Calculus Examples

Evaluate the Integral integral of (e^x)/(1+e^x) with respect to x
Step 1
Let . Then , so . Rewrite using and .
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Step 1.1
Let . Find .
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Step 1.1.1
Differentiate .
Step 1.1.2
Differentiate.
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Step 1.1.2.1
By the Sum Rule, the derivative of with respect to is .
Step 1.1.2.2
Since is constant with respect to , the derivative of with respect to is .
Step 1.1.3
Differentiate using the Exponential Rule which states that is where =.
Step 1.1.4
Add and .
Step 1.2
Rewrite the problem using and .
Step 2
The integral of with respect to is .
Step 3
Replace all occurrences of with .