The value of integral $\int \sqrt{4x^2 + 9}\, dx$ is

$\int_0^{4\pi} \frac{x}{1 + |\cos x|} dx =$

If $\displaystyle\int_0^3 (8x^3+5x^2-2x-k)\,dx = 3$, where $k$ is constant, then $k$ is equal to

Which of the following statements are TRUE?

A. $\displaystyle\int_4^9 \dfrac{1}{\sqrt{x}}\, dx = 2$

B. $\displaystyle\int_{-4}^4 (x^{101} + x^{201} + x^{301})\, dx = 4\left(\dfrac{1}{102} + \dfrac{1}{202} + \dfrac{1}{302}\right)$

C. $\displaystyle\int_{-1}^1 x^{1012}\, dx = \dfrac{2}{1013}$

D. $\displaystyle\int (x^2 + 2x + 1)\, dx = \dfrac{(x+1)^3}{3} + c$ where $c$ is an arbitrary constant

Choose the correct answer from the options given below:

$\displaystyle\int \dfrac{1+\cos\theta}{1-\cos\theta}\,d\theta =$

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

$\int_{4}^{10} \frac{\log(x^2)}{\log(x^2)+\log(196-28x+x^2)}dx$ is equal to : (Consider $\log_e x = \log x$)