Question Number 137055 by mathmax by abdo last updated on 29/Mar/21 $$\mathrm{find}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\frac{\mathrm{dx}}{\left(\mathrm{1}+\mathrm{cosx}\:+\mathrm{3sinx}\right)^{\mathrm{2}} } \\ $$ Commented by MJS_new last updated on 30/Mar/21 $$\mathrm{0}\leqslant\left(\mathrm{1}+\mathrm{cos}\:{x}\:+\mathrm{3sin}\:{x}\right)^{\mathrm{2}}…
Question Number 137048 by mnjuly1970 last updated on 29/Mar/21 $$\:\:\:\:\:\:\:\:\:\:\:……..{advanced}\:\:…\:…\:…\:{calculus}……. \\ $$$$\:\:\:\:{evaluate}:::: \\ $$$$\:\:\:\:\:\:\boldsymbol{\chi}=\int_{\mathrm{0}} ^{\:\infty} {x}^{\mathrm{2}} \:{e}^{−{x}^{\mathrm{2}} } {ln}\left({x}\right)=??? \\ $$$$\:\: \\ $$ Answered by…
Question Number 71499 by petrochengula last updated on 16/Oct/19 Commented by petrochengula last updated on 16/Oct/19 $$\mathrm{help}\:\mathrm{2a} \\ $$ Answered by MJS last updated on…
Question Number 71490 by oyemi kemewari last updated on 16/Oct/19 Commented by mathmax by abdo last updated on 16/Oct/19 $${let}\:{A}=\int_{\mathrm{0}} ^{\frac{\mathrm{1}}{\mathrm{2}}} \:\frac{\mathrm{1}+\sqrt{\mathrm{3}}}{\left(^{\mathrm{4}} \sqrt{\left(\mathrm{1}+{x}\right)^{\mathrm{2}} \left(\mathrm{1}−{x}\right)^{\mathrm{6}} }\right.}{dx}\:\Rightarrow{A}=\left(\mathrm{1}+\sqrt{\mathrm{3}}\right)\int_{\mathrm{0}}…
Question Number 137004 by Mathspace last updated on 28/Mar/21 $${find}\:\int\:\frac{\sqrt{{x}}}{\:\sqrt{{x}−\mathrm{1}}+\sqrt{{x}+\mathrm{1}}}{dx} \\ $$ Answered by aleks041103 last updated on 28/Mar/21 $$\frac{\sqrt{{x}}}{\:\sqrt{{x}−\mathrm{1}}+\sqrt{{x}+\mathrm{1}}}= \\ $$$$=\frac{\sqrt{{x}}}{\:\sqrt{{x}−\mathrm{1}}+\sqrt{{x}+\mathrm{1}}}\:\frac{\sqrt{{x}+\mathrm{1}}−\sqrt{{x}−\mathrm{1}}}{\:\sqrt{{x}+\mathrm{1}}−\sqrt{{x}−\mathrm{1}}}= \\ $$$$=\sqrt{{x}}\left(\sqrt{{x}+\mathrm{1}}−\sqrt{{x}−\mathrm{1}}\right) \\…
Question Number 137003 by Mathspace last updated on 28/Mar/21 $${find}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\:\frac{{cos}^{\mathrm{5}} {t}}{{cos}\left(\mathrm{5}{t}\right)}{dt} \\ $$ Answered by bobhans last updated on 29/Mar/21 $$\mathrm{cos}\:\left(\mathrm{5t}\right)=\mathrm{cos}\:^{\mathrm{5}} \mathrm{t}−\mathrm{10sin}\:^{\mathrm{2}} \mathrm{t}\:\mathrm{cos}\:^{\mathrm{3}}…
Question Number 137001 by Mathspace last updated on 28/Mar/21 $${calculate}\:\:\int_{\mathrm{3}} ^{\infty} \:\frac{{dx}}{\left({x}^{\mathrm{2}} −\mathrm{4}\right)^{\mathrm{5}} \left({x}+\mathrm{1}\right)^{\mathrm{3}} } \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 136999 by mnjuly1970 last updated on 28/Mar/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:……{advanced}\:\:……\:\:\:{calculus}…. \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\infty} {ln}\left({x}\right).{sin}\left({x}\right).{e}^{−{x}} {dx}=? \\ $$$$\:\:\:\:\:\:\:\:\:\:\: \\ $$ Answered by mnjuly1970 last…
Question Number 136992 by liberty last updated on 28/Mar/21 $$\ell\:=\:\int\:\frac{\mathrm{cos}\:\mathrm{7x}−\mathrm{cos}\:\mathrm{8x}}{\mathrm{1}+\mathrm{2cos}\:\mathrm{5x}}\:\mathrm{dx}\:=? \\ $$ Answered by EDWIN88 last updated on 28/Mar/21 $$\:\ell\:=\:\int\:\frac{\mathrm{cos}\:\mathrm{7x}−\mathrm{cos}\:\mathrm{8x}}{\mathrm{1}+\mathrm{2cos}\:\mathrm{5x}}\:\mathrm{dx} \\ $$$$\mathrm{Simplify}\:\mathrm{the}\:\mathrm{integrand}\:\mathrm{by}\:\mathrm{Euler}'\mathrm{s}\:\mathrm{formula} \\ $$$$\frac{\mathrm{cos}\:\mathrm{7x}−\mathrm{cos}\:\mathrm{8x}}{\mathrm{1}+\mathrm{2cos}\:\mathrm{5x}}\:=\:\frac{\mathrm{e}^{\mathrm{i7x}} +\mathrm{e}^{−\mathrm{i7x}}…
Question Number 136968 by Eric002 last updated on 28/Mar/21 $$\left.\mathrm{1}\right)\int\frac{\mathrm{8}}{{x}^{\mathrm{2}} \sqrt{\mathrm{4}−{x}^{\mathrm{2}} }}{dx} \\ $$$$\left.\mathrm{2}\right)\int\frac{{x}−\mathrm{6}\:}{\mathrm{2}{x}^{\mathrm{2}} −\mathrm{5}{x}+\mathrm{3}} \\ $$ Answered by EDWIN88 last updated on 28/Mar/21 $$\left(\mathrm{1}\right)\int\:\frac{\mathrm{8}}{\mathrm{x}^{\mathrm{3}}…