∫2/x﹙x²-1﹚½dx=?
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![∫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)
∫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