Calculus Examples

Evaluate the Integral integral of 7x^2 natural log of x with respect to x
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
Simplify.
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Step 3.1
Combine and .
Step 3.2
Combine and .
Step 3.3
Combine and .
Step 3.4
Multiply by .
Step 3.5
Cancel the common factor of and .
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Step 3.5.1
Factor out of .
Step 3.5.2
Cancel the common factors.
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Step 3.5.2.1
Factor out of .
Step 3.5.2.2
Cancel the common factor.
Step 3.5.2.3
Rewrite the expression.
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
Simplify the answer.
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Step 6.1
Combine and .
Step 6.2
Rewrite as .
Step 6.3
Reorder terms.