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

If $\int e^x\left(\frac{x-1}{(x+1)^3}\right)dx = \frac{Ae^x}{(x+1)^B} + C$, where C is constant of integration then which of the following are correct?

(A) $A = -1$

(B) $A = 1$

(C) $B = 3$

(D) $B = 2$

Choose the correct answer from the options given below:

The integral $I = \int \frac{(1+\log_e x)^3}{x} dx$ is equal to

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

$\int \frac{\sqrt{9+(\log x)^2}}{x} dx$ is equal to: (where $C$ is an arbitrary constant and consider $\log_e x = \log x$)

$\displaystyle\int_1^3 \dfrac{\sqrt{x}}{\sqrt{x}+\sqrt{4-x}}dx$ is equal to:

$\int \left\{\frac{1}{\log x} - \frac{1}{(\log x)^2}\right\} dx$ is equal to:(where C is an arbitrary constant)