What is the mistake in solving this derivative?

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Hi everyone,

I'm having trouble solving this one. I just don't really see what I'm doing wrong.

Homework Statement


X² - x - 2
X² + 5x + 6


Homework Equations





The Attempt at a Solution


(( x-1 ) * x² + 5x + 6 ) - (( x + 5 ) * x²-x-2 )
( x² + 5x + 6)²

So 8x² -6x-16
(x² + 5x + 6)²

Now I know this isn't the correct awnser. Because it should say
6x² + 16x + 4
( x² + 5x+6)²

Could anyone point out to me what I'm doing wrong?
Thanks in advance.
Tim
 
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The derivative of x^2 is 2x, not x.
 

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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