JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Hard

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Understanding +4 | -1

\ell^{\mathrm{r}}

means

(\log \log \log \ldots.) \mathrm{x}

, the

\log

being repeated

\mathrm{r}

times, then

\int\left\{\mathrm{x} \ell(\mathrm{x}) \ell^2(\mathrm{x}) \ell^3(\mathrm{x}) \ldots \ell^{\mathrm{r}}(\mathrm{x})\right\}^{-1} \mathrm{dx}

is equal to -

View answer and explanation

Correct option: A

\ell^{r+1}(\mathrm{x})+\mathrm{c}

Option A (

\ell^{r+1}(\mathrm{x})+\mathrm{c}

) is correct because the integral simplifies to the (r+1)-th iterated logarithm of x plus a constant, through a series of substitutions.

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