Hi, I have been getting a different answer to the answer in my sheet, but

I could not tell my error, when I checked online, different integral calculators gave different answers.

Question:

Integrate x^3/(1+x^2)

My answer:

Rearrange to 1/2[x^2 * 2x/(1+x^2)]

Let u = x^2 + 1, so dx = 1/2x, and x^2 = u -1

so $\displaystyle 1/2\int (u-1)/u \,du$

$\displaystyle = 1/2\int 1 \,du - 1/2\int 1/u \,du $

$\displaystyle = u/2 - 1/2 \ln u + c$

$\displaystyle = (x^2)/2 + 1/2 -1/2*\ln (x^2 +1) +c$

However the answer sheet, and most of the online calculators say the answer is:

$\displaystyle = (x^2)/2 -1/2*\ln (x^2 +1) +c$

Please can you tell me what I'm missing