text: evaluate the integral where a is any constant.   (x^2)(sin(ax)) dx ...?   you will need to use integration by parts. let u = x^2 and dv = sin(ax)dx, then du = 2x dx and v = (-1/a)cos(ax) uv - integral(v du) = (-1/a)x^2 cos(ax) + integral [ (2/a)x cos(ax) dx] now to integrate (2/a) cos(ax) dx, we need to use integration by parts one more time. let u = (2/a)x and dv = cos(ax) dx, then du = (2/a)x and v = (1/a)sin(ax) uv - integral(v du) = (2/a^2)x sin(ax) - integral [ (2/a^2)sin(ax) dx] = (2/a^2)x sin(ax) - (2/a^2)(-1/a)cos(ax) + c = (2/a^2)x sin(ax) + (2/a^3)cos(ax) + c now you need to put this with the first part to get your final answer. answer: (-1/a)x^2 cos(ax) + (2/a^2)x sin(ax) + (2/a^3)cos(ax) + c