Question Number 126274 by bramlexs22 last updated on 19/Dec/20 Answered by liberty last updated on 19/Dec/20 $$\:{letting}\:{x}=\sqrt{\mathrm{2}}\:\mathrm{sec}\:\ell\:{with}\:\rightarrow\begin{cases}{\ell=\frac{\pi}{\mathrm{2}}}\\{\ell=\frac{\pi}{\mathrm{4}}}\end{cases} \\ $$$$\:\int_{\pi/\mathrm{4}} ^{\:\pi/\mathrm{2}} \:\frac{\sqrt{\mathrm{2}}\:\mathrm{sec}\:\ell\:\mathrm{tan}\:\ell}{\:\sqrt{\mathrm{2}}\:\mathrm{sec}\:\ell\:\sqrt{\mathrm{2tan}\:^{\mathrm{2}} \ell}}\:{d}\ell\:= \\ $$$$\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\int\:{d}\ell\:=\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\:\left[\:\frac{\pi}{\mathrm{2}}−\frac{\pi}{\mathrm{4}}\:\right]\:=\:\frac{\pi}{\mathrm{4}\sqrt{\mathrm{2}}}\:=\:\frac{\pi\sqrt{\mathrm{2}}}{\mathrm{8}}\: \\…
Question Number 191811 by mathlove last updated on 01/May/23 $$\int{x}^{\mathrm{2}} {e}^{−{x}} {dx}=? \\ $$ Answered by Spillover last updated on 01/May/23 $${use}\:{by}\:{parts} \\ $$ Answered…
Question Number 60739 by Forkum Michael Choungong last updated on 25/May/19 $${evaluate}\:\: \\ $$$${i}.\int\:\left(\frac{{x}+\mathrm{1}}{{x}−\mathrm{1}}\right){dx} \\ $$$${ii}.\:\:\int_{\mathrm{0}} ^{\pi} \left(\mathrm{2}{cosxsinx}\right){dx}\:\: \\ $$$${iii}.\:\:\int_{\frac{\pi}{\mathrm{3}\:}\:} ^{\pi} \left(\frac{{sin}\mathrm{2}{x}}{{cos}\mathrm{2}{x}}\right){dx} \\ $$ Commented…
Question Number 126273 by bramlexs22 last updated on 19/Dec/20 Commented by talminator2856791 last updated on 19/Dec/20 $$\:\mathrm{we}\:\mathrm{dont}\:\mathrm{do}\:\mathrm{science}\:\mathrm{here}.\:\mathrm{only}\:\mathrm{mathematics} \\ $$ Commented by mr W last updated…
Question Number 60731 by aliesam last updated on 25/May/19 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 126266 by bramlexs22 last updated on 18/Dec/20 $$\:{solve}\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\mathrm{1}−{x}^{\mathrm{2}} }{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\sqrt{\mathrm{1}+{x}^{\mathrm{4}} }}\:{dx}\:?\: \\ $$ Answered by liberty last updated on 19/Dec/20 $${N}=\int_{\mathrm{0}}…
Question Number 60728 by Mr X pcx last updated on 25/May/19 $${calculate}\:\int_{\mathrm{1}} ^{+\infty} \:\:\frac{{ln}\left({lnx}\right)}{{x}^{\mathrm{2}} −{x}\:+\mathrm{1}}{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 60727 by Mr X pcx last updated on 25/May/19 $${calculate}\:\int_{\mathrm{1}} ^{+\infty} \:\frac{{ln}\left({lnx}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx} \\ $$ Commented by maxmathsup by imad last updated on…
Question Number 60716 by peter frank last updated on 24/May/19 Commented by maxmathsup by imad last updated on 25/May/19 $${let}\:{A}\left({x}\right)\:=\left(\frac{{x}}{{x}+\mathrm{1}}\right)^{{x}} \:\Rightarrow{A}\left({x}\right)\:=\left(\mathrm{1}−\frac{{x}+\mathrm{1}}{{x}}\right)^{{x}} \:={e}^{{x}\:{ln}\left(\mathrm{1}−\frac{\mathrm{1}}{{x}+\mathrm{1}}\right)} \\ $$$${but}\:{we}\:{have}\:{for}\:{u}\:\in{V}\left(\mathrm{0}\right)\:{ln}\left(\mathrm{1}−{u}\right)\:\sim−{u}\:\Rightarrow{ln}\left(\mathrm{1}−\frac{\mathrm{1}}{{x}+\mathrm{1}}\right)\sim−\frac{\mathrm{1}}{{x}+\mathrm{1}}\:{for}\:{x}\in{V}\left(+\infty\right) \\…
Question Number 126230 by I want to learn more last updated on 18/Dec/20 $$\int\:\boldsymbol{\mathrm{e}}^{\:\boldsymbol{\mathrm{cos}}^{−\:\mathrm{1}} \left(\boldsymbol{\mathrm{x}}\right)} \:\:\:\mathrm{dx} \\ $$ Answered by Olaf last updated on 18/Dec/20…