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:(adsbygoogle = window.adsbygoogle || []).push({});

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.

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# Homework Help: Integration via substitution problem.

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