积分求助∫(根号(1+t))/tdt

Question

积分求助∫(根号(1+t))/t dt

Answer 1

设√1+t=n,t=n²-1
∫(√(1+t))/t dt
=∫ndn/（n²-1）d（n²-1）+C
=∫2n²dn/（n²-1）+C
=2+2∫dn/（n²-1）+C
=2+∫dn[1/（n-1）-1/(1+n)]+C
=2+ln（n-1）/（n+1）+C