Value of $\int_2^3 \frac{\sqrt{x}}{\sqrt{x} + \sqrt{5-x}}dx$ is

$\int \frac{dx}{\sqrt{5 - 4x - x^2}}$ is equal to

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

If $\int_0^{\pi/2} \sqrt{\tan x} \, dx = \frac{\lambda}{\sqrt{2}}$, then the value of $\lambda$ is

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

$\displaystyle\int_{-\pi/3}^{\pi/3} 2x^5\cos^4 x\, dx$ equals

$\int \frac{dx}{9x^2 - 16}$ is equal to