$$ \int \frac{1}{f(x)f''(x)}\mathrm{d}x $$
Does this antiderivative have a closed formula?
I am asking with respect to a particular application, where $f(x):=\sqrt{1-x^2}+x\arcsin{x}$ (therefore $f'(x)=\arcsin{x}$ and $f''(x)=\frac{1}{\sqrt{1-x^2}}$).
