Question Number 128956 by mathmax by abdo last updated on 11/Jan/21 $$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\pi} \:\frac{\mathrm{sin}\left(\mathrm{2x}\right)}{\mathrm{3}+\mathrm{cos}\left(\mathrm{4x}\right)}\mathrm{dx} \\ $$ Answered by chengulapetrom last updated on 11/Jan/21 $${cos}\mathrm{4}{x}=\mathrm{2}{cos}^{\mathrm{2}} \mathrm{2}{x}−\mathrm{1}…
Question Number 128954 by mathmax by abdo last updated on 11/Jan/21 $$\mathrm{calculate}\:\:\mathrm{f}\left(\lambda\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{ln}\left(\mathrm{x}^{\mathrm{4}} \:+\lambda^{\mathrm{4}} \right)\mathrm{dx}\:\:\:\mathrm{with}\:\lambda>\mathrm{0}\:\mathrm{then}\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{ln}\left(\mathrm{1}+\mathrm{x}^{\mathrm{4}} \right)\mathrm{dx} \\ $$ Answered by…
Question Number 128955 by mathmax by abdo last updated on 11/Jan/21 $$\mathrm{find}\:\int_{\mathrm{0}} ^{\infty} \:\mathrm{e}^{−\mathrm{3x}} \mathrm{ln}\left(\mathrm{1}+\mathrm{e}^{\mathrm{2x}} \right)\mathrm{dx} \\ $$ Answered by Dwaipayan Shikari last updated on…
Question Number 128952 by mathmax by abdo last updated on 11/Jan/21 $$\mathrm{calculate}\:\mathrm{A}_{\mathrm{n}} =\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{dx}}{\left(\mathrm{x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{n}} }\:\:\:,\:\mathrm{n}\:\mathrm{integr}\:\mathrm{and}\:\mathrm{n}\geqslant\mathrm{1} \\ $$ Answered by Dwaipayan Shikari last updated…
Question Number 128953 by mathmax by abdo last updated on 11/Jan/21 $$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{ln}\left(\mathrm{1}+\mathrm{x}^{\mathrm{6}} \right)\mathrm{dx} \\ $$ Answered by Lordose last updated on 12/Jan/21 $$…
Question Number 128950 by mathmax by abdo last updated on 11/Jan/21 $$\mathrm{calculate}\:\mathrm{f}\left(\mathrm{a}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{dx}}{\left(\mathrm{x}^{\mathrm{2}} +\mathrm{a}\right)^{\mathrm{2}} \left(\mathrm{x}^{\mathrm{2}} −\mathrm{x}+\mathrm{1}\right)^{\mathrm{2}} }\:\:\mathrm{with}\:\mathrm{a}>\mathrm{0} \\ $$ Terms of Service Privacy Policy…
Question Number 128951 by mathmax by abdo last updated on 11/Jan/21 $$\mathrm{solve}\:\mathrm{y}^{,,} −\mathrm{2y}^{'} \:+\mathrm{3y}\:=\mathrm{xe}^{−\mathrm{x}} \mathrm{sin}\left(\mathrm{2x}\right)\:\:\mathrm{with}\:\mathrm{y}\left(\mathrm{0}\right)=\mathrm{0}\:\mathrm{and}\:\mathrm{y}^{'} \left(\mathrm{0}\right)=−\mathrm{1} \\ $$ Answered by mnjuly1970 last updated on 11/Jan/21…
Question Number 128947 by ajfour last updated on 11/Jan/21 Commented by ajfour last updated on 11/Jan/21 $${Find}\:{radius}\:{of}\:{the}\:{blue}\:{arc}. \\ $$ Answered by mr W last updated…
Question Number 63410 by aliesam last updated on 03/Jul/19 Commented by mathmax by abdo last updated on 03/Jul/19 $$\left.\mathrm{2}\right)\:{let}\:{I}\:=\int\:\:\:\frac{{xdx}}{\mathrm{1}+{sinx}}\:\:\:{changement}\:{tan}\left(\frac{{x}}{\mathrm{2}}\right)={t}\:{give}\: \\ $$$${I}\:=\:\int\:\:\:\frac{\mathrm{2}{arctan}\left({t}\right)}{\left(\mathrm{1}+\frac{\mathrm{2}{t}}{\mathrm{1}+{t}^{\mathrm{2}} }\right)\left(\mathrm{1}+{t}^{\mathrm{2}} \right)}{dt}\:=\:\mathrm{2}\int\:\:\:\:\frac{{arctan}\left({t}\right)}{\mathrm{1}+{t}^{\mathrm{2}} \:+\mathrm{2}{t}}\:{dt}\:=\mathrm{2}\:\int\:\:\:\frac{{arctan}\left({t}\right)}{\left({t}+\mathrm{1}\right)^{\mathrm{2}} }\:{dt}\:\:…
Question Number 128944 by ajfour last updated on 11/Jan/21 Commented by ajfour last updated on 11/Jan/21 $${Find}\:{radius}\:{ratio}\:\frac{{R}}{{r}}. \\ $$$${The}\:{polygon}\:{is}\:{a}\:{regular} \\ $$$${pentagon}. \\ $$ Answered by…