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# differential equation stuff watch

1. Can anyone integrate: sin(theta) * e^(2k*theta) with respect to theta (k is a constant

I got: ((e^(2k*theta))/(4k^2-1))(2ksin(theta)-cos(theta)) + c

when i used integration by parts, however the answer book says that it should be (4k^2 +1) where I've got (4k^2-1)

2. Let I denote the integral. Then integrating by parts twice yields:
I = -e^(2kx) cos(x) + 2k e^(2kx) sin(x) - 4k^2 I
=> (4k^2 + 1) I = e^(2kx) (2k sin(x) - cos(x)) + C
3. I dont get the same thing as you by integrating by parts twice, bugger, I know I've made a mistake but can work out where

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Updated: February 5, 2006
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