A question about Indefinite trigonometric integration

A question about Indefinite trigonometric integration

I am practising a unit on Integration. I am going through some past year
papers, and there are some types of questions that I could not solve. So
if anyone could help me in this, I'd really appreciate this.
Evaluate the following integrals: $$
i)\quad\int\left(\frac{2}{\sqrt{x}}+2e^{-4x}+\frac{1}{3(1-x)}\right)\:\mathrm{d}x
$$
In this, I managed to get to a point where the answer is: $$
4\sqrt{x}-\frac{e^{-4x}}{2}+\frac{\ln|x+1|}{3}+C $$
Is this the final answer or there's more I can do here. I'm specially
confused about the $|x+1|$ part.
Next is a trigonometric substituition question. I've tried basic ones of
this type, but this one is very difficult and complicated for me. If
someone could point me into a direction then maybe I can try solving.
Show that: $$
\int\frac{x^2}{\sqrt{36-x^2}}\:\mathrm{d}x=18\sin^{-1}\left(\frac{x}{6}\right)-\frac{1}{2}x\sqrt{36-x^2}+C
$$ with an appropriate trigonometric substitution.