$\int \sin x \sin 2x \sin 3x dx$ is equal to

$\int \frac{\sin 2x \, dx}{\sqrt{9 - \cos^4 x}}$ equals

The value of which of the following integrals is zero?

(A) $\int_0^1 x dx$

(B) $\int_{-1}^1 x dx$

(C) $\int_{-1}^1 x^2 dx$

(D) $\int_0^1 \log\left(\frac{x}{1-x}\right) dx$

Choose the correct answer from the options given below:

$\int \left(\frac{1}{\log_e x} - \frac{1}{(\log_e x)^2}\right)dx$ is equal to

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

Integral $I = \displaystyle\int \dfrac{e^{3\log x} - 3x^4}{e^{2\log x} + x^2}\, dx$ (where $x>0$) is equal to

$\int \frac{dx}{\sin^2 x \cos^2 x} =$