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Math Help - Integrat with substitution

  1. #1
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    Integrat with substitution

    I need to find the Integral with respect to x of (e^(-.02x))/(8-e^(-.02x))

    I use u=8-e^(-.02x)

    and find that dx= du/.02e^(-.02x) or dx=50du/e^(-.02x)

    when i substitute that back into the integral, the integral reduces to:

    integral of (50/u)du which equals 50ln(abs(u))+ c

    after substituting back in for u I finished with

    50ln(abs(8-e^(-.02x)))

    Where did I mess up?
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  2. #2
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    e^(i*pi)'s Avatar
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    Re: Integrat with substitution

    Your maths looks fine, just don't forget your +C on the final answer

    50\ln\left(|8-e^{-.02x}|\right) + C

    You can simplify using log laws to either:

    50\ln \left(k\left(|8-e^{-.02x}|\right)\right) where k = \ln(C)

    \ln \left(|8-e^{-.02x}|\right)^{50} + C


    Personally I'd pick the first answer
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  3. #3
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    Re: Integrat with substitution

    Thanks, I looked back through it and I thought it was ok... Thanks for reminding me about the constant!

    Also, I'm new to the forum, I can't copy and past microsoft equation editor into the post, how do you type your equations? Does it automatically format them if you use the proper code?
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  4. #4
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    e^(i*pi)'s Avatar
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    Re: Integrat with substitution

    [tex]CODE[/tex]. Hence my final answer is: [TEX]50\ln\left(|8-e^{-.02x}|\right) + C[/TEX]


    The codes for various LaTeX is given inthis thread (although the images don't work so it's either google or the PDF)
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  5. #5
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    Re: Integrat with substitution

    Quote Originally Posted by wintermath View Post
    I'm new to the forum, I can't copy and past microsoft equation editor into the post, how do you type your equations? Does it automatically format them if you use the proper code?
    Here is the code that e^{i\pi} used.

    [TEX]50\ln\left(|8-e^{-.02x}|\right) + C[/TEX]

    [tex]50\ln \left(k\left(|8-e^{-.02x}|\right)\right) [/TEX] where [TEX]k = \ln(C)[/TEX]

    [tex]\ln \left(|8-e^{-.02x}|\right)^{50} + C[/TEX]
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  6. #6
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    Re: Integrat with substitution

    Quote Originally Posted by e^(i*pi)
    although the images don't work so it's either google or the PDF
    Actually, I believe the images are working again, thanks to our admins.

    Test:

    Integrat with substitution-calculating-grid-cells.jpg
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  7. #7
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    Re: Integrat with substitution

    Quote Originally Posted by Ackbeet View Post
    Actually, I believe the images are working again, thanks to our admins.

    Test:

    Click image for larger version. 

Name:	Calculating Grid Cells.JPG 
Views:	9 
Size:	27.6 KB 
ID:	21720
    That one works. For now I'd recommend anyone who wishes to open an image does so in a new tab since for me it opens in a new tab but the back button is disabled
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