Match List-I with List-II.

Choose the correct answer from the options given below :

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

The correct answer is Option (4) → (A)-(III), (B)-(I), (C)-(II), (D)-(IV)

(A) $I.F.=e^{\int -\frac{1}{x}dx}=e^{-\log x}=\frac{1}{x}$ (III)

(B) $I.F.=e^{\int\frac{2x}{x^2-1}dx}=e^{\log|x^2-1|}=x^2-1$ (I)

(C) $I.F.=e^{\int\frac{-x}{1-x^2}dx}=e^{\frac{1}{2}\log|1-x^2|}=\sqrt{1-x^2}$ (II)

(D) $I.F.=e^{\int\frac{2x}{1+x^2}dx}=e^{\log|1+x^2|}=1+x^2$ (IV)