Question

$\int_{}^{}\frac{x^{2} + \cos^{2}x}{1 + x^{2}}$cosec² xdx =

• A. cot x + tan^–1 x + c
• B. cot x – tan^–1 x + c
• C. – cot^–1x – tan^–1x + c
• D. None of these

Answer 1

Answer: (C)

– cot^–1x – tan^–1x + c

Answer 2

$\int \frac { x ^ { 2 } + \cos ^ { 2 } x } { \left( 1 + x ^ { 2 } \right) \sin ^ { 2 } x }$ dx = $\int \frac { \left( 1 + x ^ { 2 } \right) - \sin ^ { 2 } x } { \left( 1 + x ^ { 2 } \right) \sin ^ { 2 } x }$dx

= $\int \left( \operatorname { cosec } ^ { 2 } x - \frac { 1 } { 1 + x ^ { 2 } } \right)$ dx = – cot x– tan^–1x + c