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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 $e^{x} + e^{- x} = t$
Then $e^{x} - e^{- x} = d t$
Therefore, required integral = $\int \frac{1}{t} d t$
$= ln | t | + C$
$= ln (e^{x} + e^{- x}) + C$

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