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Calculus Examples
Step 1
Since is constant with respect to , move out of the integral.
Step 2
Integrate by parts using the formula , where and .
Step 3
Step 3.1
Combine and .
Step 3.2
Combine and .
Step 3.3
Combine and .
Step 4
Since is constant with respect to , move out of the integral.
Step 5
Step 5.1
Multiply by .
Step 5.2
Multiply by .
Step 6
Since is constant with respect to , move out of the integral.
Step 7
Step 7.1
Let . Find .
Step 7.1.1
Differentiate .
Step 7.1.2
Since is constant with respect to , the derivative of with respect to is .
Step 7.1.3
Differentiate using the Power Rule which states that is where .
Step 7.1.4
Multiply by .
Step 7.2
Rewrite the problem using and .
Step 8
Step 8.1
Move the negative in front of the fraction.
Step 8.2
Combine and .
Step 9
Since is constant with respect to , move out of the integral.
Step 10
Since is constant with respect to , move out of the integral.
Step 11
Step 11.1
Multiply by .
Step 11.2
Multiply by .
Step 12
The integral of with respect to is .
Step 13
Step 13.1
Rewrite as .
Step 13.2
Simplify.
Step 13.2.1
Combine and .
Step 13.2.2
Combine and .
Step 13.2.3
Combine and .
Step 14
Replace all occurrences of with .
Step 15
Reorder terms.