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Math Help - Simple exponential integral

  1. #1
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    Simple exponential integral

    Solve the following integral (showing the steps):

    \int {t{e^t}dt}
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  2. #2
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    Quote Originally Posted by baseballman View Post
    Solve the following integral (showing the steps):

    \int {t{e^t}dt}
    See - Wolfram|Alpha Click on Show steps.
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  3. #3
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    That's good. But I'm looking for a solution in which integration by parts is NOT used.
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  4. #4
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    Quote Originally Posted by baseballman View Post
    That's good. But I'm looking for a solution in which integration by parts is NOT used.
    there's no scape dear.
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  5. #5
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    Quote Originally Posted by baseballman View Post
    That's good. But I'm looking for a solution in which integration by parts is NOT used.
    Consider y = t \sin t.

    Then \frac{dy}{dt} = \sin t + t \cos t.

    Now integrate both sides:

    y = \int \sin t + t \cos t \, dt = \int \sin t \, dt + \int t \cos t \, dt .

    Substitute y = t \sin t:

    t \sin t = \int \sin t \, dt + \int t \cos t \, dt .

    Re-arrange to make the required integral the subject:

     \int t \cos t \, dt = t \sin t - \int \sin t \, dt = t \sin t + \cos t + C.
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