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Math Help - integral with e^x (substitution rule)

  1. #1
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    Red face integral with e^x (substitution rule)

    I solved the following indefinite integral but my calculator tells me a different answer than what I got.

    integral from ln4 to ln7 of e^x/(e^x-3)^2 dx

    I set u=e^x -3 and du=e^x dx my new integral read:
    integral from ln4 to ln7 of 1/u^2 du. My answer was u^-1 from ln4 to ln7 (1/e^x -3) I plugged in bounds and I got a value of -3/4.

    I can't find my mistake
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by swimmergirl View Post
    I solved the following indefinite integral but my calculator tells me a different answer than what I got.

    integral from ln4 to ln7 of e^x/(e^x-3)^2 dx

    I set u=e^x -3 and du=e^x dx my new integral read:
    integral from ln4 to ln7 of 1/u^2 du. My answer was u^-1 from ln4 to ln7 (1/e^x -3) I plugged in bounds and I got a value of -3/4.

    I can't find my mistake
    \int u^{-2}~du = {\color{red}-}u^{-1} + C
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