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Homework Help: Integration problem, please help

  1. Jun 22, 2010 #1
    Could you please confirm my answers as correct or incorrect, if incorrect please point out errors and assist in correcting errors.

    Thanks in advance


    1. The problem statement, all variables and given/known data

    Intergrate the following functions with respect to x using recognition, substitution or intergration by parts:

    x^2(2+x^3)^4

    x(x^2+2)^5

    xcosx


    3. The attempt at a solution

    1)
    integral(x^2(2+x^3)^4)
    put (2+x^3) =x
    thus
    3x^2dx = dz
    or
    x^2dx = dz/3

    the integral becomes
    integral(z^4dz)/3
    = z^5/15
    =(2+x^3)^5/15 + c

    2)
    integral(x(x^2+2)^5)
    put x^2+2=z
    or
    2xdx = dz
    thus
    xdx = dz/2
    integral(z^5/2)dz
    = z^6/12+c
    =(x^2+2)^6/12 + c

    3) integral(xcosx)
    x(sinx) - integral(sinx)
    = -xsinx+cosx +c
     
  2. jcsd
  3. Jun 22, 2010 #2
    You can test your final result using either mathematical software like Maple, Mathematica and or google Wolfram integrator it using the integration engine of Mathematica.
     
  4. Jun 22, 2010 #3
    while I appreciate your reply, I would rather ask here to see if the steps taken are correct as well as the final result!

    Thanks
     
  5. Jun 22, 2010 #4
    I think you mean (2+x^3) = z

    Last one is definitely correct and, albeit a little tedious, the other 2 can easily be confirmed by expanding the brackets and integrating directly.
     
  6. Jun 22, 2010 #5
    Okay, but as you know which I learned yesterday its forbidden to reply with re-calculations to you.

    2) and 3) are correct but you need to redo 1) using integration by parts and integration by substitution!
     
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