The value of the integral $\int_{-6}^{0} |x+3|\,dx$ is

If $\int \frac{1}{\tan x + \cot x}dx = k\cos 2x + C$, where C is an arbitrary constant, then the value of $k$ is

The value of $\int_0^1 \log_e\left(\frac{1}{x} - 1\right)dx$ is:

$\int_{\frac{\pi}{6}}^{\frac{\pi}{3}} \frac{dx}{1 + \sqrt{\tan x}}$ is equal to :

$\displaystyle\int \dfrac{1}{e^x-1}\,dx$ is equal to:

(where C is an arbitrary constant)

$\int_{\frac{\pi}{6}}^{\frac{\pi}{3}} \frac{dx}{1 + \sqrt{tanx}}$ is equal to

$\int_0^1 tan^{-1}\left(\frac{2x-1}{1+x-x^2}\right)dx$ is equal to