# Math Help - Integration: Fraction With 'x' Variable

1. ## Integration: Fraction With 'x' Variable

$\int \frac{x}{(x^2-1)^\frac12} \ \mathrm{d}x$

There is something really simple that I am not seeing? Help please, Thanks in advance.

2. Originally Posted by Air
$\int \frac{x}{(x^2-1)^\frac12} \ \mathrm{d}x$

There is something really simple that I am not seeing? Help please, Thanks in advance.
With the substitution $u =x^2 - 1$,

$\int \frac{x}{(x^2-1)^\frac12} \ \mathrm{d}x = \frac12 \int \frac{1}{u^\frac12} \ \mathrm{d}u = \frac12 \int u^{-\frac12} \ \mathrm{d}u$

3. Originally Posted by Air
$\int \frac{x}{(x^2-1)^\frac12} \ \mathrm{d}x$

There is something really simple that I am not seeing? Help please, Thanks in advance.
Substitution, let $u = x^2 -1$

Then $du = 2x dx$

Your new integral is $\int 0.5u^{\frac{-1}{2}} du$

4. Or make $z^2=x^2-1.$