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Calculus Examples
Step 1
Integrate by parts using the formula , where and .
Step 2
Step 2.1
Combine and .
Step 2.2
Combine and .
Step 3
Step 3.1
Apply the distributive property.
Step 3.2
Reorder and .
Step 3.3
Reorder and .
Step 3.4
Combine and .
Step 3.5
Multiply by .
Step 3.6
Combine and .
Step 3.7
Raise to the power of .
Step 3.8
Use the power rule to combine exponents.
Step 3.9
Write as a fraction with a common denominator.
Step 3.10
Combine the numerators over the common denominator.
Step 3.11
Add and .
Step 3.12
Combine and .
Step 3.13
Multiply by .
Step 4
Step 4.1
Move the negative in front of the fraction.
Step 4.2
Factor out of .
Step 4.3
Cancel the common factors.
Step 4.3.1
Factor out of .
Step 4.3.2
Cancel the common factor.
Step 4.3.3
Rewrite the expression.
Step 4.3.4
Divide by .
Step 5
Split the single integral into multiple integrals.
Step 6
Since is constant with respect to , move out of the integral.
Step 7
Since is constant with respect to , move out of the integral.
Step 8
By the Power Rule, the integral of with respect to is .
Step 9
Combine and .
Step 10
Since is constant with respect to , move out of the integral.
Step 11
By the Power Rule, the integral of with respect to is .
Step 12
Step 12.1
Combine and .
Step 12.2
Simplify.
Step 12.3
Simplify.
Step 12.3.1
Move to the left of .
Step 12.3.2
Move the negative in front of the fraction.
Step 12.3.3
Multiply by .
Step 12.3.4
Multiply by .
Step 12.3.5
Multiply by .
Step 12.3.6
Combine and .
Step 12.3.7
Multiply by .
Step 12.3.8
Move the negative in front of the fraction.
Step 12.3.9
To write as a fraction with a common denominator, multiply by .
Step 12.3.10
Combine and .
Step 12.3.11
Combine the numerators over the common denominator.
Step 12.3.12
Multiply by .
Step 13
Reorder terms.