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Math Help - Evaluate the indefinite integral

  1. #1
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    Evaluate the indefinite integral

    I can't seem to figure out how to integrate

    2x
    ---- dx ?
    x-4

    I tried U substitution for both 2x and x-4 but to no avail
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  2. #2
    Senior Member DeMath's Avatar
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    Quote Originally Posted by nottheface View Post
    I can't seem to figure out how to integrate

    2x
    ---- dx ?
    x-4

    I tried U substitution for both 2x and x-4 but to no avail
    Hint:

    \dfrac{2x}{x-4}=\dfrac{2x-8+8}{x-4}=\dfrac{2(x-4)+8}{x-4}=2+\dfrac{8}{x-4}
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  3. #3
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    Another way to do the same thing: substitute u= x- 4 as you did. Then x= u+ 4 so 2x= 2u+ 8. du= dx and the integral becomes \int \frac{2u+ 8}{u}du= \int \left(2+ \frac{8}{u}\right) du
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