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Question Number 96672 by 175 last updated on 03/Jun/20

$$Evaluate:$$$$\int \frac{{log}_{x}a}{x}dx$$

Commented by bemath last updated on 03/Jun/20

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

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