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## Homework Statement

[tex] \int \sqrt{tanx} dx[/tex]

## The Attempt at a Solution

I used the substitution u = sqrt(tanx), then x = arctan(x^2)

so:

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

now, I suspect that some kind of partial fractions method can be used here, I have 2 irreducible quadratic factors in my denominator, but my numerator has a quadratic term as well.. not sure what to do with that. Please let me know, or give me an idea!

thanks (I'm not looking for a solution, I just need to know how to use the partial fraction method..)