Evaluate: ∫ x tan − 1 x d x

∫ x tan − 1 x d x = 2 x 2 tan − 1 x − 2 1 ∫ 1 + x 2 x 2 d x = 2 x 2 tan − 1 x − 2 1 ∫ [ 1 − 1 + x 2 1 ] d x = 2 1 ( x 2 + 1 ) tan − 1 x − 2 1 x + c

Mathematics - Definite Integration Question with Solution | TestHub

MathematicsDefinite IntegrationDefinite Integration by SubstitutionEasy2 minPYQ_2009

MathematicsEasysingle choice

Evaluate: $\int x tan^{- 1} x d x$

Options:

Answer:

Solution:

$\int x tan^{- 1} x d x = \frac{x ^{2}}{2} tan^{- 1} x - \frac{1}{2} \int \frac{x ^{2}}{1 + x ^{2}} d x = \frac{x ^{2}}{2} tan^{- 1} x - \frac{1}{2} \int [1 - \frac{1}{1 + x ^{2}}] d x = \frac{1}{2} (x^{2} + 1) tan^{- 1} x - \frac{1}{2} x + c$

Stream:BITSATSubject:MathematicsTopic:Definite IntegrationSubtopic:Definite Integration by Substitution

⏱ 2mℹ️ Source: PYQ_2009

Doubts & Discussion

Loading discussions...