Integrating any power of
Recall from differential calculus that the derivative of a function like
and then you decrease the exponent by one:
Since integration is essentially the opposite of differentiation, integrating powers of
1. Bring the exponent to the front and multiply it by
2. Decrease the exponent by one.
Now, let's think about how to do this in reverse (because integration is reverse differentiation). We need go backwards, starting at step 2. And since we're reversing the process, instead of decreasing the exponent by
1. Increase the power by
2. Divide by the new power.
Therefore, if we need to integrate
And divide by the new power:
All that's left is to add a constant of integration