Have a look at this.
use integration by arts to solve the following 5x cos (4x) dx so I have u = 5x, du = 5, v=1/4sin(4x) and dv =cos (4x) now my first step getting the formula correct and I chose uv-integral vdu step one was (5x) 1/4sin(4x) - integreal 1/4 sin(4x) (5) which lead to 5x/4 sin(4x) - 5/4 integral sin(4x) dx then step three was 5x/4 sin(4x) - 5/4 (-1/4 cos(4x)) +c which lead to 5x/4 sin4x +5/16cos4x+c and a I have two final answers not sure which is correct answer one 5/16(cos(4x)+4xsin(4x))+c or answer two 5(4xsin(4x)+cos4x)/16 +c if someone can clear up the confusion that would be great and also see if my steps to the final abswer are correct please......