I have no idea how to go about solving this integral:
$$ \int\_0^{\frac{\pi}{2}-}\frac{dx}{1+\tan^{\sqrt{2}}\left(x\right)} .$$
The most I've come up with is rewriting it as a series to obtain
$$ \int\_0^{\frac{\pi}{2}-}\sum\limits\_{n=0}^\infty \left\{-\tan^{\sqrt{2}}\left(x\right)\right\}^n{dx}, $$
but then I realized that this resulted in a hideous set of integrations if I were to try integrating term-by-term and then turning the answer back:
$$ \int\_0^{\frac{\pi}{2}-}\left[1-\tan^{\sqrt{2}}\left(x\right)+\tan^2 (x)-\tan^{2\cdot\sqrt{2}}(x)+\cdots\right]\,dx, $$
because then I couldn't solve
$$ \int \tan^\sqrt{2} (x) \, dx. $$
So to cope with the above I thought I might expand even further, but then I realized I must be waaayyyyy off track from where I should be.