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Integration by Substitution

Evaluate ∫e...

Question

Evaluate $\int \frac{e^{x} - e^{- x}}{e^{x} + e^{- x}} d x$ .

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Solution

Let, $I = \int \frac{e^{x} - e^{- x}}{e^{x} + e^{- x}} d x$

Let $e^{x} + e^{- x} = t$
$(e^{x} - e^{- x}) d x = d t$

Therefore,
$I = \int \frac{d t}{t} = log t + C$

$I = log | e^{x} + e^{- x} | + C$

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