# Calculus Examples

Divide by .
Split the single integral into multiple integrals.
Since is constant with respect to , move out of the integral.
Factor the numerator and denominator of .
Rewrite as .
Since both terms are perfect cubes, factor using the difference of cubes formula, where and .
Simplify.
Multiply by .
One to any power is one.
Write the fraction using partial fraction decomposition.
Simplify.
Split the single integral into multiple integrals.
Remove unnecessary parentheses.
Since is constant with respect to , move out of the integral.
Let . Then . Rewrite using and .
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.
Remove parentheses.
Let . Then , so . Rewrite using and .
The integral of with respect to is .
Simplify.
Write as a fraction with denominator .
Multiply and .
Replace all occurrences of with .
Replace all occurrences of with .
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 .
Combine.
Multiply by .
Combine the numerators over the common denominator.
Simplify the numerator.
Move to the left of the expression .
Multiply by .
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 .
Combine.
Multiply by .
Combine the numerators over the common denominator.
Simplify the numerator.
Simplify .
Reorder and .
Simplify by moving inside the logarithm.
Multiply the exponents in .
Apply the power rule and multiply exponents, .
Cancel the common factor of .
Write as a fraction with denominator .
Factor out the greatest common factor .
Cancel the common factor.
Rewrite the expression.
Simplify.
Multiply and .
Divide by .
Simplify by moving inside the logarithm.
Rewrite the expression using the negative exponent rule .
Use the product property of logarithms, .
Simplify the log argument.
Write as a fraction with denominator .
Multiply and .
Reorder terms.