Question Number 27495 by abdo imad last updated on 07/Jan/18 $${find}\:\alpha\:{and}\:\beta\:{from}\:{R}\:/\int_{\mathrm{0}} ^{\pi} \left(\alpha{t}^{\mathrm{2}} +\beta{t}\right){cos}\left({nt}\right){dt}=\:\frac{\mathrm{1}}{{n}^{\mathrm{2}} } \\ $$$${for}\:{all}\:{number}\:{n}\:{from}\:{N}^{\ast\:} \:{then}\:{find} \\ $$$$\sum_{{n}=\mathrm{1}} ^{\propto} \:\:\frac{\mathrm{1}}{{n}^{\mathrm{2}} }\:. \\ $$…
Question Number 27481 by abdo imad last updated on 07/Jan/18 $${find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\propto} \:\frac{\sqrt{{x}}}{{e}^{{x}} −\mathrm{1}}{dx}\:. \\ $$ Commented by abdo imad last updated on 10/Jan/18 $${we}\:{have}\:{proved}\:{that}\:\int_{\mathrm{0}}…
Question Number 93004 by john santu last updated on 10/May/20 $$\int\:\frac{\mathrm{sin}^{−\mathrm{1}} \left(\mathrm{sin}\:\left(\mathrm{x}\right)\right)}{\mathrm{sin}\:^{\mathrm{4}} \left(\mathrm{x}\right)+\mathrm{cos}\:^{\mathrm{2}} \left(\mathrm{x}\right)}\:\mathrm{dx}\:? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 93005 by i jagooll last updated on 10/May/20 $$\int\:\mathrm{sec}\:\mathrm{x}\:\sqrt{\mathrm{sec}\:\mathrm{x}+\mathrm{tan}\:\mathrm{x}}\:\mathrm{dx}\:=\: \\ $$ Answered by john santu last updated on 10/May/20 $$\int\:\mathrm{sec}\:\mathrm{x}\:\sqrt{\mathrm{sec}\:\mathrm{x}+\mathrm{tan}\:\mathrm{x}}\:\mathrm{dx}\: \\ $$$$\mathrm{set}\:\sqrt{\mathrm{sec}\:\mathrm{x}+\mathrm{tan}\:\mathrm{x}}\:=\:\mathrm{r}\: \\…
Question Number 27464 by tawa tawa last updated on 07/Jan/18 $$\mathrm{Show}\:\mathrm{that}:\:\:\:\:\int_{\:\mathrm{0}} ^{\:\mathrm{2}\pi} \:\frac{\mathrm{cos}\left(\mathrm{3x}\right)}{\mathrm{5}\:−\:\mathrm{4cos}\left(\mathrm{x}\right)}\:\mathrm{dx}\:\:=\:\:\frac{\pi}{\mathrm{12}} \\ $$ Commented by abdo imad last updated on 07/Jan/18 $${let}\:{put}\:{I}=\:\int_{\mathrm{0}} ^{\mathrm{2}\pi}…
Question Number 92993 by mathmax by abdo last updated on 10/May/20 $${calculate}\:\:\int_{−\infty} ^{+\infty} \:\frac{{cos}\left({cosx}−{sinx}\right)}{{x}^{\mathrm{2}} \:+\mathrm{4}}{dx} \\ $$ Commented by mathmax by abdo last updated on…
Question Number 158517 by cortano last updated on 05/Nov/21 $$\:\:\:\vartheta\:=\int_{\:\mathrm{0}} ^{\:\pi/\mathrm{2}} \frac{{dx}}{\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{sin}\:^{\mathrm{2}} {x}}\right)^{\mathrm{2}} }\:? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 92976 by frc2crc last updated on 10/May/20 $${define} \\ $$$$\Delta_{{n}} =\frac{{n}\left(\mathrm{1}+{n}\right)}{\mathrm{2}} \\ $$$${find}\:{a}\:{closer}\:{form}\:{for} \\ $$$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\Delta_{{n}} ^{{m}} } \\ $$ Answered by…
Question Number 92971 by abdomathmax last updated on 10/May/20 $$\left.\mathrm{1}\right)\:{decompose}\:{F}\left({x}\right)\:=\frac{\mathrm{1}}{{x}^{\mathrm{4}} \left({x}−\mathrm{3}\right)^{\mathrm{5}} } \\ $$$$\left.\mathrm{2}\right){calculate}\:\int_{\mathrm{5}} ^{+\infty} \:\frac{{dx}}{{x}^{\mathrm{4}} \left({x}−\mathrm{3}\right)^{\mathrm{5}} } \\ $$ Commented by mathmax by abdo…
Question Number 92960 by i jagooll last updated on 10/May/20 $$\int\:\frac{\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}\:\mathrm{dx}}{\left(\mathrm{1}+\mathrm{cos}\:\mathrm{x}\right)^{\mathrm{2}} }\: \\ $$ Answered by i jagooll last updated on 10/May/20 $$\frac{\mathrm{1}−\mathrm{cos}\:^{\mathrm{2}} \mathrm{x}}{\left(\mathrm{1}+\mathrm{cos}\:\mathrm{x}\right)^{\mathrm{2}}…