Integrating √(x²+4) | Calculating Integrals Homework

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Homework Statement


Calculate the integral.
Code:
[tex]\int\frac{d}{dx}\sqrt{x^{2} + 4}dx[/tex]

Homework Equations


The Attempt at a Solution


All i know is that i am suppose to factor out the
Code:
[tex]\frac{d}{dx}[/tex]
to become
Code:
[tex]\frac{d}{dx}\int\sqrt{x^{2} + 4}dx[/tex]
 
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Here is a hint: Integration is the reverse of differentiation.There is no factoring out the d/dx
 
"Fundamental Theorem of Calculus" (which is basically what rock.freak667 said).
 
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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