Calculus Examples

Evaluate the Integral integral of ( natural log of x)/(x^5) with respect to x
Step 1
Apply basic rules of exponents.
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Step 1.1
Move out of the denominator by raising it to the power.
Step 1.2
Multiply the exponents in .
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Step 1.2.1
Apply the power rule and multiply exponents, .
Step 1.2.2
Multiply by .
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
Multiply by .
Step 3.3
Raise to the power of .
Step 3.4
Use the power rule to combine exponents.
Step 3.5
Add and .
Step 4
Since is constant with respect to , move out of the integral.
Step 5
Simplify.
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Step 5.1
Multiply by .
Step 5.2
Multiply by .
Step 6
Since is constant with respect to , move out of the integral.
Step 7
Apply basic rules of exponents.
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Step 7.1
Move out of the denominator by raising it to the power.
Step 7.2
Multiply the exponents in .
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Step 7.2.1
Apply the power rule and multiply exponents, .
Step 7.2.2
Multiply by .
Step 8
By the Power Rule, the integral of with respect to is .
Step 9
Simplify the answer.
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Step 9.1
Rewrite as .
Step 9.2
Simplify.
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Step 9.2.1
Multiply by .
Step 9.2.2
Move to the left of .
Step 9.2.3
Multiply by .
Step 9.2.4
Multiply by .