Integration with square root in denominator I am honestly embarrassed to ask this because i feel like i should know how to do this but:
$
\int \frac{x}{\sqrt{2x-1}}dx
$
Try to use u-substitution please

Substitute $u=2x-1, du = 2dx$ so that you get
$$\int \dfrac{x}{\sqrt{2x-1}} \, dx = \frac12\int\frac{u+1}{2\sqrt{u}}\, du = \frac12\int\frac{\sqrt{u}}{2} + \frac{1}{2\sqrt{u}}\, du.$$
Do you see how to proceede?
