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Thread: Calculating the integral of a logarithmic function

  1. #1
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    Question Calculating the integral of a logarithmic function

    Hi guys,

    I have a problem trying to calculate the integral of this function:
     ln(h/z)
    This function is part of a physics problem, where h is a constant that determines the height.
    In the solutions, the integral is supposed to be  z ln(h/z) + z

    I know that the integral of ln(x) is x(ln(x)-1)
    What I got from calculating this function with the formula is:
     (-z ln(z)+z)/h
    I don't understand how to get to the solution  z ln(h1/z) + z
    Last edited by jojojo; Jun 6th 2017 at 01:17 AM.
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  2. #2
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    Re: Calculating the integral of a logarithmic function

    Hey jojojo.

    Hint - Try using integration by parts and isolate the constant with log laws.
    Thanks from jojojo
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  3. #3
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    Re: Calculating the integral of a logarithmic function

    Hey chiro, thanks for the hint. I tried doing that and it keeps getting messier. I have  hln(z)^2/Z .
    If you could tell me exactly what the steps are it would be great
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  4. #4
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    Re: Calculating the integral of a logarithmic function

    The simplest thing to do is to write \int ln(h/z)dz= \int ln(h)- ln(z) dz= z ln(y)- \int ln(z)dz.
    (That's the "log law" chiro is referring to.)

    That last integral is given in every Calculus text. Use integration by parts taking u= ln(z) and dv= dz.
    Thanks from jojojo
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  5. #5
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    Re: Calculating the integral of a logarithmic function

    I got it! Thank you so much it was so helpful
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