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Question
Integrate the functions:
`1/(x-sqrtx)`
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Solution
Let `I = int 1/(x - sqrtx) dx`
`= int 1/(sqrt x - (sqrtx - 1)) dx`
Taking `sqrt x - 1 = t`
`1/(2 sqrt x) dx = dt`
or `1/sqrt x dx = 2 dt`
Hence, `I = int 1/2. 2 dt = 2 int1/t dt`
= 2 log t + C
`= 2 log (sqrtx - 1) = C`
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