1. Help with indefinite integral

int( -x*dx / (x+1 - sqrt(x+1) ). The book shows two answers:

a) -x -1 -2*sqrt(x+1) + C

b) -x -2*sqrt(x+1) + C

By using substitution method and pattern recognition I managed to find answer (b). But I'm curious about the (a) answer.

Thanks for any help,

2. Originally Posted by CalculusFan
int( -x*dx / (x+1 - sqrt(x+1) ). The book shows two answers:

a) -x -1 -2*sqrt(x+1) + C

b) -x -2*sqrt(x+1) + C

By using substitution method and pattern recognition I managed to find answer (b). But I'm curious about the (a) answer.

Thanks for any help,
Either you have mistyped something here, or they are the same thing.

If $\displaystyle C$ is an arbitary conatant then so is $\displaystyle K = C-1$ so look at (a):

$\displaystyle -x -1 -2\sqrt{x+1} + C=-x -2\sqrt{x+1} + (C-1)=-x -2\sqrt{x+1} + K$

RonL

3. Maybe you are wright, CaptainBlak; but what intrigued me was Maple's answer: it also shows -x -1 -2*sqrt(x+1); and Maple is known for being carefree with constants.

4. Originally Posted by CalculusFan
Maybe you are wright, CaptainBlak; but what intrigued me was Maple's answer: it also shows -x -1 -2*sqrt(x+1); and Maple is known for being carefree with constants.
The Integrator also gives that answer