Calculus Examples

Evaluate the Integral integral of cube root of x(x-4) with respect to x
Step 1
Integrate by parts using the formula , where and .
Step 2
Simplify.
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Step 2.1
Combine and .
Step 2.2
Combine and .
Step 3
Since is constant with respect to , move out of the integral.
Step 4
By the Power Rule, the integral of with respect to is .
Step 5
Simplify the answer.
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Step 5.1
Rewrite as .
Step 5.2
Simplify.
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Step 5.2.1
Combine and .
Step 5.2.2
Multiply by .
Step 5.2.3
Multiply by .
Step 5.2.4
Multiply by .
Step 5.2.5
To write as a fraction with a common denominator, multiply by .
Step 5.2.6
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Step 5.2.6.1
Multiply by .
Step 5.2.6.2
Multiply by .
Step 5.2.7
Combine the numerators over the common denominator.
Step 5.2.8
Multiply by .
Step 5.2.9
Subtract from .
Step 5.2.10
Factor out of .
Step 5.2.11
Cancel the common factors.
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Step 5.2.11.1
Factor out of .
Step 5.2.11.2
Cancel the common factor.
Step 5.2.11.3
Rewrite the expression.
Step 5.3
Reorder terms.