The value of $\int \left(\sqrt{x} + \frac{1}{\sqrt{x}}\right)^2 dx$ is:

Let $f(x)=\int \frac{3x-2}{(x+1)^2(x+3)}dx = \alpha\log\left|\frac{x+1}{x+3}\right|+\beta\left(\frac{1}{x+1}\right)+\gamma$, where $\gamma$ is the constant of integration. If $f(0)=\frac{11}{4}\log\left(\frac{1}{3}\right)+4$, then which of the following are correct?

(A) $4\alpha+2\beta+6\gamma=22$

(B) $f(1)=\alpha[1-\log 2]$

(C) $\alpha+\beta+\gamma=\frac{27}{4}$

(D) $\gamma=-\frac{5}{2}$

Choose the correct answer from the options given below:

Value of $\int_{-2}^{2}|2x+1|dx$ is:

The value of $\int \frac{x^5}{\sqrt{1 + x^3}} dx$ is

Match the LIST-I with LIST-II (where $[x]$ denotes greatest integer function)

Choose the correct answer from the options given below:

The value of $\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} (\sin|x| + \cos|x|)dx$, is equal to:

$\int_0^2 (|x| + |x - 2|) dx =$