$\int \frac{x^2 + 4}{(x^2 + 3)(x^2 + 5)} \, dx = u \tan^{-1}\left(\frac{x}{\sqrt{3}}\right) + v \tan^{-1}\left(\frac{x}{\sqrt{5}}\right) + c$, where c is arbitrary constant, then value of $\frac{1}{u^2} + \frac{1}{v^2}$ is equal to :

$\int \frac{xe^x}{(x+1)^2} dx =$

$\displaystyle\int \dfrac{dx}{(x^2+4)^{\frac{3}{2}}}$ is equal to ( where $c$ is an arbitrary constant)

$\int e^x \left(\frac{1}{x} - \frac{2}{x^3}\right) dx =$

If $\int \frac{1}{\sqrt{(x-1)(x-2)}}\,dx = \log\left|(x-m)+\sqrt{ax^2+bx+n}\right| + C$ where C is an arbitrary constant and $m,n,a$ and $b$ are constant, then $2m+n+a+b$ is equal to:

Value of $\int_{-2}^{2}|2x+1|dx$ is:

$\int e^{-x}(\cot x + \cosec^2 x)dx =$