基本公式:
(uv)' = u'v + v'u 则
∫(uv)' dx = ∫u'v dx + ∫v'u dx
∫u'v dx = ∫(uv)' dx - ∫v'u dx = uv - ∫v'u dx
sinx/x为f(x)的一个原函数,即
∫f(x) dx = sinx/x
f(x) = (sinx/x)' =(sinx)'/x + sinx *(1/x)' = cosx /x - sinx /x^2
∫xf'(x) dx = x*f(x) - ∫x' f(x) dx = xf(x) - ∫f(x) dx =
= xf(x) - sinx/x + C
= x*(cosx /x - sinx /x^2) - sinx/ x + C
= cosx - 2(sinx /x) + C