Question

Solve :
$\int x\sqrt{x^2-1dx}$

Answer 1

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

Let $x^2-1=t_{1}2xdx=dt$

$xdx=\frac{dt}{2}$

$=\frac{1}{2}\int \sqrt{t}dt$

$=\frac{1}{2}\frac{t^{3/2}}{3/2}+C$

$=\frac{1}{2}.\frac{2}{3}(x^2-1{)}^{3/2}+C$

$=\frac{(x^2-1)}{3}+C$