Kainui
  • Kainui
I'm having trouble figuring out how to find the integral of \[\int\limits_{}^{}e^{5x}\cos(4x)dx\] any ideas how to solve it?
Mathematics
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
integrate by parts? gimme a sec to think about it
Kainui
  • Kainui
Yeah actually I think that'll work. I started doing it but ended up with the same integral with sine instead of cosine. But once I integrate by parts again I'll have the same term and I'll cancel it out I think.
anonymous
  • anonymous
Oh i know its one of those stupid ones where you actually have to do it twice, then divide, ill do it though LOL

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Kainui
  • Kainui
Nah, I got it thanks though haha.
anonymous
  • anonymous
u=e^5x dv = cos(4x) du = 5e^5x v = sin(4x)/4 uv - integral (vdu (e^5x)(sin(4x)/4) - integral (sin(4x)/4)(5e^5x) so integral (sin(4x)/4)(5e^5x) do parts again u = 5e^5x dv = sin4x/4 du = 25e^5x v = -cos(4x)/16 uv-int vdu (5e^5x)(-cos(4x)/16) - integral (-cos(4x)/16)(25e^5x) soo from the first integral you add this in (e^5x)(sin(4x)/4) - (5e^5x)(-cos(4x)/16) +(16*25) integral (cos(4x))(e^5x) = integral of (e^5x)(cos4x) then do algebra so add the integral on the left to the right and figure out what to do with the extra stuff so like i think the answer is (e^5x)(sin(4x)/4) - (5e^5x)(-cos(4x)/16) /2 or something i dont know wolframalpha it but i know you have to do 2 integration by parts then algebra
anonymous
  • anonymous
i know i made a mistake somewhere, i just dont care to fix it, since im typing it and its not on paper LOL

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