# maths

posted by .

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

## Similar Questions

1. ### Maths

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) + …
2. ### Calculus part 3 so sorry

y = e^2xsin3x Find the derivative. So I used the product rule and I got sin3x(e^2x)+cos^3x(e^2x). But the actual answer is sin3x(2e^2x)+cos^3x(3e^2x) Where the the 2 and 3 before the e come from?
3. ### maths

prove that cos3x+sin3x/cos x-sin x=1+2sin2x
4. ### math(advanced algebra&trigonometry)

the expression cos4x cos3x + sin4x sin3x is equivalent to which one of the following is the answer: 1) sinx 2) sin7x 3) cosx 4) cos7x
5. ### precalc

(cos3x)^4+(sin3x)^4=cos(g(x)) find g(x)
6. ### precalc

(cos3x)^4+(sin3x)^4=cos(g(x)) find g(x)
7. ### Calculus

In the interval (0 is less than or equal to x which is less than or equal to 5), the graphs of y=cos(2x) and y=sin(3x) intersect four times. Let A, B, C, and D be the x-coordinates of these points so that 0<A<B<C<D<5. …
8. ### Maths

Prove that: (sinx-2sin2x+sin3x)/(sinx+2sin2x+sin3x)= -tan^2 x/2.
9. ### maths

proof that (sinx+sin3x-2sin2x)/(sinx+sin3x+2sin2x)=-tan(x/2)
10. ### Maths

Prove By induction that sinx + sin3x + sin5x +.... Sin(2n-1) =sin^2(nx)/sin3x

More Similar Questions