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Integrate e^x cos(x)dx, how to do this?

  1. Sep 24, 2004 #1
    Some one plz show me how to do this problem below
    Integral of e^x cos(x) dx
    how to I integrate that?
  2. jcsd
  3. Sep 24, 2004 #2


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    Try Integration by parts

    [tex] \int u dv = uv -\int v du [/tex]

    try using [tex] u = e^x [/tex] and [tex] dv = \cos (x) dx[/tex]
    Last edited: Sep 24, 2004
  4. Sep 24, 2004 #3


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    Your book will have this example (or one nearly identical to it) perfored step by step.
  5. Sep 24, 2004 #4
    [tex]u = e^x \ dv = cos(x) dx[/tex]
    [tex]du = e^x dx \ v = sin(x)[/tex]

    [tex]\int e^x cos(x) dx = e^x sin(x) - \int sin(x) e^x dx[/tex]

    [tex]u = e^x \ dv = sin(x) dx [/tex]
    [tex]du = e^x dx \ v = -cos(x) dx[/tex]
    [tex] \int e^x cos(x) dx = e^x sin(x) - (-e^x cos(x) + \int e^x cos(x) dx)[/tex]
    [tex] = e^x sin(x) + e^x cos(x) - \int e^x cos(x) dx [/tex]
    [tex]\int e^x cos(x) dx + \int e^x cos(x) = e^x (sin(x) + cos(x))[/tex]
    [tex]2 \int e^x cos(x) dx = e^x(sin(x) + cos(x))[/tex]
    [tex]\int e^x cos(x) dx = 1/2 e^x (sin(x) + cos(x))[/tex] there you go intergration by parts follow
    [tex]u v - \int v du[/tex]
    Last edited: Sep 24, 2004
  6. Sep 24, 2004 #5
    thanks so much
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