x 51 ( tan - 1 x + cot - 1 x ) d x =

Question

$\int x^{51} (\tan^{- 1} x + \cot^{- 1} x) d x =$

Smart Achievers · Accepted Answer

(1)

Ans. $\frac{x^{52}}{52} (\tan^{- 1} x + \cot^{- 1} x) + C$

Explanation

$\int x^{51} (\tan^{- 1} x + \cot^{- 1} x) d x$

$= \int x^{51} \cdot \frac{π}{2} d x$ $[∵ \tan^{- 1} x + \cot^{- 1} x = \frac{π}{2}]$

$= \frac{π x^{52}}{104} + C$ $= \frac{x^{52}}{52} (\tan^{- 1} x + \cot^{- 1} x) + C$

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