# Help with indefinite integral

• May 21st 2007, 08:19 PM
CalculusFan
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. :confused:

Thanks for any help,
• May 21st 2007, 11:03 PM
CaptainBlack
Quote:

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. :confused:

Thanks for any help,

Either you have mistyped something here, or they are the same thing.

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

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

RonL
• May 22nd 2007, 09:36 AM
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.
• May 22nd 2007, 09:44 AM
Jhevon
Quote:

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