$\int (1+e^{-x})^{-1} dx =$

$\int \sec x \log(\sec x + \tan x) \, dx = $

$\int \frac{e^x(x + 1)}{\cos^2(x e^x)} dx = $

$\int x^2 \sec(x^3) \, dx = $

If $\int \frac{x^3 \, dx}{\sqrt{1+x^2}} = a(1+x^2) \sqrt{1+x^2} + b \sqrt{1+x^2} + c$ (where $c$ is a constant of integration),then the value of $3ab$ is

Integrate the function: $\frac{x^{3}}{\sqrt{1-x^{8}}}$