Question

integrate∫5x sin(6x) dx

Answer 1

let u = 5x → du = 5 dx
let dv = sin(6x) dx → v = (-1/6)cos(6x)
\[\int u dv = uv - \int v du\]
\[\int 5xsin(6x)dx = (-5/6)xcos(6x) + (5/6) \int \cos(6x)dx\]
\[\int 5xsin(6x)dx = (-5/6)xcos(6x) + (5/24) \sin(6x)\]

Answer 2

\[-\frac{5}{6}xcos(6x)+\frac{5}{36}\sin(6x)+C\]

Answer 3

EDIT: my bad, I can't multiply. nadeem's answer is correct, 6*6 = 36, not 24.