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Question-32126




Question Number 32126 by mondodotto@gmail.com last updated on 20/Mar/18
Commented by mondodotto@gmail.com last updated on 20/Mar/18
please help
$$\boldsymbol{{please}}\:\boldsymbol{{help}} \\ $$
Answered by mrW2 last updated on 20/Mar/18
∫((ln x −1)/((ln x)^2 )) dx  =∫(1/(ln x)) dx−∫(1/((ln x)^2 )) dx  =(x/(ln x))+∫(x/(x(ln x)^2 )) dx−∫(1/((ln x)^2 )) dx  =(x/(ln x))+C
$$\int\frac{\mathrm{ln}\:{x}\:−\mathrm{1}}{\left(\mathrm{ln}\:{x}\right)^{\mathrm{2}} }\:{dx} \\ $$$$=\int\frac{\mathrm{1}}{\mathrm{ln}\:{x}}\:{dx}−\int\frac{\mathrm{1}}{\left(\mathrm{ln}\:{x}\right)^{\mathrm{2}} }\:{dx} \\ $$$$=\frac{{x}}{\mathrm{ln}\:{x}}+\int\frac{{x}}{{x}\left(\mathrm{ln}\:{x}\right)^{\mathrm{2}} }\:{dx}−\int\frac{\mathrm{1}}{\left(\mathrm{ln}\:{x}\right)^{\mathrm{2}} }\:{dx} \\ $$$$=\frac{{x}}{\mathrm{ln}\:{x}}+{C} \\ $$
Commented by mondodotto@gmail.com last updated on 20/Mar/18
thanx a lot
$$\mathrm{thanx}\:\mathrm{a}\:\mathrm{lot} \\ $$

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