/tex]

At this point I no longer know where to go. Factoring the numerator appeared to bear no fruit, no u substitutions make any sense to me at the moment.