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Evaluate: int(e^x-e^(-x))/(e^x+e^(-x))\ ...

Evaluate: `int(e^x-e^(-x))/(e^x+e^(-x))\ dx`

Text Solution

Verified by Experts

Note that `frac{d}{d x}(e^{x}+e^{-x})=e^{x}-e^{-x} so`
`frac{e^{x}-e^{-x}}{e^{x}+e^{-x}}=frac{d}{d x} log (e^{x}+e^{-x})` and finally
`int frac{e^{x}-e^{-x}}{e^{x}+e^{-x}} d x=int frac{d}{d x} log (e^{x}+e^{-x}) d x=log (e^{x}+e^{-x})+C`
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