Calculus Examples

Evaluate the Integral integral of cos(x)^7sin(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
The derivative of with respect to is .
Step 1.2
Rewrite the problem using and .
Step 2
Since is constant with respect to , move out of the integral.
Step 3
By the Power Rule, the integral of with respect to is .
Step 4
Rewrite as .
Step 5
Replace all occurrences of with .