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If `l^r(x)` means `logloglog.......x` being repeated `r` times, then `int [ (x l(x) l^2(x) l^3(x) .... l^r (x)]^(-1) dx` is equal to :A. `l^(r+1) (x) +c`B. `(l^(r+1)(x))/(r+1)+c`C. `l^(r)(x) +c`D. None of these |
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Answer» Correct Answer - A `int(1)/(xl(x)l^(2)(x)....l^(r-1)(x)l^(r)(x))dx` f(x)=t `rArr(1)/(l^(r-1)x.l^(r-2)x...x)dx=dt` `:. int(dt)/(t)=ln|t|+c` `" " l^(r+1)(x)+c` |
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