- #1
- 8
- 0
Integral of e^(2x)sin[3x]??
Integration by parts of: e^(2x)sin[3x]
result:e^2x(2sin3x-3cos3x)/13+C
can't get that result =(
Integration by parts of: e^(2x)sin[3x]
result:e^2x(2sin3x-3cos3x)/13+C
can't get that result =(
Excuse my ignorance (I'm only a highschool student), but how did you get fromdextercioby said:Here's a very elegant way
[tex] \int e^{2x}\sin 3x \ dx=\mbox{Im}\left(\int e^{(2+3i)x} \ dx\right)=\mbox{Im}\left(\frac{e^{2x+3ix}}{2+3i}\right)+C=...=\frac{2\sin 3x-3\cos 3x}{13}e^{2x}+C [/tex]