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Calculus Examples
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
Step 3.1
Let . Find .
Step 3.1.1
Differentiate .
Step 3.1.2
Differentiate.
Step 3.1.2.1
By the Sum Rule, the derivative of with respect to is .
Step 3.1.2.2
Since is constant with respect to , the derivative of with respect to is .
Step 3.1.3
Evaluate .
Step 3.1.3.1
Since is constant with respect to , the derivative of with respect to is .
Step 3.1.3.2
Differentiate using the Power Rule which states that is where .
Step 3.1.3.3
Multiply by .
Step 3.1.4
Subtract from .
Step 3.2
Rewrite the problem using and .
Step 4
Since is constant with respect to , move out of the integral.
Step 5
By the Power Rule, the integral of with respect to is .
Step 6
Step 6.1
Simplify.
Step 6.1.1
Combine and .
Step 6.1.2
Move to the left of .
Step 6.1.3
Combine and .
Step 6.1.4
Multiply by .
Step 6.1.5
Multiply by .
Step 6.2
Rewrite as .
Step 6.3
Simplify.
Step 6.3.1
Combine and .
Step 6.3.2
Move the negative in front of the fraction.
Step 6.3.3
Combine the numerators over the common denominator.
Step 6.3.4
Multiply by .
Step 6.3.5
Multiply by .
Step 6.3.6
Multiply by .
Step 7
Replace all occurrences of with .
Step 8
Reorder terms.