Match List-I with List-II Where C is arbitrary constant., List-I, List-II, (A) dx/(x^2 - a^2) =, (I) x + √(x^2+a^2) + C, (B) dx/(a^2 - x^2) =, (II) x + √(x^2-a^2) + C, (C) dx/(√(x^2 - a^2)) =, (III) 1/2a (x-a)/(x+a) + C, (D) dx/(√(x^2 + a^2)) =, (IV) 1/2a (a+x)/(a-x) + C, Choose the correct answer from the options given below:

Question

Match List-I with List-II

Where C is arbitrary constant.

List-I List-II
(A) $\displaystyle\int \dfrac{dx}{x^2 - a^2} =$ (I) $\log\left\vert x + \sqrt{x^2+a^2}\right\vert + C$
(B) $\displaystyle\int \dfrac{dx}{a^2 - x^2} =$ (II) $\log\left\vert x + \sqrt{x^2-a^2}\right\vert + C$
(C) $\displaystyle\int \dfrac{dx}{\sqrt{x^2 - a^2}} =$ (III) $\dfrac{1}{2a}\log\left\vert \dfrac{x-a}{x+a}\right\vert + C$
(D) $\displaystyle\int \dfrac{dx}{\sqrt{x^2 + a^2}} =$ (IV) $\dfrac{1}{2a}\log\left\vert \dfrac{a+x}{a-x}\right\vert + C$

Choose the correct answer from the options given below:

Accepted Answer

(A) - (III), (B) - (IV), (C) - (II), (D) - (I)

Answer

(A) - (IV), (B) - (III), (C) - (II), (D) - (I)

Answer

(A) - (II), (B) - (III), (C) - (IV), (D) - (I)

Answer

(A) - (II), (B) - (I), (C) - (IV), (D) - (III)

List-I	List-II
(A) $\displaystyle\int \dfrac{dx}{x^2 - a^2} =$	(I) $\log\left\vert x + \sqrt{x^2+a^2}\right\vert + C$
(B) $\displaystyle\int \dfrac{dx}{a^2 - x^2} =$	(II) $\log\left\vert x + \sqrt{x^2-a^2}\right\vert + C$
(C) $\displaystyle\int \dfrac{dx}{\sqrt{x^2 - a^2}} =$	(III) $\dfrac{1}{2a}\log\left\vert \dfrac{x-a}{x+a}\right\vert + C$
(D) $\displaystyle\int \dfrac{dx}{\sqrt{x^2 + a^2}} =$	(IV) $\dfrac{1}{2a}\log\left\vert \dfrac{a+x}{a-x}\right\vert + C$