Match the following : | Column I | Column II | |---|---| |

MATHEMATICS · Subjective · CBSE · Mathematics · Integrals · Integrals

Problem

Match the following :

Column I	Column II
(A) If $\int \left( \frac{x^2 + \cos^2 x}{1 + x^2} \right) \csc^2 x dx = A \cot^{-1} x + B \frac{\csc x}{\sec x}$ , then	(p) $A = 1$
(B) If $\int \sqrt{x + \sqrt{x^2 + 2}} dx = \frac{A}{3} (x + \sqrt{x^2 + 2})^{3/2} - \frac{B}{(x + \sqrt{x^2 + 2})}$ , then	(q) $B = -1$
(C) If $\int \frac{\sqrt{2-x-x^2}}{x^2} dx = A \sqrt{\frac{2-x-x^2}{x}} + \frac{B}{4\sqrt{2}} \log \left( \frac{4-x+4\sqrt{2-x-x^2}}{x} \right) - \sin^{-1} \left( \frac{2x+1}{3} \right)$ , then	(r) $B = 2$
(D) If $\int \frac{\sin 2x}{\sin^4 x + \cos^4 x} dx = B \cot^{-1} (\tan^2 x)$ , then	(s) $A = -1$