Question

Find the area:
\(\Huge \int\limits_{0}^{\pi/8} \sqrt{\tan x} dx\)

NOTE: Inky wants to inform you that this IS a troll question. You can choose to answer it, but it's definitely not worth inky's homework credit or inky's test grade.

Answer 1

let tan(x) = u^2
dx = u/sqrt(1-u^2) du

Answer 2

*2udu/sqrt(1-u^2)

Answer 3

the hard part is the partial fractions :3

Answer 4

the indefintie integral appears to be in closed form.
\[ \frac{2 \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (x)}+1\right)-2 \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (x)}\right)-\log \left(\tan (x)+\sqrt{2} \sqrt{\tan (x)}+1\right)+\log \left(\tan (x)-\sqrt{2} \sqrt{\tan (x)}+1\right)}{2 \sqrt{2}} \]

Answer 5

okay, you tried hard enough.

Answer 6

haven't ... just woke up.