Calculus Examples

Factor the numerator and denominator of .
Write as .
Replace each of the partial fraction coefficients with the actual values.
Since integration is linear, the integral of with respect to is .
Since is constant with respect to , the integral of with respect to is .
The integral of with respect to is .
Since is constant with respect to , the integral of with respect to is .
Let . Then , so . Rewrite using and .
Combine fractions.
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Multiply and to get .
Simplify the expression.
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Move to the left of the expression .
Multiply by to get .
Since is constant with respect to , the integral of with respect to is .
Combine fractions.
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Multiply and to get .
Multiply by to get .
The integral of with respect to is .
Since is constant with respect to , the integral of with respect to is .
Since is constant with respect to , the integral of with respect to is .
Remove parentheses around .
Let . Then . Rewrite using and .
The integral of with respect to is .
Simplify the answer.
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Simplify.
Write as a fraction with denominator .
Multiply and to get .
Replace all occurrences of with .
Replace all occurrences of with .
Use the product property of logarithms, .
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Combine.
Multiply by to get .
Combine the numerators over the common denominator.
Simplify each term.
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Simplify the numerator.
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Simplify .
Apply the product rule to .
Multiply the exponents in .
Multiply the exponents in .
Simplify.
Use the quotient property of logarithms, .
Rewrite as a product.
Simplify by moving inside the logarithm.
Apply the product rule to .
Simplify the numerator.
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Apply the product rule to .
Multiply the exponents in .
Reorder terms.
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