# Integral using Euler's formula.

by cragar
Tags: euler, formula, integral
 P: 2,453 If I have $\int e^{2x}sin(x)sin(2x)$ And then I use Eulers formula to substitute in for the sine terms. So I have $\int e^{2x}e^{ix}e^{2ix}$ then I combine everything so i get $e^{(2+3i)x}$ so then we integrate the exponential, so we divide by 2+3i and then i multiply by the complex conjugate. now since sine is the imaginary part of his formula I took the imaginary part when I back substituted for e^(3i) but I didn't get the correct answer doing this, so am i not using Eulers formula correctly?
 P: 44 e^i3x = sin3x+isin2x , so the imaginary part is different from i(sinxsin2x)
 P: 2,453 why does e^i3x = sin3x+isin2x , i guess im not seeing it off hand I probably should look at it more and try to manipulate it more.
P: 44

## Integral using Euler's formula.

sry typos , its sin3x
 P: 2,453 how come one part is not cos(3x)
 P: 44 another typos , sry =='
 P: 2,453 But we could get it in the form of $sin(x)e^{2ix}=isin(2x)sin(x)+cos(2x)sin(x)$ Do we need to get an expression where we have just exponentials on the left hand side and then isin(x)sin(2x)+cos(2x)cos(x)
 P: 44 but then ur integral cant become e^i3x now , can it
 P: 2,453 ok, im not sure exactly what you mean, How do you recommend I approach the problem.
 P: 44 sina*sinb = -0.5[cos(a+b)+cos(a-b)] , then u have 2 solvable integrals