(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

[itex]\int \frac{x^2}{\sqrt{x^2+3}}[/itex]

2. Relevant equations

sinh-1(u) = u' / (u^2 + 1)

3. The attempt at a solution

Make the x^2 + 3 look like x^2 + 1 by taking out a sqrt(3). Giving you

[itex]\int \frac{x^2}{\sqrt{3} \sqrt{\frac{x^2}{3}+1}}[/itex]

Set the constant outside the integral.

[itex] \frac{1}{\sqrt{3}} \int \frac{x^2}{\sqrt{\frac{x^2}{3}+1}}[/itex]

Now we find where [itex]u^2 = \frac{x^2}{3} [/itex] , which is [itex]u = \frac{x}{\sqrt{3}} [/itex]. Now we know the u of the sinh-1, we find u'

[itex]u' = \frac{1}{\sqrt{3}} [/itex]

So now we taken care of everything but x^2...

Where to go now?

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# Intergal of x^2/sqrt(x^2+3)

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