Integtration...?

Question

Any help with this question this would be much appreciated - I appear to be making it more difficult than it should be! Thanks!

Integrate:

x^2/x+1

Answer 1

x^2/(x + 1) = (x^2 + 2x + 1)/(x + 1) - (2x +1)/(x + 1) = (x + 1)^2 / (x + 1) - (2x + 2)/(x + 1) + 1/(x + 1) =
= (x + 1) - 2 + 1/(x + 1) = x - 1 + 1/(x + 1)

int x^2/(x + 1) dx = int x - 1 + 1/(x + 1) dx =
= (x^2)/2 - x + ln|x + 1| + c

Answer 2

hi, it's rather difficult to type out the mathematical symbols, but i hope that you could understand.

Firstly, it is an improper fraction, thus, you will have to do long division.

After which, you will get (x-1)+ 1/(x+1)
Now, you can start integrating.

Integrate (x) dx - Integrate (1) dx + Integrate 1/(x+1)
= 1 - x + ln |x+1| + c

Hope this helps yea.