For a homework problem, I have to integrate this:
$$\int{4^{(4+x)^x}}dx$$
How would I go around to starting this question? I don't know how to evaluate this, and I've tried to use u-subs and integration by parts, but to no avail. Could anyone lead me in the right direction?
There is almost certainly no closed form solution. Even the much simpler integral $\int x^x$ cannot be expressed in terms of elementary functions.
You could do various numerical approximations to find bounds, or maybe write down a power series expansion. But that's as far as you can really go here.