Integrals! please help!

integral of (e^(3x)sin(4x))

please show all steps :)

Integrate by parts...twice

int(u * dv) = u * v - int(v * du)

u = e^(3x)
du = 3 * e^(3x) * dx
dv = sin(4x) * dx
v = (-1/4) * cos(4x)

int(e^(3x) * sin(4x) * dx) = (-1/4) * e^(3x) * cos(4x) - int((-1/4) * 3 * e^(3x) * cos(4x) * dx)
int(e^(3x) * sin(4x) * dx) = (-1/4) * e^(3x) * cos(4x) + (3/4) * int(e^(3x) * cos(4x) * dx)

u = e^(3x)
du = 3 * e^(3x) * dx
dv = cos(4x) * dx
v = (1/4) * sin(4x)

int(e^(3x) * sin(4x) * dx) = (-1/4) * e^(3x) * cos(4x) + (3/4) * ((1/4) * e^(3x) * sin(4x) - int((3/4) * e^(3x) * sin(4x) * dx))

Let int(e^(3x) * sin(4x) * dx) = t

t = (-1/4) * e^(3x) * cos(4x) + (3/16) * e^(3x) * sin(4x) - (9/16) * t

Solve for t

(25/16) * t = (1/16) * e^(3x) * (3 * sin(4x) - 4 * cos(4x))
25 * t = e^(3x) * (3 * sin(4x) - 4 * cos(4x))
t = (1/25) * e^(3x) * (3 * sin(4x) - 4 * cos(4x))

Add in the constant of integration

t = (1/25) * e^(3x) * (3 * sin(4x) - 4 * cos(4x)) + C

There you go,

http://www3.wolframalpha.com/Calculate/MSP/MSP49441a367bb839cfbd1b000010462517h6h50gd5?MSPStoreType=image/gif&s=37&w=550&h=174