Question Number 173529 by Shrinava last updated on 13/Jul/22 $$\mathrm{Find}\:\mathrm{without}\:\mathrm{softs}:\:\:\:\Omega\:=\:\int_{\frac{\boldsymbol{\pi}}{\mathrm{5}}} ^{\:\frac{\mathrm{3}\boldsymbol{\pi}}{\mathrm{10}}} \:\frac{\mathrm{x}}{\mathrm{sin2x}}\:\mathrm{dx} \\ $$ Answered by Ar Brandon last updated on 13/Jul/22 $${I}=\int_{\frac{\pi}{\mathrm{5}}} ^{\frac{\mathrm{3}\pi}{\mathrm{10}}} \frac{{x}}{\mathrm{sin2}{x}}{dx}\:,\:{x}=\frac{\pi}{\mathrm{2}}−{u}\:\Rightarrow{I}=\int_{\frac{\pi}{\mathrm{5}}}…
Question Number 173535 by mnjuly1970 last updated on 13/Jul/22 Answered by mr W last updated on 13/Jul/22 $${in}\:{expansion}\:{of}\:\left({x}_{\mathrm{1}} +{x}_{\mathrm{2}} +{x}_{\mathrm{3}} +…+{x}_{{n}} \right)^{{m}} \\ $$$${the}\:{general}\:{term}\:{is}\:{x}_{\mathrm{1}} ^{{k}_{\mathrm{1}}…
Question Number 173531 by mnjuly1970 last updated on 13/Jul/22 $$ \\ $$$$\:\:\:\:{Q}: \\ $$$$\:\:{what}\:{is}\:{the}\:{greatest}\:{coefficient} \\ $$$$\:\:{of}\:{the}\:{following}\:\:{expansion}. \\ $$$$\:\:\:\:\:\:\:\mathrm{P}:=\:\left(\:{a}+\:{b}\:+{c}\:+{d}\:\right)^{\:\mathrm{10}} \\ $$$$\:\:\:\:\:\:\:−−−−−−− \\ $$ Answered by mr…
Question Number 107976 by anonymous last updated on 13/Aug/20 $${Rewrite}\:\mathrm{cos6}{x}\mathrm{cos}\:\mathrm{4}{x}\:{as}\:{a}\:{sum}\:{or} \\ $$$${difference} \\ $$ Answered by mathmax by abdo last updated on 13/Aug/20 $$\mathrm{cos}\left(\mathrm{4x}\right)\mathrm{cos}\left(\mathrm{6x}\right)\:=\frac{\mathrm{1}}{\mathrm{2}}\left\{\mathrm{cos}\left(\mathrm{10x}\right)\:+\mathrm{cos}\left(\mathrm{2x}\right)\right\} \\…
Question Number 173504 by AgniMath last updated on 12/Jul/22 Answered by behi834171 last updated on 12/Jul/22 $${A}=\sqrt{{x}}+\frac{\mathrm{1}}{\:\sqrt{{x}}}\Rightarrow{A}^{\mathrm{2}} ={x}+\frac{\mathrm{1}}{{x}}+\mathrm{2}=\mathrm{4}\Rightarrow{A}=\mathrm{2}\:\:.\:\:\blacksquare \\ $$ Commented by Rasheed.Sindhi last updated…
Question Number 173500 by Shrinava last updated on 12/Jul/22 $$\mathrm{Find}\:\mathrm{without}\:\mathrm{any}\:\mathrm{software}: \\ $$$$\Omega\:=\:\int\:\left(\mathrm{x}\:+\:\frac{\mathrm{5}}{\mathrm{x}}\right)\left(\mathrm{1}\:−\:\frac{\mathrm{5}}{\mathrm{x}^{\mathrm{2}} }\right)\mathrm{sin}\left(\mathrm{ln}\left(\mathrm{x}\:+\:\frac{\mathrm{5}}{\mathrm{x}}\right)\right)\mathrm{dx} \\ $$ Answered by thfchristopher last updated on 12/Jul/22 $$\mathrm{Let}\:{u}={x}+\frac{\mathrm{5}}{{x}} \\ $$$${du}=\left(\mathrm{1}−\frac{\mathrm{5}}{{x}^{\mathrm{2}}…
Question Number 173503 by Shrinava last updated on 12/Jul/22 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 173497 by SIENSE last updated on 12/Jul/22 $$\:\:\: \\ $$$$\:\:{Bonus}\:{du}\:{Mardi}\:\mathrm{12}/\mathrm{07}/\mathrm{2022} \\ $$$$\:\:\:\:{I}=\:\:\int_{\mathrm{0}} ^{\frac{\Pi}{\mathrm{2}}} \:\frac{{sin}^{\mathrm{2}} \left({x}\right)}{\mathrm{1}+{cos}^{\mathrm{2}} \left({x}\right)}{dx}\:=\:? \\ $$$$\:\:\:\:\:\:\:\:\:\:{J}\:\:=\:\int_{\mathrm{0}} ^{\frac{\Pi}{\mathrm{2}}} \:\frac{{dx}}{\mathrm{1}+{cos}^{\mathrm{2}} \left({x}\right)} \\ $$$$\:{I}\:=\:\int_{\mathrm{0}}…
Question Number 173489 by AgniMath last updated on 12/Jul/22 Answered by Rasheed.Sindhi last updated on 12/Jul/22 $${x}+{y}+{z}=\mathrm{0}\:;\:\frac{{x}^{\mathrm{2}} }{{yz}}+\frac{{y}^{\mathrm{2}} }{{zx}}+\frac{{z}^{\mathrm{2}} }{{xy}}=? \\ $$$$\:\frac{{x}^{\mathrm{2}} }{{yz}}+\frac{{y}^{\mathrm{2}} }{{zx}}+\frac{{z}^{\mathrm{2}} }{{xy}}=\:\frac{{x}^{\mathrm{3}}…
Question Number 173485 by mnjuly1970 last updated on 12/Jul/22 $$ \\ $$$$\:\:\:\:\:{Solve}\:\:\:\:\:\:\:\left({x}\:\in\:\mathbb{R}\:\right) \\ $$$$\:\:\:\:\:\:{x}\mathrm{2}^{\:\frac{\mathrm{1}}{{x}}} \:+\frac{\mathrm{1}}{{x}}\:\mathrm{2}^{\:{x}} =\:\mathrm{4} \\ $$$$\:\:\:\:\:\:\:\:−{Source}:\:{L}.{Panaitopol} \\ $$ Answered by aleks041103 last updated…