Question

int e^5xsin3xdx =

Answer 1

∫ e^(5x) sin(3x) dx

=(i/2)∫ e^(5x) (e^(-3ix)-e^(3ix)) dx

=(i/2)∫ e^((5-3i)x)-e^((5+3i)x) dx

=(i/2)((5+3i)e^((5-3i)x)/34-(5-3i)e^((5+3i)x)/34) + C

= (5i/78)e^(5x)(e^(-3ix)-e^(3ix))+(-3/78)e^(5x)(e^(-3ix)+e^(3ix)) + C

= (5/34)e^(5x)sin(3x) - (3/34)e^(5x)cos(3x)

= e^(5x)(5sin(3x)-3cos(5x))/34