0-pi-1-1-tan-x-2-dx-

Question Number 82450 by M±th+et£s last updated on 21/Feb/20

\int_{0}^{π} \frac{1}{1 + {(t a n (x))}^{\sqrt{2}}} d x

Commented by MJS last updated on 21/Feb/20

\tan^{\sqrt{2}} x \notin R for \frac{π}{2} < x < π

\underset{0}{\int^{\frac{π}{2}}} \frac{d x}{1 + \tan^{\sqrt{2}} x} = \frac{π}{4} (found by approximation)

changement t = \tan x \to d x = \frac{d t}{t^{2} + 1} gives

\int \frac{d t}{(t^{2} + 1) (t^{\sqrt{2}} + 1)}

maybe someone can solve this using the

residue theorem

Answered by M±th+et£s last updated on 22/Feb/20