# Getting different answers with integrating x^3/(1+x^2)

• Apr 12th 2009, 03:35 AM
Doran
Getting different answers with integrating x^3/(1+x^2)
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)

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

$= 1/2\int 1 \,du - 1/2\int 1/u \,du$
$= u/2 - 1/2 \ln u + c$
$= (x^2)/2 + 1/2 -1/2*\ln (x^2 +1) +c$

However the answer sheet, and most of the online calculators say the answer is:
$= (x^2)/2 -1/2*\ln (x^2 +1) +c$

Please can you tell me what I'm missing
• Apr 12th 2009, 03:50 AM
Calculus26
you're not wrong
The extra 1/2 you have can be incorporated into the integration constant c.
• Apr 12th 2009, 04:44 AM
Doran
Argh, thanks, can't believe I missed that.
• Apr 12th 2009, 05:30 AM
Calculus26
I've been doing Calculus for 30 years --do you know how many Aargh!!