Calculus Examples

Factor the numerator and denominator of .
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Factor out of .
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Factor out of .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Factor by grouping.
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For a polynomial of the form , rewrite the middle term as a sum of two terms whose product is and whose sum is .
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Factor out of .
Rewrite as plus
Apply the distributive property.
Factor out the greatest common factor from each group.
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Group the first two terms and the last two terms.
Factor out the greatest common factor (GCF) from each group.
Factor the polynomial by factoring out the greatest common factor, .
Write the fraction using partial fraction decomposition.
Simplify.
Split the single integral into multiple integrals.
Since is constant with respect to , move out of the integral.
The integral of with respect to is .
Since is constant with respect to , move out of the integral.
Let . Then , so . Rewrite using and .
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Let . Find .
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Rewrite.
Divide by .
Rewrite the problem using and .
Simplify.
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Multiply and .
Move to the left of .
Since is constant with respect to , move out of the integral.
Simplify.
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Multiply and .
Multiply by .
The integral of with respect to is .
Since is constant with respect to , move out of the integral.
Since is constant with respect to , move out of the integral.
Let . Then . Rewrite using and .
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Let . Find .
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Differentiate .
By the Sum Rule, the derivative of with respect to is .
Differentiate using the Power Rule which states that is where .
Since is constant with respect to , the derivative of with respect to is .
Add and .
Rewrite the problem using and .
The integral of with respect to is .
Simplify.
Substitute back in for each integration substitution variable.
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Replace all occurrences of with .
Replace all occurrences of with .
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