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:

If C is an arbitrary constant, then

Match the LIST-I with LIST-II

Choose the correct answer from the options given below:

If $0 < x < \frac{\pi}{4}$, then $\int\sqrt{1-\sin2x}\,dx$ is:

[where C is an arbitrary constant]

If $\int_0^1 \frac{1-x}{1+x} dx = A\log 2 + B$, then the value of A and B are

$\int (e^{x\log a} + e^{a\log x}) dx$ is equal to (where $a > 1$)

The value of $\displaystyle\int_{\pi/6}^{\pi/3} \dfrac{\sin x+\cos x}{\sqrt{\sin 2x}}\,dx$ is:

Value of $\displaystyle\int \dfrac{dx}{\sin^{\frac{3}{5}}x \cdot \cos^{\frac{7}{5}}x}$ is (where c is an arbitrary constant)