∫(x-2)dx/x²+2x+3=?
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/01 23:11:00
![∫(x-2)dx/x²+2x+3=?](/uploads/image/z/3966437-29-7.jpg?t=%E2%88%AB%EF%BC%88x-2%EF%BC%89dx%2Fx%26%23178%3B%2B2x%2B3%3D%3F)
∫(x-2)dx/x²+2x+3=?
∫(x-2)dx/x²+2x+3=?
∫(x-2)dx/x²+2x+3=?
令u=x+1,则du=dx
原式=∫(u-3)du/(2+u^2)
=∫udu/(2+u^2)-∫3du/(2+u^2)
=1/2·ln(2+u^2)-3/√2·arctan(u/√2)+C
=1/2·ln(x^2+2x+3)-3/√2·arctan((x+1)/√2)+C
没看懂题、除是怎么除