I have been asking this question, but I never seem to get a direct answer.... Is there any type of formula to find an antiderivative?
it depends , but alot of the time when you have a variable with a power, you just add 1 to the power and divide all of that by what you get for instance :
$\displaystyle \int x^{2}$
becomes
$\displaystyle \frac{x^{2+1}}{3}$
$\displaystyle \frac{x^{3}}{3}$
finding an anti derivative is based on these steps:
1) Known formula,which gives an immediate integral
now,when things get serious,you have to use at least one of those:
2)U substitution
3)Integration by parts
4)Partial Fractions
5)Trig substitution
6)complete the square
that`s about it i think
You have to see it as $\displaystyle 2x^{-2}$
if you integrate, your 2 goes in front because it's a constant and you just have to apply the trick :
$\displaystyle 2\int x^{-2}$
which is
$\displaystyle 2(\frac {x^{-1}}{-1})$
=
$\displaystyle \frac{-2}{x}$