Match List – I with List – II.

Choose the correct answer from the options given below:

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

The correct answer is Option (3) → A-III, B-IV, C-I, D-II

(A) $\frac{3}{3}\int x^2 e^{x^3} d x=\frac{e^{x^3}}{3}+ C$ (III)

(B) $\int e^x\left(\underset{f(x)}{\underbrace{\tan ^{-1} x}}+\underset{f'(x)}{\underbrace{\frac{1}{1+x^2}}\right) d x=e^x \tan ^{-1} x+ C$ (IV)

(C) $\int \frac{d x}{a^2-x^2}=\frac{1}{2a}\int\left(\frac{1}{a-x}+\frac{1}{a+x}\right)dx$

$=\frac{1}{2a}(\log|a+x|-\log|a-x|)=\frac{1}{2a}\log|\frac{a+x}{a-x}|+C$ (I)

(D) $\int \frac{d x}{x^2+a^2}=\frac{1}{a} \tan ^{-1}\left(\frac{x}{a}\right)+ C$ (II)