1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    Math_QED

    User Avatar
    Homework Helper

    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

    Math_QED

    User Avatar
    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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Show Wolfram Alpha's answer is equivalent to my answer.
  1. Is my answer correct? (Replies: 9)

Loading...