I can't figure out why when integrating
you get
and not
Why does it become a fraction?
You shouldn't get either of those answers you've listed...
If then it's antiderivative is .
In other words, you add 1 to your power, and then divide by the new power.
In your case you have .
Add 1 to the power and you get .
Divide by your new power and you get
.
So your antiderivative is where C is a constant.