Answer
$\int \frac{x^2-1}{\sqrt {2x-1}}$ = $\frac{\sqrt {2x-1}^5}{20} + \frac{\sqrt {2x-1}^3}{6} + \frac{\sqrt {2x-1}}{4} + c$
Work Step by Step
Use u-substitution to solve $\int\frac{x^2-1}{\sqrt {2x-1}}dx$:
Let $u = \sqrt {2x-1}$ and solve for x:
$x = \frac{u^2 + 1}{2}$
Now differentiate $x$:
$dx = udu$
Now substitute:
$\int\frac{(\frac{u^2+1}{2})^2-1}{u}udu$
Simplify:
$\int\frac{u^4+2u^2-3}{4}du$
Integrate:
$\frac{u^5}{20} + \frac{u^3}{6} + \frac{u}{4} + c$
Substitute back:
$\frac{\sqrt {2x-1}^5}{20} + \frac{\sqrt {2x-1}^3}{6} + \frac{\sqrt {2x-1}}{4} + c$
