$\int {{e^x}(1 + \tan x + {{\tan }^2}x)\,dx = } $

$\int \frac{x+100}{(x+101)^2} e^x \, dx = $ . . . . . . $+ C$.

The value of $\int \frac{e^{\tan ^{-1}(x)}}{1+x^2} \left[\left(\sec ^{-1} \sqrt{1+x^2}\right)^2+\cos ^{-1}\left(\frac{1-x^2}{1+x^2}\right)\right] d x$,for $x>0$ is

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

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

$\int {{e^x}[\tan x - \log (\cos x)]\,dx = }$