Calculus Examples

Evaluate the Integral integral of ( natural log of (x)^6)/x with respect to x
Step 1
Rewrite as .
Step 2
Since is constant with respect to , move out of the integral.
Step 3
Let . Then , so . Rewrite using and .
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Step 3.1
Let . Find .
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Step 3.1.1
Differentiate .
Step 3.1.2
The derivative of with respect to is .
Step 3.2
Rewrite the problem using and .
Step 4
By the Power Rule, the integral of with respect to is .
Step 5
Simplify.
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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
Cancel the common factor of and .
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Step 5.2.2.1
Factor out of .
Step 5.2.2.2
Cancel the common factors.
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Step 5.2.2.2.1
Factor out of .
Step 5.2.2.2.2
Cancel the common factor.
Step 5.2.2.2.3
Rewrite the expression.
Step 5.2.2.2.4
Divide by .
Step 6
Replace all occurrences of with .