Calculus Examples

Evaluate the Integral integral of (x^2)/(3-x^3) with respect to x
Step 1
Rewrite as .
Step 2
Let . Then , so . Rewrite using and .
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Step 2.1
Let . Find .
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Step 2.1.1
Differentiate .
Step 2.1.2
Differentiate using the Power Rule which states that is where .
Step 2.2
Rewrite the problem using and .
Step 3
Simplify.
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Step 3.1
Simplify.
Step 3.2
Multiply by .
Step 3.3
Move to the left of .
Step 4
Since is constant with respect to , move out of the integral.
Step 5
Let . Then , so . Rewrite using and .
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Step 5.1
Let . Find .
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Step 5.1.1
Rewrite.
Step 5.1.2
Divide by .
Step 5.2
Rewrite the problem using and .
Step 6
Move the negative in front of the fraction.
Step 7
Since is constant with respect to , move out of the integral.
Step 8
The integral of with respect to is .
Step 9
Simplify.
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Step 9.1
Simplify.
Step 9.2
Combine and .
Step 10
Substitute back in for each integration substitution variable.
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Step 10.1
Replace all occurrences of with .
Step 10.2
Replace all occurrences of with .
Step 11
Reorder terms.