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one of the questions is this:

## \displaystyle \int \dfrac{dx}{2\sqrt{x}\sqrt{1-x}} ##

I can't see at all how this is by recognition

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- #1

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one of the questions is this:

## \displaystyle \int \dfrac{dx}{2\sqrt{x}\sqrt{1-x}} ##

I can't see at all how this is by recognition

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Office_Shredder

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Pretty much that, you should be able to deduce what the integral is by just looking at it. You're obviously supposed to know how to prove it, but it saves time I guess.

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sophiecentaur

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verty

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sophiecentaur

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pasmith

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I think you're supposed to recognise that [itex]\displaystyle\frac{1}{2\sqrt{x}}[/itex] is the derivative of [itex]\sqrt{x}[/itex]. That's of the form [itex](x^n)' = nx^{n-1}[/itex], ie. fairly basic. You may also be supposed to recognise [itex]\displaystyle\frac{1}{\sqrt{1 - u^2}}[/itex] as being the derivative of a known function.

Although only very few will instantly recognise [itex]\displaystyle\frac{1}{2\sqrt{x}\sqrt{1-x}}[/itex] as being the derivative of

arcsin(x^(1/2))

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sophiecentaur

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