Q. $\int_{}^{}x^{51}\left( \tan^{- 1}x + \cot^{- 1}x \right)dx$
A) $\frac{x^{52}}{52}\ \left( \tan^{- 1}x + \cot^{- 1}x \right) + c$
B) $\frac{x^{52}}{52}\ \left( \tan^{- 1}x - \cot^{- 1}x \right) + c$
C) $\frac{\pi x^{52}}{104} + \frac{\pi}{2} + c$
D) $\frac{x^{52}}{52} + \frac{\pi}{2} + c$
Explanation
(a)
$\int_{}^{}x^{51}\left( \tan^{- 1}x + \cot^{- 1}x \right)dx = \int_{}^{}x^{51}.\frac{\pi}{2}dx$
$= \frac{\pi x^{52}}{104} + c$
$= \frac{x^{52}}{52}\ \left( \tan^{- 1}x + \cot^{- 1}x \right) + c$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.