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Need Help Doing Integation by Parts

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  1. Feb 10, 2015 #1
    • Member warned about not showing an attempt
    1. The problem statement, all variables and given/known data
    Find the integral of z^3 e^z^2

    2. Relevant equations
    The integration by part formula

    3. The attempt at a solution
    I have no idea what to do, I'm just turning in circles
     
  2. jcsd
  3. Feb 10, 2015 #2

    SteamKing

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    Well, show us your latest turn around the circle in working out this integral. You may have overlooked something simple.
     
  4. Feb 10, 2015 #3
    Some integration by parts problems require using it a few times :D
     
  5. Feb 10, 2015 #4
    Here's my attempt that doesn't work... 1423589596666-962910281.jpg
     
  6. Feb 10, 2015 #5
    And another one 1423589706639-37914461.jpg
     
  7. Feb 10, 2015 #6
    If dv = e^(z^2), v is not e^(z^2)/z^2. You cannot simply reverse the chain rule going backwards because if you take the derivative of that, you'll get something different from the quotient rule.

    So when doing parts and one way doesn't work, what to do next?
     
  8. Feb 10, 2015 #7
    Wel, normally you try going the other way around, but it still doesn't work as shown in the first picture...
     
  9. Feb 10, 2015 #8

    SteamKing

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    If you are going to make dv = ez2 dz, then u = z3.

    However, it is easier to integrate ez2 dz if you analyze it first using a u-substitution for z2.

    Hint: you may not want to make u = z3 for this integral.
     
  10. Feb 10, 2015 #9
    Oh ok! I think I get now! Thank you to everybody on this thread for your help! I'll try that!
     
  11. Feb 10, 2015 #10

    Mark44

    Staff: Mentor

    And when you post again, @Airp, be sure to include at least some of what you have tried.
     
  12. Feb 10, 2015 #11
    This is what I finally did! Thank you again! 14235934962312124757711.jpg
     
  13. Feb 10, 2015 #12

    Mark44

    Staff: Mentor

    Also, it's better to include your work right here in the form rather than an image of it. Everything you wrote on paper can be done right here using LaTeX, which isn't really that difficult.

    Here is one of the lines from the last image you posted.
    $$\frac{z^2e^{z^2}}{2} - \int \frac{2ze^{z^2}dz}{2}$$

    The LaTeX script before it is rendered looks like this:
    $ $\frac{z^2e^{z^2}}{2} - \int \frac{2ze^{z^2}dz}{2}$ $
    Note that I put an extra space between each pair of $ symbols. That prevents the browser from rendering the script.

    Fractions: \frac{}{}, with numerator in first pair of braces, and denominator in the second pair
    Exponents: Use ^{} after the thing being raised to the power. If the exponent is a single character, the braces aren't needed.
    Integrals (indefinite): \int
    Integrals (definite): \int_a^b --Here a is the lower limit and b is the upper limit

    More info: https://www.physicsforums.com/help/latexhelp/
     
  14. Feb 10, 2015 #13
    Whoa didn't know that thanks!
     
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