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

Let $I_{n}(x)=\int_{0}^{x} \frac{1}{(t^{2}+5)^{n}} dt, n=1, 2, 3, \ldots$. Then

Find the following integral: $\int \frac{x+2}{2 x^{2}+6 x+5} d x$

Let $\alpha \in (0, \frac{\pi}{2})$ be fixed. If the integral $\int \frac{\tan x+\tan \alpha}{\tan x-\tan \alpha} dx = A(x) \cos 2\alpha + B(x) \sin 2\alpha + c$ (where $c$ is a constant of integration),then functions $A(x)$ and $B(x)$ are respectively

Evaluate the integral: $\int \frac{dx}{2+\cos x}$

$\int \frac{x^2-1}{x^3 \sqrt{2 x^4-2 x^2+1}} d x=$