Write as a function.
The function can be found by finding the indefinite integral of the derivative .
Set up the integral to solve.
Set the argument in the absolute value equal to to find the potential values to split the solution at.
Simplify the answer.
Create intervals around the solutions to find where is positive and negative.
Substitute a value from each interval into to figure out where the expression is positive or negative.
Integrate the argument of the absolute value.
Set up the integral with the argument of the absolute value.
By the Power Rule, the integral of with respect to is .
On the intervals where the argument is negative, multiply the solution of the integral by .
Combine and .
The answer is the antiderivative of the function .
Find the Anti-Derivative |x|