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

Evaluate the integral: $\int \sqrt{x^2+x+1} \, dx$

Let $\alpha \in (0, \pi /2)$ 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 the functions $A(x)$ and $B(x)$ are respectively:

The primitive of $\frac{3x^4 - 1}{(x^4 + x + 1)^2}$ with respect to $x$ is:

If $\int \sin (101 x)(\sin x)^{99} d x=\frac{\sin (100 x)(\sin x)^\lambda}{\mu}+c$ then $\frac{\lambda}{\mu}=$

$\int \frac{x^4+1}{x^6+1} \, dx =$