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Integrate the following functions 1/(x-sqrtx) |
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Answer» SOLUTION :`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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