Integrating (x-5)/√(x-6) with u-Substitution

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Homework Statement


Solve with u-substitution
∫ (x-5)/√(x-6) dx

Homework Equations





The Attempt at a Solution


This is what I have done so far and it doesn't seem to work out. I have a feeling I'm missing something. Any help would be appreciated.
u=x-6
du=dx
x=u+6
∫ (u+6-5)(u^(-1/2) du
∫ u^(1/2) + u^(-1/2) du
 
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You were doing just fine until your nerve failed. What's the integral of u^(1/2)du and u^(-1/2)du?
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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