Question Number 128721 by rs4089 last updated on 09/Jan/21 $$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{ln}\:\mathrm{x}}{{x}\left({x}^{\mathrm{2}} +\mathrm{1}\right)}\:\mathrm{dx} \\ $$ Commented by Dwaipayan Shikari last updated on 09/Jan/21 $$\frac{\mathrm{1}}{\mathrm{2}}\int_{\mathrm{0}} ^{\mathrm{1}}…
Question Number 128710 by rs4089 last updated on 09/Jan/21 $$\int{e}^{{x}} \left(\frac{\mathrm{1}+{sinx}+{cosx}}{{cos}^{\mathrm{2}} {x}}\right)\:{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 128707 by mnjuly1970 last updated on 09/Jan/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…\mathrm{nice}\:\:\mathrm{calculus}… \\ $$$${prove}\:\:{that}::\: \\ $$$$\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\infty} \frac{{ln}\left(\mathrm{1}+\varphi^{\mathrm{2}} {x}^{\mathrm{2}} \right)}{\mathrm{1}+\pi^{\mathrm{2}} {x}^{\mathrm{2}} }\:{dx}={ln}\left(\frac{\pi+\varphi}{\pi}\right) \\ $$$$\varphi::=\:\:{golen}\:{ratio}… \\ $$$$ \\…
Question Number 128702 by bemath last updated on 09/Jan/21 $$\:\mathrm{If}\:\frac{\mathrm{sin}\:^{\mathrm{4}} \mathrm{x}}{\mathrm{2}}\:+\:\frac{\mathrm{cos}\:^{\mathrm{4}} \mathrm{x}}{\mathrm{3}}\:=\:\frac{\mathrm{1}}{\mathrm{5}}\:\mathrm{then}\: \\ $$$$\:\frac{\mathrm{sin}\:^{\mathrm{8}} \mathrm{x}}{\mathrm{8}}\:+\:\frac{\mathrm{cos}\:^{\mathrm{8}} \mathrm{x}}{\mathrm{27}}\:=\:? \\ $$ Answered by liberty last updated on 09/Jan/21…
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}}…