If means , the log being repeated times, then is equal…

MATHEMATICS · Single correct · A Level · Mathematics · Integration · Integration

Problem

If lr(x)l^{r}(x) means log⁡log⁡log⁡…x\log\log\log\dots x, the log being repeated rr times, then ∫[x l(x) l2(x) l3(x)…lr(x)]−1 dx\int [x\,l(x)\,l^2(x)\,l^3(x)\dots l^r(x)]^{-1}\,dx is equal to (a) lr+1(x)+Cl^{r+1}(x)+C (b) lr+1(x)r+1+C\frac{l^{r+1}(x)}{r+1}+C (c) lr(x)+Cl^r(x)+C (d) none of these

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