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

$\int {{e^{{x^2}}}} \cdot {e^x}\left( {2{x^2} + x + 1} \right)dx = {e^{{x^2} + x}}\left( {f\left( x \right)} \right) + c$ where $c$ is the constant of integration. If the minimum value of $f(x)$ is equal to $m$,then find the value of $\left[ { - \frac{1}{m}} \right]$,where $[\cdot]$ denotes the Greatest Integer Function $(GIF)$.

$\int e^{4x}(\sin 3x - \cos 3x) dx = $

$\int e^x \left( \frac{\sec^2 x + \tan x - \cot x}{\sin x} \right) dx =$

$ \int e^{\sin x} \cdot \left(\frac{\sin x+1}{\sec x}\right) d x $ is equal to

Integrate the function: $\frac{2+\sin 2x}{1+\cos 2x} e^x$