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Question Number 67069 by mRDv143 last updated on 22/Aug/19

Commented by Prithwish sen last updated on 22/Aug/19

$$\int \frac{{(1+\mathrm{logx})}^2}{1+\mathrm{xlogx}+\mathrm{logx}+\mathrm{x}{\left(\mathrm{logx}\right)}^2}\mathrm{dx}$$$$=\int \frac{{(1+\mathrm{logx})}^2}{(1+\mathrm{logx})(1+\mathrm{xlogx})}\mathrm{dx}$$$$=\int \frac{1+\mathrm{logx}}{1+\mathrm{xlogx}}\mathrm{dx}\mathrm{put}1+\mathrm{xlogx}=\mathrm{u}\Rightarrow (1+\mathrm{logx})\mathrm{dx}=\mathrm{du}$$$$=\int \frac{\mathrm{du}}{\mathrm{u}}=\ln \mid 1+\mathrm{logx}\mid +\mathrm{C}\mathrm{please}\mathrm{check}.$$

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