What is the algorithm for antiderivatives???
I know $\displaystyle x^n dy/dx = n * x^ {n-1}$ is the way you do the derivative, but how to you get the antiderivative...
I just need the method... It's just bothering me.... lol
Let's take your example:
$\displaystyle \int x^n~dx = \frac{1}{n + 1} \cdot x^{n + 1} + C$
because
$\displaystyle \frac{d}{dx} \left ( \frac{1}{n + 1} \cdot x^{n + 1} + C \right ) = x^n$
Basically what rules there are for antiderivatives come from the derivative shortcut formulas. However they aren't always as easy as the derivative rules. You will eventually get to integration by parts, which is the reverse of the product rule for derivatives. It isn't all that hard a method, but it is much more difficult that the product rule.
-Dan