I am trying to evaluate $\int_{-\pi/4}^{\pi/4}(x^3+x^4\tan x)\,dx.$
I tried to factor out an $x^3$ but that did nothing for me, and I also attempted to split it up into $x^3$ and $x^4 \tan x$ but that didn't help and I am not sure if it is legal. Nothing really seems to be quite right for this.