Now that you can take derivatives of polynomial
functions, we are going to reverse the process. It is
called finding the antiderivative (similar to the
expression for undoing a logarithm by finding an
This section gives only an intuitive idea. We will
develop some rules in the next section. Finding an
antiderivative here is a trial/guess process. We will take
the derivative of your guess to see if you guessed right.
In finding derivatives, the exponent was decreased by 1 so increasing the exponent by 1 should help reverse the process.
Find the antiderivative of 4 (5x +3)³
This is not quite the same. The guess gave 20, we only wanted 4.
Lets try 1/5 of our guess this time.