I'm asked to transform the improper integral $$\int_{0}^{\infty}e^{-x^4}dx$$ into a proper integral.
What I tried:
Substituting $x = \tan(x)$ and $\frac{dx}{ds} = \sec^2(s)$
The integral becomes $$\int_{0}^{+ \frac{\pi}{2}} e^{- \tan^4(s)} \sec^2{(s)} ds$$
Is that correct ? Is there a way to go further ?