Question Number 53599 by maxmathsup by imad last updated on 23/Jan/19 $$\left.\mathrm{1}\right)\:{calculate}\:{A}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{x}^{{n}−\mathrm{1}} }{{e}^{{x}} \:+\mathrm{1}}\:{dx}\:\:\:{with}\:{n}\:{integr}\:{natural}\:\:\left({n}\geqslant\mathrm{2}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{x}}{{e}^{{x}} \:+\mathrm{1}}{dx} \\ $$ Commented…
Question Number 119070 by benjo_mathlover last updated on 22/Oct/20 $$\int\:\frac{{x}^{\mathrm{2}} −{x}+\mathrm{6}}{{x}^{\mathrm{3}} +\mathrm{3}{x}}\:{dx}\: \\ $$$$\int\:\frac{\mathrm{5}{x}^{\mathrm{2}} +\mathrm{3}{x}−\mathrm{2}}{{x}^{\mathrm{3}} +\mathrm{2}{x}^{\mathrm{2}} }\:{dx}\: \\ $$ Answered by Olaf last updated on…
Question Number 53536 by gunawan last updated on 23/Jan/19 $$\mathrm{If}\:\left[{x}\right]\:\mathrm{stands}\:\mathrm{for}\:\mathrm{the}\:\mathrm{gratest}\:\mathrm{integer}\:\mathrm{function} \\ $$$$\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\int_{\mathrm{4}} ^{\mathrm{10}} \frac{\left[{x}^{\mathrm{2}} \right]}{\left[{x}^{\mathrm{2}} −\mathrm{28}{x}+\mathrm{196}\right]+\left[{x}^{\mathrm{2}} \right]}\:{dx}\:\mathrm{is} \\ $$$$ \\ $$ Answered by tanmay.chaudhury50@gmail.com last…
Question Number 119038 by MJS_new last updated on 21/Oct/20 $$\underset{−\pi/\mathrm{4}} {\overset{+\pi/\mathrm{4}} {\int}}\frac{\sqrt{\mathrm{1}+\mathrm{tan}\:{x}}}{\:\sqrt{\mathrm{1}−\mathrm{tan}\:{x}}}{dx} \\ $$ Answered by mindispower last updated on 21/Oct/20 $$=\int_{−\frac{\pi}{\mathrm{4}}} ^{\frac{\pi}{\mathrm{4}}} \frac{\sqrt{\mathrm{1}−{tg}\left({x}\right)}}{\:\sqrt{\mathrm{1}+{tg}\left({x}\right)}}{dx},{I}=\int\frac{\sqrt{\mathrm{1}+{tg}\left({x}\right)}}{\:\sqrt{\mathrm{1}−{tg}\left({x}\right)}}{dx} \\…
Question Number 53483 by dwdkswd last updated on 22/Jan/19 Commented by maxmathsup by imad last updated on 22/Jan/19 $${let}\:{A}_{{s}} =\int_{\mathrm{0}} ^{\infty} \:\:\frac{{x}^{{s}} }{{e}^{{x}} −\mathrm{1}}\:{dx}\:\Rightarrow{A}_{{s}} =\int_{\mathrm{0}}…
Question Number 119021 by A8;15: last updated on 21/Oct/20 Answered by MJS_new last updated on 21/Oct/20 $$\int\frac{\sqrt{\mathrm{sin}\:{x}}}{\:\sqrt{\mathrm{sin}\:{x}}+\sqrt{\mathrm{cos}\:{x}}}{dx}=\int\frac{\sqrt{\mathrm{tan}\:{x}}}{\mathrm{1}+\sqrt{\mathrm{tan}\:{x}}}{dx}= \\ $$$$\:\:\:\:\:\left[{t}=\sqrt{\mathrm{tan}\:{x}}\:\rightarrow\:{dx}=\frac{\mathrm{2}{t}}{{t}^{\mathrm{4}} +\mathrm{1}}{dt}\right] \\ $$$$=\mathrm{2}\int\frac{{t}^{\mathrm{2}} }{\left({t}+\mathrm{1}\right)\left({t}^{\mathrm{4}} +\mathrm{1}\right)}{dt} \\…
Question Number 184552 by Frix last updated on 08/Jan/23 $${I}_{\mathrm{1}} =\underset{\mathrm{0}} {\overset{\infty} {\int}}\left(\frac{\sqrt{{x}+\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}}}{\:\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}}−\frac{\sqrt{\mathrm{2}}}{\:\sqrt{{x}}}\right){dx}=? \\ $$$${I}_{\mathrm{2}} =\underset{\mathrm{0}} {\overset{\infty} {\int}}\left(\frac{\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}}{\:\sqrt{{x}+\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}}}−\frac{\sqrt{{x}}}{\:\sqrt{\mathrm{2}}}\right){dx}=? \\ $$ Answered…
Question Number 53477 by maxmathsup by imad last updated on 22/Jan/19 $${let}\:{f}\left({a}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{dt}}{\:\sqrt{{x}+{a}}\:+\mathrm{3}} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}\left({a}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{also}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{dt}}{\:\sqrt{{x}+{a}}\left(\sqrt{{x}+{a}}\:+\mathrm{3}\right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{3}\right)\:{find}\:{the}\:{values}\:{of}\:{integrals}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{dt}}{\:\sqrt{{x}+\mathrm{1}}+\mathrm{3}}\:\:{and}\:\int_{\mathrm{0}}…
Question Number 53476 by maxmathsup by imad last updated on 22/Jan/19 $${let}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{{x}} \:{t}\sqrt{\mathrm{2}{t}−\mathrm{1}}{dt}\:\:\:\:{calculate}\:\mid{sup}_{\mathrm{1}\leqslant{x}\leqslant\mathrm{2}} \:{f}\left({x}\right)\:−{inf}_{\mathrm{1}\leqslant{x}\leqslant\mathrm{2}} {f}\left({x}\right)\mid \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 53474 by maxmathsup by imad last updated on 22/Jan/19 $${calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{\mathrm{5}^{\mathrm{2}{x}+\mathrm{1}} \:−\mathrm{2}^{\mathrm{2}{x}−\mathrm{1}} }{\mathrm{10}^{{x}} }\:{dx} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on…