$\int {e^{\log (\sin x)}} \, dx = $

Find the integral of the function $\frac{\sin ^{3} x+\cos ^{3} x}{\sin ^{2} x \cos ^{2} x}$.

If $\int f'(x) \cdot e^{x^2} dx = (x - 1) \cdot e^{x^2} + k$, where $k$ is the constant of integration, then $f(x) = \dots$

$\int \frac{\cos 2x - \cos 2\alpha}{\cos x - \cos \alpha} dx =$

$\int \sin^{-1}(\cos x) \, dx = $

If $a > 0, b > 0$ and $\int \frac{1}{ax^2+b} dx = \frac{1}{\sqrt{6}} \tan^{-1} \left(\frac{\sqrt{2}x}{\sqrt{3}}\right) + c$, then $\int \frac{1}{bx^2+a} dx = \dots$