$\int\left(1+x-\frac{1}{x}\right) e^{x+\frac{1}{x}} d x$ equal to

The function $f(x)=\frac{\log _e(\pi+x)}{\log _e(e+x)}$ is

Let $y=y(x)$ be the solution of the differential equation $\sin x \frac{\mathrm{~d} y}{\mathrm{~d} x}+y \cos x=4 x, x \in(0, \pi)$. If $y\left(\frac{\pi}{2}\right)=0$, then $y\left(\frac{\pi}{6}\right)$ is equal to

The value of $\mathrm{I}=\int \frac{x^2}{(\mathrm{a}+\mathrm{bx})^2} \mathrm{dx}$ is