Question Number 162112 by amin96 last updated on 26/Dec/21 $$\int\frac{\:\boldsymbol{{cos}}\left(\boldsymbol{{x}}\right)}{\left(\mathrm{1}−\boldsymbol{{cos}}\left(\boldsymbol{{x}}\right)\right)^{\mathrm{2}} }\boldsymbol{{dx}}=? \\ $$ Answered by Ar Brandon last updated on 26/Dec/21 $${I}=\int\frac{\mathrm{cos}{x}}{\left(\mathrm{1}−\mathrm{cos}{x}\right)^{\mathrm{2}} }{dx}=\int\frac{\mathrm{cos}^{\mathrm{2}} \frac{{x}}{\mathrm{2}}−\mathrm{sin}^{\mathrm{2}} \frac{{x}}{\mathrm{2}}}{\mathrm{4sin}^{\mathrm{4}}…
Question Number 96567 by bemath last updated on 02/Jun/20 Commented by john santu last updated on 02/Jun/20 $$\mathrm{set}\:{y}\:=\:\sqrt{−\mathrm{1}+\sqrt{\frac{\mathrm{4}}{{x}}−\mathrm{3}}}\: \\ $$$${x}\:=\:\frac{\mathrm{4}}{\mathrm{3}+\left(\mathrm{1}+{y}^{\mathrm{2}} \right)^{\mathrm{2}} } \\ $$$$\underset{\mathrm{0}} {\overset{\mathrm{1}}…
Question Number 162099 by mnjuly1970 last updated on 26/Dec/21 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\mathscr{PROVE}\:\:\:\mathscr{THAT}\:\: \\ $$$$\:\:\:\:\Omega=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\:\mathrm{Li}_{\:\mathrm{2}} \:\left({x}\:\right).\:\mathrm{ln}\left(\:{x}\:\right)}{{x}}\:{dx}\:\overset{?} {=}\:\frac{\:−\pi^{\:\mathrm{4}} }{\mathrm{90}} \\ $$$$\:\:\:\:\:−−−−−−−−−− \\ $$$$\:\:\:\:\:\Omega=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \mathrm{ln}\:\left({x}\:\right)\underset{{n}=\mathrm{1}}…
Question Number 96554 by student work last updated on 02/Jun/20 $$\int\frac{\mathrm{dx}}{\mathrm{x}!}=? \\ $$ Commented by student work last updated on 02/Jun/20 $$\mathrm{or}\:\int\frac{\mathrm{x}}{\mathrm{x}!}\mathrm{dx}=? \\ $$ Commented…
Question Number 162073 by mnjuly1970 last updated on 26/Dec/21 $$ \\ $$$$\:\:\:\:{prove}\:{that} \\ $$$$ \\ $$$$\:\Omega\:=\int_{−\infty} ^{\:+\infty} \frac{\:{cos}\:\left({x}\right)}{\left(\mathrm{2}+\:\mathrm{2}{x}\:+{x}^{\:\mathrm{2}} \right)^{\:\mathrm{2}} }\:{dx}\:=\:\frac{\pi}{{e}}\:{cos}\left(\mathrm{1}\right) \\ $$ Answered by mindispower…
Question Number 162066 by amin96 last updated on 25/Dec/21 $$\underset{\boldsymbol{\mathrm{n}}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{\boldsymbol{\mathrm{n}}} \boldsymbol{\mathrm{H}}_{\boldsymbol{\mathrm{n}}} }{\boldsymbol{\mathrm{n}}^{\mathrm{2}} }=??? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 96524 by selea last updated on 02/Jun/20 $$\int\left(\mathrm{sinx}^{\mathrm{cosx}^{\mathrm{sinx}} } −\mathrm{cosx}^{\mathrm{sinx}^{\mathrm{cosx}} } \right)\mathrm{dx} \\ $$ Commented by Sourav mridha last updated on 02/Jun/20 it should be impose intervels..like [0,π/2].. otherwise this is not done..…
Question Number 162055 by Astro last updated on 25/Dec/21 $$\int{e}^{\mathrm{2x}} \sqrt{\left(\mathrm{1}\:−{e}^{\mathrm{2}{x}} \right)}{dx} \\ $$ Answered by aleks041103 last updated on 25/Dec/21 $${u}=\mathrm{1}−{e}^{\mathrm{2}{x}} \\ $$$${du}=−\mathrm{2}{e}^{\mathrm{2}{x}} {dx}\Rightarrow{e}^{\mathrm{2}{x}}…
Question Number 162054 by amin96 last updated on 25/Dec/21 Answered by aleks041103 last updated on 25/Dec/21 $$\underset{{R}} {\int\int}{ydxdy}\:=\:{I} \\ $$$${R}=\left\{\left({x},{y}\right)\mid\mathrm{2}{x}<{y}<\mathrm{3}−{x}^{\mathrm{2}} ,\:−\mathrm{3}<{x}<\mathrm{1}\right\} \\ $$$$\Rightarrow{I}=\underset{{R}} {\int\int}{ydxdy}=\int_{−\mathrm{3}} ^{\:\mathrm{1}}…
Question Number 96495 by abdomathmax last updated on 01/Jun/20 $$\mathrm{calculateI}\:=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \mathrm{ln}\left(\mathrm{cosx}\:+\mathrm{sinx}\right)\mathrm{dx} \\ $$$$\mathrm{and}\:\mathrm{J}\:=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \mathrm{ln}\left(\mathrm{cosx}−\mathrm{sinx}\right)\mathrm{dx} \\ $$ Answered by Sourav mridha last updated on…