If C is an arbitrary constant, then

Match the LIST-I with LIST-II

	LIST-I		LIST-II
A.	$\displaystyle\int \sqrt{x^2+a^2}\, dx$	I.	$\dfrac{x}{2}\sqrt{a^2-x^2} + \dfrac{a^2}{2}\sin^{-1}\dfrac{x}{a} + C$
B.	$\displaystyle\int \sqrt{a^2-x^2}\, dx$	II.	$\log\left\vert x + \sqrt{x^2+a^2}\right\vert + C$
C.	$\displaystyle\int \dfrac{1}{\sqrt{x^2+a^2}}\, dx$	III.	$\sin^{-1}\dfrac{x}{a} + C$
D.	$\displaystyle\int \dfrac{1}{\sqrt{a^2-x^2}}\, dx$	IV.	$\dfrac{x}{2}\sqrt{x^2+a^2} + \dfrac{a^2}{2}\log\left\vert x + \sqrt{x^2+a^2}\right\vert + C$

Choose the correct answer from the options given below:

The value of $\int_{-4}^{4} \log_e \left( \frac{1-x}{1+x} \right) dx$ is equal to

$\int \frac{2\cos 2x \, dx}{(\sin x+\cos x)^2}$ is equal to:(where C is an arbitrary constant)

If $\int (x + \sqrt{x^2 - 1})^2 \, dx = \alpha \cdot x + \beta x^3 + \gamma (x^2 - 1)^{\frac{3}{2}} + C$, where $C$ is arbitrary constant, then the value of $3(\alpha + \beta + \gamma)$ is

If $I_n = \int_{0}^{\pi/4} \tan^n x dx$ then $I_{2024} + I_{2026}$ is equal to:

The value of $\int_0^{\pi/2} \frac{\cos x}{\cos\frac{x}{2}+\sin\frac{x}{2}}\,dx$ is

$\int \frac{(x-1)e^x}{x^2} dx, x > 0$ equals (where C is an arbitrary constant)