∫xcos(x-1)dx不定积分

∫xcos(x-1)dx不定积分
∫xcos(x-1)dx不定积分

∫xcos(x-1)dx不定积分
∫xcos(x-1)dx
=∫cos(x-1)d(x^2/2)
=cos(x-1)*x^2/2-∫xd(cos(x-1)+c
=cos(x-1)*x^2/2+∫sin(x-1)d(x^2/2)+c
=cos(x-1)*x^2/2+∫sin(x-1)*x^2/2)+c
=cos(x-1)*x^2/2+sin(x-1)*x^2/2-∫xcos(x-1)dx+c
到此方程两边都有∫xcos(x-1)dx,移项得：
2∫xcos(x-1)dx=cos(x-1)*x^2/2+sin(x-1)*x^2/2+c
化简得∫xcos(x-1)dx=√2/4[sin(x-1+π/4)]+c