find the intergral

so i did long divisoin, this will look messy but this is what it simplified to

i double checked with the tutor about this answer but wolf ram gets somthing different.

5x^2 + 3x - 5 + ((8x-1)/(x^2 + 1))

so the intergral of that

ended up looking liiike

(5x^3)/3 - 3x^2 / 2 - 5x + 4log(x^2 + 2) - arctan x

is that right

wolf ram go, instead of 8x- 1 as the remainder 8x - 11

and i got 8x - 11 the first time ,but i made a mistake in the calculation