# Evaluate integral of (e to the power of x minus e to the power of(minus x)) divide(e to the power of x plus e to the power of(minus x)) with respect to x

Evaluate integral of (e^x-e^(-x))/(e^x+e^(-x)) with respect to x
Let . Then , so . Should be rewritten using and .
Let . Find .
Differentiate .
By the Sum Rule, the derivative of with respect to is .
Differentiate using the Exponential Rule which states that is where =.
Evaluate .
Differentiate using the chain rule, which states that is where and .
To apply the Chain Rule, set as .
Differentiate using the Exponential Rule which states that is where =.
Replace all occurrences of with .
Since is constant with respect to , the derivative of with respect to is .
Differentiate using the Power Rule which states that is where .
First, multiply by .
Move to the left of .
Rewrite as .
Rewrite the problem using and .
The integral of with respect to is .
Replace all occurrences of with .
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