Integration, u substitution with limits

[sg001]

Homework Statement

find ∫x/√(x+1).dx with limits 1 & 0

using substitution x = u^2 -1

Homework Equations

The Attempt at a Solution

dx = du

x = u^2 -1

u = √( x+1)

sub limits of 1 & 0 into u.
Hence new limits of √2 & 1

Therefore,

∫ u^2 -1/ u

= ∫ u - 1/u
= 1/2 (u)^2 - ln u

Plugging in limits of √2& 1

(1/2 * 2 - ln √ 2 ) - (1/2)

= ( 1/2 - 1/2 ln (2))

Cant work out where I have stumbled, any ideas?

 

[tiny-tim]

hi sg001!

dx = du

noooo

 

[sg001]

ohh that makes sense now because i had the same question but with different sub involved. ie u= x + 1,,, so I kinda got ahead of myself and skipped that step.
Thanks for pointing that out, I probabaly would never have realized.