Match List-I with List-II

List-I	List-II
(A) $\int_{-1}^{1} \lvert x \rvert dx =$	(I) 3
(B) $\int_{-\pi}^{\pi} \cos x \, dx =$	(II) 1
(C) $\int_{-1}^{1} (\lvert x \rvert-1) dx =$	(III) 0
(D) $\int_{-1}^{1} (\lvert x \rvert+1) dx =$	(IV) -1

Choose the correct answer from the options given below:

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

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

$\int \frac{x}{(x-1)(x-2)} dx =$

(where c is an arbitrary constant)

The value of $\int_{-1}^{1} \dfrac{x^6}{6^x+1}\,dx$ is

$\int \frac{\log x - 3}{(\log x)^4} dx$ is equal to

(where C is an arbitrary constant and $\log_e x = \log x$)

If $\int_0^{\pi/2} \sqrt{\tan x} \, dx = \frac{\lambda}{\sqrt{2}}$, then the value of $\lambda$ is