Question Number 59274 by Mr X pcx last updated on 07/May/19 $${calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} {arctan}\left(\mathrm{1}+{x}+{x}^{\mathrm{2}} \right){dx} \\ $$ Commented by maxmathsup by imad last updated on…
Question Number 59275 by Mr X pcx last updated on 07/May/19 $${let}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\mathrm{1}+{xe}^{−{t}} \right){dt} \\ $$$$\left.\mathrm{1}\right){find}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right){calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\mathrm{1}+\mathrm{2}{e}^{−{t}} \right){dt} \\ $$$$\left.\mathrm{3}\right)\:{developp}\:{f}\left({x}\right){at}\:{integr}\:{serie}\:{if}\:\mid{x}\mid<\mathrm{1} \\…
Question Number 124794 by benjo_mathlover last updated on 06/Dec/20 $${If}\:{f}\left({x}\right)=\begin{cases}{\mathrm{2}{x}\:;\:\mathrm{0}<{x}<\mathrm{1}}\\{\mathrm{3}\:;\:{x}=\mathrm{1}\:}\\{\mathrm{6}{x}−\mathrm{1}\:;\:\mathrm{1}<{x}<\mathrm{2}}\end{cases} \\ $$$${find}\:\underset{\mathrm{0}} {\overset{\mathrm{2}} {\int}}\:{f}\left({x}\right)\:{dx}\:? \\ $$ Answered by TITA last updated on 06/Dec/20 $$\int_{\mathrm{0}} ^{\mathrm{2}}…
Question Number 124785 by Lordose last updated on 06/Dec/20 $$\int_{\:\mathrm{0}} ^{\:\mathrm{a}} \int_{\:\mathrm{0}} ^{\:\sqrt{\mathrm{a}^{\mathrm{2}} −\mathrm{x}^{\mathrm{2}} }} \frac{\mathrm{1}}{\left(\mathrm{1}+\mathrm{e}^{\mathrm{y}} \right)\sqrt{\mathrm{a}^{\mathrm{2}} −\mathrm{x}^{\mathrm{2}} −\mathrm{y}^{\mathrm{2}} }}\mathrm{dxdy} \\ $$$$ \\ $$ Terms…
Question Number 59247 by maxmathsup by imad last updated on 06/May/19 $${let}\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {ln}\left(\mathrm{1}−{xcost}\right){dt}\:\:{with}\:\mid{x}\mid<\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{developp}\:{f}\:{at}\:{integr}\:{serie} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{3}\right)\:{find}\:{the}\:{values}\:{of}\:{integrals}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {ln}\left(\mathrm{1}−{cost}\right){dt}\:\:{and}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {ln}\left(\mathrm{1}+{cost}\right){dt} \\…
Question Number 190318 by Rupesh123 last updated on 31/Mar/23 Answered by som(math1967) last updated on 31/Mar/23 $$\:{let}\:\mathrm{2}{x}−{x}^{\mathrm{2}} −\mathrm{1}={t}^{\mathrm{2}} \\ $$$$\:\left(\mathrm{2}−\mathrm{2}{x}\right){dx}=\mathrm{2}{tdt} \\ $$$$\int\frac{\mathrm{2}{tdt}}{{t}}=\mathrm{2}{t}+{C}=\mathrm{2}\sqrt{\mathrm{2}{x}−{x}^{\mathrm{2}} −\mathrm{1}}+{C} \\ $$…
Question Number 124742 by TANMAY PANACEA last updated on 05/Dec/20 $$\int\frac{\mathrm{3}^{{t}} +\mathrm{11}}{\mathrm{6}^{{t}} +\mathrm{11}}{dt}\:\:\:\boldsymbol{{collected}}\:\boldsymbol{{problem}} \\ $$ Commented by MJS_new last updated on 05/Dec/20 $$\mathrm{I}\:\mathrm{get}\:\mathrm{to}\:\mathrm{this}\:\mathrm{point}: \\ $$$$\frac{\mathrm{3}^{{t}}…
Question Number 124738 by mnjuly1970 last updated on 05/Dec/20 $$\:\:\:\:\:\:\:\:\:\:\:\:\:…{nice}\:\:\:{calculus}… \\ $$$$\:{simple}\:{limit}:: \\ $$$$\:\:\:{lim}_{{n}\rightarrow\infty} \:\left\{\frac{\mathrm{1}^{{a}+\mathrm{1}} +\mathrm{2}^{{a}+\mathrm{1}} +…+{n}^{{a}+\mathrm{1}} }{{n}\left(\mathrm{1}^{{a}} +\mathrm{2}^{{a}} +….{n}^{{a}} \right)}\right\}=? \\ $$$$\:{where}\:{a}\:\neq−\mathrm{2}\:,\:−\mathrm{1} \\ $$…
Question Number 59190 by maxmathsup by imad last updated on 05/May/19 $${find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{x}^{\mathrm{2}} }{\mathrm{1}−{cosx}}{dx}\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 59184 by maxmathsup by imad last updated on 05/May/19 $${find}\:\:\:\int\:\:\:\:\frac{{cos}\left(\mathrm{3}{x}\right)}{{ch}\left(\mathrm{2}{x}\right)}{dx}\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com