Posted by **Tom** on Saturday, January 20, 2007 at 10:51am.

given (e^x)sin3x = Im((e^x)(e^i3x)) Integrate (e^x)sin3x.dx

You can just take the imaginary part of the integral of ((e^x)(e^i3x))= e^([3i +1)x] which is IM(3i +1)e^(3ix + x)

= IM (3i +1)e^x*e^(3ix)

= IM {(3i +1)*e^x* [ cos (3x) + i sin (3x)]

= e^x* sin (3x)+ 3 e^x cos (3x)

Check my algebra. I don't guarantee it

I follow your working but my book says the answer is (1/10)e^x(sin3x - 3cos3x) + C

so is the book wrong or can I manipulate your answer in some way to get the same as the book

By the way Thanks for your fast response

I follow your working but my book says the answer is (1/10)e^x(sin3x - 3cos3x) + C

so is the book wrong or can I manipulate your answer in some way to get the same as the book

By the way Thanks for your fast response

I get e^x(cos3x-3sin3x)

so now there 3 possible answers

## Answer This Question

## Related Questions

- maths - If (e^x)(sin3x)=Im ((e^x)(e^i3x)) integrate (e^x)(sin3x) I get the ...
- Calculus - In the interval (0 is less than or equal to x which is less than or ...
- Calculus part 3 so sorry - y = e^2xsin3x Find the derivative. So I used the ...
- mathh - Let f(x)=x+2 Ix-3I and g(x)=3x-1 Find all solutions to the equation f(g(...
- Trigonometric - sin3x=(sinx)(3-asin^2x) Wow! is that arcsin^2(x) ??? are we ...
- calc bc (condensed - is the limit as x approaches 0 of sin3x over 3x equal to ...
- College Algrebra - How would you use synthetic division to find the quotient and...
- maths - whats the for this question if sin3x=cos6x,then x=_____
- maths - prove that cos3x+sin3x/cos x-sin x=1+2sin2x
- calculus - 1) Integrate Cos^n(x) dx 2) Integrate e^(ax)Sinbx dx 3) Integrate (...

More Related Questions