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Homework Help: Integration by parts

  1. Mar 22, 2012 #1
    knowing the standard form for integration by parts is
    ∫ f(x)g'(x) dx = f(x)g(x) - ∫f'(x)g(x) dx

    I have what is an innocuous looking part of an equation which I can't solve.

    the f(x) part in this case is;
    ln(5x) which is easy enough i.e. 1/x

    the second part 1/(x(2/3)) is the bit I can't solve.

    The standard I have for
    1/x is ln(x)+c
    & the standard I have for xn is (1/(n+1))xn+1+c

    But these don't solve this for me

    I have checked on WolframAlpha & NumberEmpire & they give the same answer
    3 cuberoot 3

    I have tried just this bit by itself & go t nowhere. Could someone help with how I should get 3 cuberoot 3, please. :confused:
  2. jcsd
  3. Mar 22, 2012 #2


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    1/x^(2/3)=x^(-2/3). So put n=(-2/3) into x^(n+1)/(n+1).
  4. Mar 22, 2012 #3
    I'm being thick here, but doesn't (n+1)/(n+1) = 1

    So x1 = x ?

    Last edited: Mar 22, 2012
  5. Mar 22, 2012 #4


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    Ok, I'll be a little clearer. I meant the formula you referred to [itex]\frac{x^{n+1}}{n+1}[/itex].
  6. Mar 22, 2012 #5


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    Yes, it is true that x1= x! However, the anti-derivative of x1 is x1+1/(1+1)= x2/2.

    I am surprised that you are being asked to use "integration by parts" but do not know how to integrate xn.
  7. Mar 22, 2012 #6
    I shall try to be more numerically erudite in future!

    I think that sometimes I have to ask stupid questions when I have come to the end of my tether & I can't see the wood for the trees.

    Practice makes perfect & asking stupid questions should embarrass me into remembering it properly.

    Prepare for more along the same lines in the future.
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