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Question Number 96637 by 175 last updated on 03/Jun/20

Commented by bemath last updated on 03/Jun/20

$$\int \frac{\ln \left({\mathrm{x}}^{\mathrm{a}}\right)}{\mathrm{x}}\mathrm{dx}=\mathrm{a}\int \frac{\ln \left(\mathrm{x}\right)}{\mathrm{x}}\mathrm{dx}$$$$\mathrm{let}\mathrm{u}=\ln \left(\mathrm{x}\right)\Rightarrow \mathrm{du}=\frac{\mathrm{dx}}{\mathrm{x}}$$$$\Rightarrow \mathrm{a}\int \mathrm{u}\mathrm{du}=\frac{1}{2}\mathrm{a}{\mathrm{u}}^2+\mathrm{c}$$$$=\frac{\mathrm{a}}{2}{\left(\ln \left(\mathrm{x}\right)\right)}^2+\mathrm{c}$$

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