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May 6th, 2014, 02:33 PM   #1
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intgrate3

integrate x Sqrt[2-Sqrt[x]]
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May 6th, 2014, 07:02 PM   #2
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Is this significantly different from the last where the 2 was a 1?
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May 6th, 2014, 07:42 PM   #3
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No. Using the method found here we may obtain a general solution for

$\displaystyle \int x\sqrt{a-\sqrt{x}}\,dx;\,a-\sqrt{x}\ge0;\,a\in\mathbb{R}$

Though giving a more complicated result, that method can also be adapted to give a solution for

$\displaystyle \int x\sqrt{a-b\sqrt{x}}\,dx;\,a-b\sqrt{x}\ge0;\,a,b\in\mathbb{R}$
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