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Math Help - Integral and quick simplification problems

  1. #1
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    Integral and quick simplification problems

    Hi guys, I've been struggling with these two problems and was wondering if anyone could give me some help to get going in the right direction, thanks in advance

    the first problem is:

    Find the indefinite integral:


    i thought that the answer should be :
    plus C but that's not correct, I'm not sure how else to do this problem

    the second problem is:

    Write the expression as a logarithm of a single quantity:


    not sure how to get started on this one, I know the laws of logarithms, I'm mainly confused on what to do with the 1/2 and the 5
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  2. #2
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    Quote Originally Posted by jason0 View Post
    Hi guys, I've been struggling with these two problems and was wondering if anyone could give me some help to get going in the right direction, thanks in advance

    the first problem is:

    Find the indefinite integral:


    i thought that the answer should be :
    plus C but that's not correct, I'm not sure how else to do this problem

    the second problem is:

    Write the expression as a logarithm of a single quantity:


    not sure how to get started on this one, I know the laws of logarithms, I'm mainly confused on what to do with the 1/2 and the 5
    The integral can easily be written in the form \int\frac{f'(x)}{f(x)}dx=\ln(f(x)) +C. Do you see how to do this? The derivative of the denominator is 6e^{6x}.

    So you should write \int\frac{e^{6x}}{5+e^6x}dx=\frac{1}{6}\int\frac{6  e^{6x}}{5+e^{6x}}dx.

    Then use the formula to obtain \frac{1}{6}\ln(5+e^{6x}) +C
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  3. #3
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    Quote Originally Posted by adkinsjr View Post
    The integral can easily be written in the form \int\frac{f'(x)}{f(x)}dx=\ln(f(x)) +C. Do you see how to do this? The derivative of the denominator is 6e^{6x}.

    So you should write \int\frac{e^{6x}}{5+e^6x}dx=\frac{1}{6}\int\frac{6  e^{6x}}{5+e^{6x}}dx.

    Then use the formula to obtain \frac{1}{6}\ln(5+e^{6x}) +C
    got it, thanks so much
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