Integration via substitution problem.

[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.

 

[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.

 

[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.