Integration via substitution problem.

1. Aug 15, 2004

Gaz031

Hi, i'm currently stuck on an integration via substitution problem. I have an answer but the one given in the book of the book is different to mine. I'm wondering where exactly i've gone wrong, if i have:

Q10: Integrate:

x/ (x+1)^0.5 dx. Use the substitution, u^2 = x + 1.

Heres my working:
u^2 = x + 1.
u = (x+1)^0.5
2u(du/dx) = 1
x = u^2 - 1

So, using some substitution:

(u^2 - 1)/u 1dx
(u^2 - 1)/u 2u(du/dx)dx
(u^2 - 1)2 du
(2u^2 - 2) du

Now integrating with respect to u:

(2/3)u^3 - 2u

Substituting u = (x+1)^0.5
(2/3).(x+1)^1.5 - 2.(x+1)^0.5

However, the actual answer given in the back of the book is:

(2/3)(x-2).(x+1)^0.5

Could anyone spot my mistake for me? Thanks a lot.

2. Aug 15, 2004

Muzza

You haven't made a mistake. (2/3)(x + 1)^1.5 - 2(x + 1)^0.5 = (x + 1)^0.5( (2/3)(x + 1)^1 - 2) = (2/3 * (x - 1)) * (x + 1)^0.5, i.e what the book wrote. Also, don't forget about the constant of integration.

3. Aug 15, 2004

Gaz031

Ooops. Their version is just simplified. Trust me to get the part that was new to me right then forget to simplify with basic algebra >_<.
Thanks, sorry for the stupid topic.