If (e^x)(sin3x)=Im ((e^x)(e^i3x))

integrate (e^x)(sin3x)

I get the answer(e^x)(cos3x-3sin3x) +C

My book gets the answer
(1/10)(e^x)(sin3x-3cos3x)+C
Can any explain which answer is right and why

Integral of e^(1+3i)x =

e^(1+3i)x /(1+3i) + c

Multiplying numerator and denominator by (1-3i) gives:

(1-3i)e^(1+3i)x/10

If you take the imaginary part you get the answer given in your book.

I am such an idiot for some reason I differentiated not integrated. Thanks so much