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Integrate the following functions 1/(x-s...

Integrate the following functions `1/(x-sqrtx)`

Text Solution

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`1/(x-sqrtx) = 1/(sqrtx(sqrtx-1))`
Put `sqrtx-1 = t`
Then `dt = 1/(2sqrtx) dx gt 1/sqrtx dx = 2 dt`
therefore `int 1/(x-sqrtx) dx = int 1/(sqrtx(sqrtx-1)) dx`
=`int 2 (dt)/t = 2 log|t|+c`
`2 log|sqrtx-1|+c`
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