When integrating by parts with one factor as a variable and the other with a trig function, generally the variable will be set to u and the trig function set to dv

integral udv =  uv - integral vdu

let's take integral x^2*sinx

u = x^2
du = 2x dx
dv = sinx
v = -cosx

this gives us  -x^2(cosx) - integral -2xsinx

now we have to integral by parts again

u = -2x
du = -2 dx
dv = sinx
v = -cosx


2xcosx - integral 2cosx = 2xcosx -(1/2)sinx

answer is -x^2(cosx) - 2xcosx + (1/2)sinx + C