错,前一项∫xcos(x^2)dx=1/2∫2xcos(x^2)dx=1/2∫cos(x^2)dx^2=1/2sin(x^2)+c1,根据分部积分法,后一项 ∫-sin(x^2)/x^2dx=∫sin(x^2)d1/x=sin(x^2)/x-∫1/xdsin(x^2)=sin(x^2)/x-2∫cos(x^2)dx=sin(x^2)/x-[x+sin(2x)/2]+c2
对于2∫cos(x^2)dx=x+sin(2x)/2+c这个应该清楚吧 因为cos(x^2)=(1+cos2x)/2
所以整体∫xcos(x^2)-sin(x^2)/x^2 dx=1/2sin(x^2)+sin(x^2)/x-x-sin(2x)/2+c=(x+2)sin(x^2)/2x-x-sin(2x)/2+c