Maths  Integration by parts
posted by Anonymous on .
Integral x^2 sin(x) dx

Let I = ∫x^2 sinx dx
u = x^2
du = 2x dx
dv = sinx
v = cosx
∫u dv = uv  ∫v du
= x^2 cosx + ∫2x cosx dx
now, for ∫x cosx dx,
u = x
du = dx
dv = cosx dx
v = sinx
I = x^2 cosx + 2(x sinx  ∫sinx dx)
= x^2 cosx + 2x sinx + 2cosx + C
= 2x sinx + (2x^2)cosx + C