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Evaluate: (i)int1/(sqrt(3x+4)-sqrt(3x+...

Evaluate: `(i)int1/(sqrt(3x+4)-sqrt(3x+1))dx`

Text Solution

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`int frac{d x}{sqrt{2 x+3}+sqrt{2 x-3}}`
` =int frac{(sqrt{2 x+3}-sqrt{2 x-3})}{(2 x+3-2 x+3)} d x`
` =frac{1}{6} int(sqrt{2 x+3}-sqrt{2 x-3}) d x`
` =frac{1}{6}(frac{(2 x+3)^{3 / 2}}{3}-frac{(2 x-3)^{3 / 2}}{3})+c`
`
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