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Question Number 197226 by sonukgindia last updated on 10/Sep/23 Answered by Frix last updated on 10/Sep/23 $$\int \frac{dx}{1+\sqrt{x^2+x+1}}\stackrel{t=\frac{2x+1+2\sqrt{x^2+x+1}}{\sqrt{3}}}{=}$$$$=\int\frac{{t}^{\mathrm{2}} +\mathrm{1}}{{t}\left({t}^{\mathrm{2}} +\frac{\mathrm{4}{t}}{\:\sqrt{\mathrm{3}}}+\mathrm{1}\right)}{dt}=\int\left(\frac{\mathrm{1}}{{t}}+\frac{\mathrm{2}}{{t}+\sqrt{\mathrm{3}}}−\frac{\mathrm{6}}{\mathrm{3}{t}+\sqrt{\mathrm{3}}}\right){dt}= \…

Question Number 197196 by sonukgindia last updated on 10/Sep/23 Answered by mahdipoor last updated on 10/Sep/23 $$blue\equiv$$$$\pi{r}^{\mathrm{2}} \left(\frac{\alpha_{\mathrm{1}} }{\mathrm{360}}+\frac{\alpha_{\mathrm{2}} }{\mathrm{360}}+\frac{\alpha_{\mathrm{3}} }{\mathrm{360}}…+\frac{\alpha_{{n}} }{\mathrm{360}}\right) \…

Question Number 197188 by sonukgindia last updated on 10/Sep/23 Answered by witcher3 last updated on 10/Sep/23 $$\mathrm{I}={\int }_0^1\ln (-\mathrm{x})(\pi -\mathrm{arcos}\left(\mathrm{x}\right))\mathrm{dx}+{\int }_0^1\ln \left(\mathrm{x}\right)\arccos \left(\mathrm{x}\right)\mathrm{dx}$$$$=\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{arccos}\left(\mathrm{x}\right)\left(−\mathrm{ln}\left(−\mathrm{x}\right)+\mathrm{ln}\left(\mathrm{x}\right)\right)+\pi\int_{\mathrm{0}}…

Question Number 197155 by otchereabdullai@gmail.com last updated on 09/Sep/23 $$Abulletofmass180gisfired$$$$horizontallyintoafixedwooden$$$$blockwithaspeedof24m/s.ifthe$$$$bulletisbroughttorestin0.4secbya$$$$constantresistance,calculatethe$$$$distancemovedbythebulletinthe$$$$wood$$ Answered…

Question Number 197146 by hardmath last updated on 08/Sep/23 $$\mathrm{Find}:\mathrm{\Omega }={\int }_0^1\frac{\mathrm{Li}\left(\mathrm{x}\right)}{\mathrm{\Psi }\left(\mathrm{x}\right)}\mathrm{dx}=?$$ Answered by Blackpanther last updated on 09/Sep/23 $$0.7823$$ Terms…