# 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

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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