Calculus Examples

Integrate By Parts integral of 5x^6 natural log of 2x 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
Simplify.
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Step 4.1
Combine and .
Step 4.2
Cancel the common factor of and .
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Step 4.2.1
Factor out of .
Step 4.2.2
Cancel the common factors.
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Step 4.2.2.1
Raise to the power of .
Step 4.2.2.2
Factor out of .
Step 4.2.2.3
Cancel the common factor.
Step 4.2.2.4
Rewrite the expression.
Step 4.2.2.5
Divide by .
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
Rewrite as .
Step 6.2
Simplify.
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Step 6.2.1
Combine and .
Step 6.2.2
Combine and .
Step 6.2.3
Multiply by .
Step 6.2.4
Multiply by .