What is the indefinite integral of #1/(1+sqrt(x+1))#?
1 Answer
May 23, 2018
Explanation:
Let
#I=int1/(1+sqrt(x+1))dx#
Apply the substitution
#I=2intu/(1+u)du#
Rearrange:
#I=2int(1-1/(1+u))du#
Integrate directly:
#I=2(u-ln|1+u|)+C#
Reverse the substitution:
#I=2sqrt(x+1)-2ln|1+sqrt(x+1)|+C#