Thread: 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,

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 is an arbitary conatant then so is so look at (a):



RonL

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.

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