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Homework Help: Show Wolfram Alpha's answer is equivalent to my answer.

  1. Jan 31, 2017 #1
    1. The problem statement, all variables and given/known data
    Integrate x2(2+x3)4dx.
    Show that Wolfram Alpha's answer is equivalent to your answer.

    2. Relevant equations
    No equations besides knowing that the integral of xpower is 1/power+1 * xpower + 1

    3. The attempt at a solution
    So I have the answer to the integral by hand as (2+x3)5)/15 + C.
    When I go to Wolfram Alpha it gives x15/15 + 2x12/3 + 8x9/3 + 16x6/3 + 16x3/3 + C

    I really truly have no idea how these two are the same. I tried multiple types of manipulation to my answer, but I am completely lost on where basically every factor comes from besides the first x15/15.

    Any help will be appreciated!!!
  2. jcsd
  3. Jan 31, 2017 #2


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    Your answer is correct.

    They expanded ##(2+x^3)^5## as ##x^{15} + 10 x^{12} + 40 x^9 + 80 x^6 + 80 x^3 + 32## (this can be found using Newton's binomium). Thus, after dividing both sides with 15, we get:

    ##\frac{(2+x^3)^5}{15} = x^{15} /15 + 2x^{12}/3 + 8x^9/3 + 16x^6/3 + 16x^3/3 + 32/15##

    However, the constant in the primitive function does not matter (as we write ##+ c## anyway), so we can drop the ##32/15## safely.
  4. Jan 31, 2017 #3
    Ok, So they simply expanded the numerator using a thing called Newton's binomium? I will do some research on that, but I do not think we have ever learned what Newton's Binomium is. Thanks for explaining how this worked. I was completely lost on how it worked, but now it seemed relatively simple.
  5. Jan 31, 2017 #4


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    Homework Helper

  6. Jan 31, 2017 #5
    OHHHHHHH that is what that is called. Ok, so I have done that before. Totally did not think of that as a solution. Thanks for the link, totally forgot that I could use that method.
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