Solving integrals?

Question

Integral of [(e^4x)(sin3x)]dx
How would you solve this?

Answer 1

ilate method

Answer 2

The standard way is to use integration by parts twice.

Answer 3

Y= ∫ [(e^4x)(sin3x)]dx;
♠ let u(x)= cos(3x)+j*sin(3x) =exp(j*3x); then
z(x)= exp(4x)*u(x)= exp(4x)*exp(j*3x) =exp(4x+j*3x);
♣ Z= ∫dx*z(x)= ∫dx*exp(4x+j*3x) =(1/(4+3j)) exp(4x+j*3x) =
= exp(4x)*(cos3x +j*sin3x)* (4-3j)/(4^2 +3^2);
♦ Y=IM(Z) = 0.04*exp(4x)*(-3cos3x +4sin3x);