Question

Solve:-
$\int t\sqrt{\frac{t^2+1}{t^2-1}}dt$

Answer 1

$=\frac{1}{2}\left[\int \frac{\frac{dz}{2}}{\sqrt{z}}+\ln \left(x+\sqrt{x^2-1}\right)\right]+c$
$=\frac{1}{2}\left[\sqrt{z}+\ln \left(x+\sqrt{x^2-1}\right)\right]+c$
$=\frac{1}{2}\left[\sqrt{x^2-1}+\ln \left(x+\sqrt{x^2-1}\right)\right]+c$
$=\frac{1}{2}\left[\sqrt{t^4-1}+\ln \left(t^2+\sqrt{t^4-1}\right)\right]$