The value of $\int_{\pi/2}^{\pi} \frac{1}{1 + \cot x} dx$ is equal to:

If $\int e^{3\log x}(x^4+1)^{-1}dx = \frac{m}{n}\log(x^4+1)+C$, where C is an arbitrary constant, $m$ and $n$ are positive integers such that g.c.d $(m,n)=1$, then $(4m^2+n^2)$ is equal to

The value of $\int_{0}^{1} \frac{a-b x^{2}}{\left(a+b x^{2}\right)^{2}} d x$ is :

$\int 3x^2 e^{x^3}\,dx$ is equal to : (where $C$ is an arbitrary constant)

The value of $\int_0^{\pi/2} \frac{\cos x}{\cos\frac{x}{2}+\sin\frac{x}{2}}\,dx$ is

The value of $\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} (\sin|x| + \cos|x|)dx$, is equal to:

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