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Question Number 61874 by aliesam last updated on 10/Jun/19

$$\int \frac{xln\left(x\right)-x}{{ln}^3\left(x\right)}dx$$

Commented by Prithwish sen last updated on 10/Jun/19

$$\int [\frac{\mathrm{x}}{{\left[\ln \left(\mathrm{x}\right)\right]}^2}-\frac{\mathrm{x}}{{\left[\ln \left(\mathrm{x}\right)\right]}^3}]\mathrm{dx}$$$$\mathrm{applying}\mathrm{by}\mathrm{parts}$$$$=\frac{{\mathrm{x}}^2}{2{\left[\ln \left(\mathrm{x}\right)\right]}^2}+\int \frac{\mathrm{x}}{{\left[\ln \left(\mathrm{x}\right)\right]}^3}\mathrm{dx}-\int \frac{\mathrm{x}}{{\left[\ln \left(\mathrm{x}\right)\right]}^3}+\mathrm{C}$$$$=\frac{{\mathrm{x}}^2}{2{\left[\ln \left(\mathrm{x}\right)\right]}^2}+\mathrm{C}$$

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