# Calculus Examples

Divide by to get .
Since integration is linear, the integral of with respect to is .
Since is constant with respect to , the integral of with respect to is .
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 to get .
One to any power is one.
Write as .
Simplify.
Since integration is linear, the integral of with respect to is .
Remove parentheses.
Since is constant with respect to , the integral of with respect to is .
Let . Then . Rewrite using and .
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 , so . Rewrite using and .
The integral of with respect to is .
Simplify.
Write as a fraction with denominator .
Multiply and to get .
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 to get .
Combine the numerators over the common denominator.
Simplify each term.
Simplify the numerator.
Move to the left of the expression .
Multiply by to get .
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 to get .
Combine the numerators over the common denominator.
Simplify each term.
Simplify the numerator.
Simplify .
Multiply the exponents in .
Simplify by moving inside the logarithm.
Remove the negative exponent by rewriting as .
Use the product property of logarithms, .
Simplify the log argument.
Reorder terms.