Question Number 128680 by mnjuly1970 last updated on 09/Jan/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…{nice}\:\:{calculus}… \\ $$$$\:\:\:\:\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\left(\mathrm{3}{n}+\mathrm{1}\right)\varphi^{\mathrm{3}{n}+\mathrm{1}} }\:=? \\ $$$$\varphi\:::\:\:{golden}\:\:{ratio}… \\ $$$$ \\ $$ Answered by mr W…
Question Number 63139 by Tawa1 last updated on 29/Jun/19 $$\underset{\mathrm{n}\:=\:\mathrm{1}} {\overset{\mathrm{m}} {\sum}}\:\frac{\mathrm{log}\:\mathrm{n}}{\mathrm{n}^{\mathrm{3}/\mathrm{2}} } \\ $$ Commented by Tawa1 last updated on 30/Jun/19 $$\mathrm{please}\:\mathrm{help}\:\mathrm{with}\:\mathrm{this}\:\mathrm{sir} \\ $$$$\:\mathrm{Test}\:\mathrm{for}\:\mathrm{convergence}.\:\:\:\:\:\underset{\mathrm{n}\:=\:\mathrm{1}}…
Question Number 128664 by bemath last updated on 09/Jan/21 $$\:\int_{\mathrm{0}} ^{\:\pi/\mathrm{2}} \left(\mathrm{1}−\mathrm{sin}\:\mathrm{x}+\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}−\mathrm{sin}\:^{\mathrm{3}} \mathrm{x}+\mathrm{sin}\:^{\mathrm{4}} \mathrm{x}−\mathrm{sin}\:^{\mathrm{5}} \mathrm{x}+…\right)\:\mathrm{dx}\:=? \\ $$ Answered by liberty last updated on 09/Jan/21…
Question Number 63117 by mugan deni last updated on 29/Jun/19 $$\int\frac{\mathrm{cos}\:{x}}{\mathrm{2}+\mathrm{3sin}\:{x}+\mathrm{sin}\:^{\mathrm{2}} {x}}{dx} \\ $$ Commented by mathmax by abdo last updated on 30/Jun/19 $${let}\:{I}\:=\int\:\:\frac{{cosx}}{{sin}^{\mathrm{2}} {x}+\mathrm{3}{sinx}\:+\mathrm{2}}{dx}\:\:{changement}\:{sinx}\:={t}\:{give}\:{cosxdx}\:={dt}\:\Rightarrow…
Question Number 63116 by mugan deni last updated on 29/Jun/19 $$\int\frac{\mathrm{1}+×}{\:\sqrt{\mathrm{1}+×^{\mathrm{2}} }}{dx} \\ $$ Commented by mathmax by abdo last updated on 30/Jun/19 $${let}\:{use}\:{the}\:{changement}\:{x}={tan}\theta\:\Rightarrow \\…
Question Number 128634 by liberty last updated on 09/Jan/21 $$\theta\:=\:\int\:\left(\mathrm{1}+\mathrm{4x}^{\mathrm{4}} \right)\mathrm{e}^{\mathrm{x}^{\mathrm{4}} } \:\mathrm{dx}\: \\ $$ Answered by john_santu last updated on 09/Jan/21 $$\theta=\int\:\mathrm{e}^{\mathrm{x}^{\mathrm{4}} } \:\mathrm{dx}\:+\:\int\:\mathrm{4x}^{\mathrm{4}}…
Question Number 128633 by Lordose last updated on 09/Jan/21 $$\Omega\:=\:\int_{\mathrm{0}} ^{\:\frac{\mathrm{1}}{\mathrm{3}}} \mathrm{x}^{\mathrm{2n}} \mathrm{ln}\left(\mathrm{1}−\mathrm{x}\right)\mathrm{dx} \\ $$ Answered by mathmax by abdo last updated on 09/Jan/21 $$\mathrm{let}\:\mathrm{try}\:\mathrm{another}\:\mathrm{way}\:\:\mathrm{x}=\frac{\mathrm{t}}{\mathrm{3}}\:\Rightarrow…
Question Number 63089 by mathmax by abdo last updated on 28/Jun/19 $${find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\frac{{dx}}{\mathrm{1}+\left({tanx}\right)^{\sqrt{\mathrm{2}}} }\:. \\ $$ Commented by edafe ovwie last updated on 29/Jun/19…
Question Number 63084 by mathmax by abdo last updated on 28/Jun/19 $${let}\:{f}\left({z}\right)\:=\frac{{cos}\left(\mathrm{3}{z}\right)}{{z}^{\mathrm{2}} } \\ $$$${calculate}\:{Res}\left({f},\mathrm{0}\right)\:. \\ $$ Commented by mathmax by abdo last updated on…
Question Number 128620 by Ahmed1hamouda last updated on 08/Jan/21 Answered by TheSupreme last updated on 09/Jan/21 $${u}={x}+{y} \\ $$$${v}={x}−{y} \\ $$$${x}=\frac{{u}+{v}}{\mathrm{2}} \\ $$$${y}=\frac{{u}−{v}}{\mathrm{2}} \\ $$$${J}=\begin{bmatrix}{\frac{\mathrm{1}}{\mathrm{2}}\:\:\:\:\:\frac{\mathrm{1}}{\mathrm{2}}}\\{\frac{\mathrm{1}}{\mathrm{2}}\:−\frac{\mathrm{1}}{\mathrm{2}}}\end{bmatrix}…