Question Number 28067 by abdo imad last updated on 19/Jan/18 $${let}\:{give}\:{f}\left({x}\right)=\:\frac{\mathrm{1}}{\mathrm{2}+{cosx}}\:\:\:{fonction}\:\mathrm{2}\pi\:{periodic}\:{even}. \\ $$$${developp}\:{f}\:\:{at}\:{fourier}\:{series}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 93587 by M±th+et+s last updated on 13/May/20 $$\int\frac{{x}+\mathrm{1}}{{x}^{\mathrm{2}} −\frac{\mathrm{1}+\sqrt{\mathrm{5}}}{\mathrm{2}}{x}+\mathrm{1}}{dx} \\ $$ Answered by niroj last updated on 13/May/20 $$\:\:\:\:\mathrm{I}=\:\int\:\frac{\:\:\mathrm{x}+\mathrm{1}}{\mathrm{x}^{\mathrm{2}} −\frac{\mathrm{1}+\sqrt{\mathrm{5}}}{\mathrm{2}}\mathrm{x}+\mathrm{1}}\mathrm{dx} \\ $$$$\:=\:\int\:\frac{\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{2x}−\frac{\mathrm{1}+\sqrt{\mathrm{5}}}{\mathrm{2}}\right)+\:\frac{\mathrm{5}+\sqrt{\mathrm{5}}}{\mathrm{4}}}{\mathrm{x}^{\mathrm{2}} −\frac{\mathrm{1}+\sqrt{\mathrm{5}}}{\mathrm{2}}\mathrm{x}+\mathrm{1}}\mathrm{dx}…
Question Number 28041 by suraj kumar last updated on 19/Jan/18 $$\int\frac{\varkappa^{\mathrm{2}} }{\left(\varkappa\mathrm{sin}\varkappa+\mathrm{cos}\varkappa\right)^{\mathrm{2}} }\mathrm{d}\left(\varkappa\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 28038 by abdo imad last updated on 19/Jan/18 $${let}\:{give}\:{f}\left({x}\right)=\sqrt{{x}+{y}}\:+\mathrm{1}\:\:{and}\:{D}=\left\{\left({x},{y}\right)\in{R}^{\mathrm{2}} /\:\mathrm{0}\leqslant{x}\leqslant\mathrm{1}\:\right. \\ $$$$\left.{and}\:−\mathrm{1}\leqslant{y}\leqslant\mathrm{1}\right\}\:\:{find}\:{the}\:{value}\:{of}\:\:\int\int\:{f}\left({x},{y}\right){dxdy}\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 28035 by abdo imad last updated on 18/Jan/18 $${find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:{x}\frac{{arctan}\left(\mathrm{2}{x}\right)}{\left(\mathrm{2}+{x}^{\mathrm{2}} \right)^{\mathrm{2}} }{dx}\:. \\ $$ Commented by abdo imad last updated on 23/Jan/18…
Question Number 159106 by Ar Brandon last updated on 13/Nov/21 $$\int_{\mathrm{0}} ^{\pi} \frac{\mathrm{sin}\left({nz}\right)}{\mathrm{z}^{\mathrm{4}} \mathrm{sin}\left(\pi{z}\right)}{dz} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 28033 by abdo imad last updated on 18/Jan/18 $$\left.\mathrm{1}\right)\:{find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{ln}\left({x}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }\:{dx} \\ $$$$\left.\mathrm{2}\right)\:\:{find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{xln}\left({x}\right)}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\mathrm{2}} }{dx}\:. \\ $$ Commented by abdo…
Question Number 93553 by Ar Brandon last updated on 13/May/20 $$\int{ln}\left(\mathrm{1}+\mathrm{e}^{\mathrm{u}} \right)\mathrm{du} \\ $$ Commented by Tony Lin last updated on 13/May/20 $${let}\:−{e}^{{u}} ={z}\:\:{dz}={zdu} \\…
Question Number 159080 by qaz last updated on 12/Nov/21 $$\underset{\mathrm{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\mathrm{n}!\left(\mathrm{n}^{\mathrm{4}} +\mathrm{n}^{\mathrm{2}} +\mathrm{1}\right)}=? \\ $$ Answered by mindispower last updated on 13/Nov/21 $$=\underset{{n}\geqslant\mathrm{0}} {\sum}\frac{\mathrm{1}}{{n}!\left({n}^{\mathrm{2}}…
Question Number 159069 by mnjuly1970 last updated on 12/Nov/21 Terms of Service Privacy Policy Contact: info@tinkutara.com