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Math Help - int by parts(almost finished)

  1. #1
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    int by parts(almost finished)

    original problem:
    \int e^xcos(2x)dx

    I've used int. by parts twice so far and I have this:
    e^xcos(2x) + 2e^xsin(2x) - 4\int e^xcos(2x)dx

    Where do I go from here? I'm lost...
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  2. #2
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    Quote Originally Posted by saiyanmx89 View Post
    original problem:
    \int e^xcos(2x)dx

    I've used int. by parts twice so far and I have this:
    e^xcos(2x) + 2e^xsin(2x) - 4\int e^xcos(2x)dx

    Where do I go from here? I'm lost...
    \int e^xcos(2x)dx= e^xcos(2x) + 2e^xsin(2x) - 4\int e^xcos(2x)dx

    so

    \int 5e^xcos(2x)dx= e^xcos(2x) + 2e^xsin(2x)

    so

    \int e^xcos(2x)dx= \frac{e^xcos(2x) + 2e^xsin(2x)}{5}
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  3. #3
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    where did you get 5e^x from? that's where I get lost....
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  4. #4
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    \textcolor{red}{\int e^xcos(2x)dx}= e^xcos(2x) + 2e^xsin(2x) \textcolor{red}{- 4\int e^xcos(2x)dx}

    note the like terms ... now move \textcolor{red}{- 4\int e^xcos(2x)dx} to the left side and combine.
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