- 362

- 0

[tex]\int\sqrt{\tan (x)}dx[/tex]

After using the substitution, u

^{2}= tan(x), I got,

[tex]2\int\frac{u^2}{u^4 + 1}du = 2\int\frac{u^2}{\left(u^2 + \sqrt{2}u + 1\right)\left(u^2 - \sqrt{2}u + 1\right)}du[/tex]

Next, I tried the partial fraction expansion. But it turned pretty ugly. Is there any easier way of doing it?