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Math Help - Getting different answers with integrating x^3/(1+x^2)

  1. #1
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    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)

    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 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
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  2. #2
    MHF Contributor Calculus26's Avatar
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    you're not wrong

    The extra 1/2 you have can be incorporated into the integration constant c.
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  3. #3
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    Argh, thanks, can't believe I missed that.
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  4. #4
    MHF Contributor Calculus26's Avatar
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    I've been doing Calculus for 30 years --do you know how many Aargh!!

    moments I've had?
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