- #1

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## Main Question or Discussion Point

My question is about this integral:

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

After using the substitution, u

[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, 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?