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What is the value of `int(sqrtx + x)^(-1) dx`?A. `ln (x + sqrtx) + c`B. `2 ln (1 + sqrtx) + c`C. `2 ln (x + sqrtx) + c`D. `2 ln (x - sqrtx) + c` |
Answer» Correct Answer - B `int (x + sqrtx)^(-1) dx = int (1)/((x + sqrtx)) dx` `= int (1)/((sqrtx.sqrtx + sqrtx)).dx` Let `sqrtx + 1 = t` then, `(1)/(2sqrtx) dx = dt rArr (1)/(sqrtx) dx = 2dt` `:. Int (1)/(sqrtx (sqrtx + 1))dx = int (2dt)/(t) = 2 log t + c` `= 2 log (1 + sqrtx) + c` |
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