被积函数为1/(根号U-U)的不定积分如题,积到现在也没积出来

Question

被积函数为1/(根号U-U)的不定积分
如题,积到现在也没积出来

Answer 1

=-1/√u(√u-1)
=1/√u-1/(√u-1)
=u^(-1/2)-1/(√u-1)
∫u^(-1/2)du=2√u
令a=√u
u=a²
du=2ada
所以∫1/(√u-1)du=∫2ada/(a-1)
=∫2(a-1+1)da/(a-1)
=∫2[1+1/(a-1)]da
=2a+2ln|a-1|
=2√u+2ln|√u-1|
所以原式=2√u-2√u-2ln|√u-1|+C
=-2ln|√u-1|+C