$\int e^x(x+1)^2 dx=$

If $\int e^{\sin x}(1+\sec x \tan x) d x=e^{\sin x} f(x)+c$,then in $0 \leq x \leq 2 \pi$,the number of solutions of $f(x)=1$ is

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

$\int {{e^{2x}}\left( {\frac{{\sin 4x - 2}}{{1 - \cos 4x}}} \right)\;dx = } $

Let $f(t) = \int \left( \frac{1 - \sin(\ln t)}{1 - \cos(\ln t)} \right) dt$, for $t > 1$. If $f(e^{\pi/2}) = -e^{\pi/2}$ and $f(e^{\pi/4}) = \alpha e^{\pi/4}$, then $\alpha$ equals:

$\int \left( \frac{2 - \sin 2x}{1 - \cos 2x} \right) e^x \, dx$ is equal to