If $\displaystyle\int \dfrac{\sin^4 x}{\cos^8 x}\, dx = a\tan^7 x + b\tan^5 x + C$, where 'C' is an arbitrary constant then

The value of $\int_{-\pi/2}^{\pi/2}(x^5 + x^3\cos x)dx$ is

$\int_0^8 (x^{\frac{2}{3}} + 1) dx$ is equal to

$\int \frac{x^2+1}{(x+1)^2} e^x \, dx$ is equal to

The value of $\int_0^1 \log_e\left(\frac{1}{x} - 1\right)dx$ is:

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:

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