∫xcos(x-1)dx不定积分
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/28 11:52:36
![∫xcos(x-1)dx不定积分](/uploads/image/z/8617700-20-0.jpg?t=%E2%88%ABxcos%28x-1%29dx%E4%B8%8D%E5%AE%9A%E7%A7%AF%E5%88%86)
∫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