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Calculus Level 3

2 ∫ 0 ∞ d x ( 1 + e x ) ( 1 + e − x ) = ? \large 2 \int_0^\infty \dfrac{dx}{(1+e^x)(1+e^{-x})} = \, ?


The answer is 1.

Hamza A by Hamza A , 19, USA

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1 solution

Prashant Kr
Jan 25, 2016

p u t ′ e x = t ′ put 'e^{x} =t' so x becomes lnt And d x = 1 t d t dx =\frac{1}{t} dt And limits changes to 1 → ∞ 1 \rightarrow \infty Our question becomes 2 ∫ 1 ∞ d t ( 1 + t ) 2 2\int_{1}^{\infty} \frac{dt}{(1+t)^2} which evaluates to 1

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