Question and Answers Forum

All Questions      Topic List

Integration Questions

Previous in All Question      Next in All Question      

Previous in Integration      Next in Integration      

Question Number 12744 by tawa last updated on 30/Apr/17

$${\int }_{{\mathrm{e}}^{-3}}^{{\mathrm{e}}^{-2}}\frac{1}{\left(\mathrm{x}\right)\log \left(\mathrm{x}\right)}\mathrm{dx}=?$$

Answered by b.e.h.i.8.3.4.1.7@gmail.com last updated on 30/Apr/17

$$logx=t\Rightarrow dx/x=dt$$$$I=\int \frac{dx/x}{logx}=\int \frac{dt}{t}=ln\mid t\mid +\mathit{C}$$$${I=\left(ln\left(lnx\right)\right)+C)}_{e^{-3}}^{e^{-2}}=(ln(-2)-ln(-3))=$$$$=ln\frac{-2}{-3}=ln\frac{2}{3}.◼$$

Commented by tawa last updated on 30/Apr/17

$$\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com