Question

求1除以[根号x乘(1+x）]的不定积分,要过程,急求!

Answer 1

令√x=t,x=t^2,dx=2tdt
∫1/[√x(1+x)]dx
=∫1/[t(1+t^2)]*2tdt
=2∫1/(1+t^2)dt
=2arctant+C
=2arctan√x+C