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 68370 by mhmd last updated on 09/Sep/19

Answered by MJS last updated on 09/Sep/19

$$\int \frac{dt}{\sqrt{{\mathrm{e}}^t-1}}=$$$$[u=\sqrt{{\mathrm{e}}^t-1}\to dt=\frac{2\sqrt{{\mathrm{e}}^t-1}}{{\mathrm{e}}^t}du]$$$$=2\int \frac{du}{u^2+1}=2\arctan u=2\arctan \sqrt{{\mathrm{e}}^t-1}$$$$\text{Missing left or extra right}$$$$2\arctan \sqrt{3}-2\arctan \sqrt{{\mathrm{e}}^a-1}=\frac{\pi }{6}$$$$\frac{\pi }{3}-\arctan \sqrt{{\mathrm{e}}^a-1}=\frac{\pi }{12}$$$$\arctan \sqrt{{\mathrm{e}}^a-1}=\frac{\pi }{4}$$$$...$$$$a=\ln 2$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com