Integrating a fraction/square roots when 'x' is on the bottom

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April 28th 2009, 05:35 PM
MikeNZ

Integrating a fraction/square roots when 'x' is on the bottom

How would I transpose this formula so I can integrate it? I'm not good with integrating fractions or square roots.

Integrate:

Q1) $\frac{dy}{dx}$ = $\frac{x^3-2x}{x}$

Q2) $(\sqrt{x}+1)^2$

It's the fractions and square roots that are annoying. For the square root, I know I'd have to write two brackets out and possibly expand, but don't know how I would expand with a square root - So does the 'x' in the square root become: $x^\frac{1}{2}$ ? Or something along those lines..

Thanks in advance.
April 28th 2009, 05:52 PM
chengbin

Am I reading this right?

$\frac{x^3-2x}{x}$

If that's right, just divide it, then it becomes $x^2-2$

That's easy to integrate.

For Q2, just expand it, and you'll get $x+2\sqrt x+1$ Integrating that is just $\frac {1}{2} x^2+\frac {4}{3} x\sqrt x+x$
April 28th 2009, 05:59 PM
MikeNZ

Quote:

Originally Posted by chengbin

Am I reading this right?

$\frac{x^3-2x}{x}$

If that's right, just divide it, then it becomes $x^2-2$

That's easy to integrate.

For Q2, just expand it, and you'll get $x+2\sqrt x+1$ Integrating that is just $\frac {1}{2} x^2+\frac {4}{3} x\sqrt x+x$

Oh ok, yep Q1 is easy to Integrate..

Just quickly, for Q2, where did you get the 4 over 3 from? and if you integrated 'x' by itself, wouldn't you get $\frac{x^2}{2}$ ?
April 28th 2009, 06:28 PM
chengbin

$\int 2\sqrt x = \int 2x^\frac {1}{2}$

$\frac{2}{\frac{3}{2}}x^\frac {3}{2}$

$\frac {4}{3} x^\frac {3}{2} = \frac {4}{3} x(x^\frac {1}{2}) = \frac {4}{3}x\sqrt x$
April 28th 2009, 06:48 PM
MikeNZ

Ohh yip, thanks :)

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