∫2/x﹙x²-1﹚½dx=?
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/15 02:28:38
![∫2/x﹙x²-1﹚½dx=?](/uploads/image/z/2590453-37-3.jpg?t=%E2%88%AB2%EF%BC%8Fx%EF%B9%99x%26%23178%3B%EF%BC%8D1%EF%B9%9A%26%23189%3Bdx%3D%3F)
x){Ա;gV)[Xk~, :&H(uv6ěd
]C8
C}#MR3ᢶΓK^tߺmO'=7Y@JSJӯ@h"B͔
[#
}Jnh{rZ.z1mCtv|Ɏ';V Ch
iZhHpĢļRmg~4v$ف e
∫2/x﹙x²-1﹚½dx=?
∫2/x﹙x²-1﹚½dx=?
∫2/x﹙x²-1﹚½dx=?
令(x²-1)^(1/2)=u,则x²-1=u²,两边微分后得:xdx=udu
∫2/x(x²-1)^(½)dx
=2∫x/x²(x²-1)^(½)dx
将里面的x²换成u²+1,(x²-1)^(½)换成u,剩下一个xdx换成udu
=2∫1/[(u²+1)u]*udu
=2∫1/(u²+1)du
=2arctanu+C
=2arctan[(x²-1)^(½)]+C