Thread: Integration: Fraction With 'x' Variable

1. Integration: Fraction With 'x' Variable

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

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

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

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

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

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

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

Then $\displaystyle du = 2x dx$

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

4. Or make $\displaystyle z^2=x^2-1.$ Search Tags

fraction, integration, variable 