求积分xdx/(x+√x^2+1)

来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/19 02:50:44
求积分xdx/(x+√x^2+1)求积分xdx/(x+√x^2+1)求积分xdx/(x+√x^2+1)先分母有理化:∫xdx/[x+√(x^2+1)]=∫x[√(x^2+1)-x]dx=∫x√(x^2

求积分xdx/(x+√x^2+1)
求积分xdx/(x+√x^2+1)

求积分xdx/(x+√x^2+1)
先分母有理化:

∫xdx/[x+√(x^2+1)]=∫x[√(x^2+1)-x]dx=∫x√(x^2+1)dx-x^3/3=1/2∫√(x^2+1)d(x^2+1)-x^3/3=(1/2*2/3)(x^2+1)^(3/2)-x^3/3+c=1/3(x^2+1)^(3/2)-x^3/3+c,其中c为常数