原式=∫(x^2-x)^(-1/2) dx
=∫[(x-1/2)^2-1/4]^(-1/2) dx
然后直接套公式
=ln|x-1/2+[(x-1/2)^2-1/4]^(1/2) |+C
=ln|x-1/2+(x^2-x)^(1/2) |+C
求∫(x^2-x)^(-1/2) dx 不定积分,麻烦写下过程
原式=∫(x^2-x)^(-1/2) dx
=∫[(x-1/2)^2-1/4]^(-1/2) dx
然后直接套公式
=ln|x-1/2+[(x-1/2)^2-1/4]^(1/2) |+C
=ln|x-1/2+(x^2-x)^(1/2) |+C