# Thread: Help with substituition integration

1. ## Help with substituition integration

When integrating I never know what to substitute. I'm not sure what to look out for to get the right substitution that will work out nicely.

For example this problem, I'm not sure what to substitute, if its 2x-1=u then I'm not sure how to carry on from there.

$\displaystyle \int \frac{x^2-1}{{\sqrt{2x-1}}}dx$

Excuse the thing, I'm still having trouble using this.

2. Originally Posted by Cakecake
When integrating I never know what to substitute. I'm not sure what to look out for to get the right substitution that will work out nicely.

For example this problem, I'm not sure what to substitute, if its 2x-1=u then I'm not sure how to carry on from there.

$\displaystyle \int \frac{x^2-1}{{\sqrt{2x-1}}}dx$

Excuse the thing, I'm still having trouble using this.
$\displaystyle u = 2x - 1 \Rightarrow x = \frac{u+1}{2}$ and $\displaystyle \frac{du}{dx} = 2 \Rightarrow dx = \frac{du}{2}$. Substitute, simplify and integrate!