For the integral

MATHEMATICS · Single correct · CBSE · Mathematics · Integrals · Integrals

Problem

For the integral ∫x3(ln⁡x)2 dx\displaystyle \int x^{3}(\ln x)^{2}\,dx, four possible selections for the factor to be differentiated are listed below. Which selection is likely to require the fewest total differentiations before the factor vanishes? (a) Differentiate (ln⁡x)2(\ln x)^{2} (b) Differentiate x2ln⁡xx^{2}\ln x (c) Differentiate x3x^{3} (d) Differentiate x(ln⁡x)2x(\ln x)^{2}

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