Question

How do I find the antiderivative of `f(x)=(5x^2) / (x^2 + 1)`?

Answer 1

You start by manipulating your function:
`f(x)=(5x^2)/(x^2+1)==5-5/(x^2+1)`

Now you can integrate:

`intf(x)dx=int(5-5/(x^2+1))dx=`
`=int5dx-int5/(x^2+1)dx=`

`=5x-5arctan(x)+c`