How do you intagrate this function?
(#1+sqrt((x+1)# ) / #1-sqrt((x+1))#
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1 Answer
Jun 9, 2018
Use the substitution
Explanation:
Let
#I=int(1+sqrt(x+1))/(1-sqrt(x+1))dx#
Apply the substitution
#I=int(2-u)/u(-2(1-u)du)#
Simplify:
#I=int(6-2u-4/u)du#
Integrate directly:
#I=6u-u^2-4ln|u|+C#
Reverse the substitution:
#I=(5+sqrt(x+1))(1-sqrt(x+1))-4ln|1-sqrt(x+1)|+C#
Simplify and rescale
#I=-x-4sqrt(x+1)-4ln|1-sqrt(x+1)|+C#