Find ∫ − 1 1 1 + e t a n − 1 x x t a n − 1 x d x .

Pair x and − x : the two denominators are complementary, so twice the integral equals ∫ − 1 1 x tan − 1 x d x . Integration by parts on [0, 1] gives π /4 − 1/2 .

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Mathematics - Definite Integration Question with Solution | TestHub

MathematicsDefinite IntegrationDefinite Integration by SubstitutionMedium2 minQB

MathematicsMediumsingle choice

Find $\int_{- 1}^{1} \frac{x t a n ^{- 1} x}{1 + e ^{t a n^{- 1} x}} d x$ .

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Solution:

Pair $x$ and $- x$ : the two denominators are complementary, so twice the integral equals $\int_{- 1}^{1} x tan^{- 1} x d x$ . Integration by parts on [0, 1] gives $π /4 - 1/2$ .

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

⏱ 2mℹ️ Source: QB

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