$\int \frac{dx}{(1+5\sin^2 x)}$ is equal to

$\int \frac{\sin(\tan^{-1} x)}{1 + x^2} dx =$

$\int_0^{\pi/2} \sqrt{1 - \sin 2x}\,dx$ is equal to:

$I=\int_{2}^{8}\frac{\sqrt[3]{x+1}}{\sqrt[3]{x+1}+\sqrt[3]{11-x}}dx$ is equal to :

$\displaystyle\int e^{x\log_e 7} e^x\, dx$ is equal to :

[where C is an arbitrary constant]

$\int \frac{dx}{x^3\sqrt{(1 + x^4)}} =$

$\displaystyle\int e^x(\sec x + \log_e(\sec x + \tan x))dx$ is equal to: (where C is an arbitrary constant)