若∫f(x)dx=cosx+C,则∫xf(x^2)dx=?
问题描述：
若∫f(x)dx=cosx+C,则∫xf(x^2)dx=?
答
∫f(x)dx=cosx+C
所以f(x)=[cosx+C]'=-sinx
所以∫xf(x^2)dx
=∫-xsin(x^2)dx
=-(1/2)∫sin(x^2)dx^2
=(1/2)cos(x^2)+C