- #1
murshid_islam
- 457
- 19
My question is about this integral:
[tex]\int\sqrt{\tan (x)}dx[/tex]
After using the substitution, u2 = 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?
[tex]\int\sqrt{\tan (x)}dx[/tex]
After using the substitution, u2 = 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?