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