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

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

Please can you tell me what I'm missing