Calculus Examples

Evaluate the Integral integral of xe^(-x) with respect to x
Step 1
Integrate by parts using the formula , where and .
Step 2
Since is constant with respect to , move out of the integral.
Step 3
Simplify.
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Step 3.1
Multiply by .
Step 3.2
Multiply by .
Step 4
Let . Then , so . Rewrite using and .
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Step 4.1
Let . Find .
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Step 4.1.1
Differentiate .
Step 4.1.2
Since is constant with respect to , the derivative of with respect to is .
Step 4.1.3
Differentiate using the Power Rule which states that is where .
Step 4.1.4
Multiply by .
Step 4.2
Rewrite the problem using and .
Step 5
Since is constant with respect to , move out of the integral.
Step 6
The integral of with respect to is .
Step 7
Rewrite as .
Step 8
Replace all occurrences of with .