# How do you integrate #int (e^x-e^-x)/(e^x+e^-x)dx#?

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To integrate ( \frac{{e^x - e^{-x}}}{{e^x + e^{-x}}} , dx ), perform the following steps:

- Let ( u = e^x + e^{-x} ).
- Find ( du ) by differentiating ( u ) with respect to ( x ).
- Rewrite the integral in terms of ( u ).
- Integrate the rewritten expression with respect to ( u ).
- Replace ( u ) with ( e^x + e^{-x} ) to obtain the final result.

The integral will simplify to ( \ln|e^x + e^{-x}| + C ), where ( C ) is the constant of integration.

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