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Having troubles integrating e^(2x)sin(x)

  1. Aug 1, 2004 #1
    Hi, I have to integrate this:

    \int e^{2x}sinx

    I've tried by parts, but [tex]e^{2x}[/tex] never goes away and [tex]sinx[/tex] just keeps going back and forth to [tex]cosx[/tex]. Is there some kind of substitution I should use? The original question was the differential:

    [tex](-e^xsinx+y)dx+dy = 0[/tex]

    and I'm trying to find the integration factor to solve for [tex]y[/tex], but I can't seem to figure out how to integrate it. Thanks!
  2. jcsd
  3. Aug 1, 2004 #2
    for your first question,
    proceed with the integration by parts ....
    label the original integral as I and continue
    at some stage, u will have,
    I = e^x something + something - I (or something like that)
    rearrange to find I.

    -- AI
  4. Aug 1, 2004 #3
    To clarify, keep integrating by parts untill you get your original integral. then move that integral to the other side of the equation and solve :D
  5. Aug 1, 2004 #4

    Use the ILATE rule which tells you which function to take as the first one. ILATE = Inverse Circular Function, Logarithmic Function, Algebraic Function, Trigonometric Function, Exponential Function (this is the order...the function appearing higher in the list should be taken as the first function).

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