Mathematics - Indefinite Integration Question with Solution | TestHub

The printed integrand would diverge; the source solution and options show that the intended numerator is $\sqrt{x}$. Put $x=t^2:I=2{\int }_0^{\infty }{t}^2/\left[\left(1+t^2\right)\left(2+t^2\right)\right]dt=2\left[-\int dt/\left(1+t^2\right)+2\int dt/\left(2+t^2\right)\right]=\pi (\sqrt{2}-1)$.