Question Number 164395 by amin96 last updated on 16/Jan/22 Answered by mnjuly1970 last updated on 17/Jan/22 Commented by mnjuly1970 last updated on 17/Jan/22 $$\:\:{thank}\:{you}\:{so}\:{much}\:{my}\:{dear}\:{friend} \\…
Question Number 33310 by abdo imad last updated on 14/Apr/18 $${let}\:{consider}\:{the}\:\mathrm{2}\pi\:{periodic}?{function}\:\:{f}\left({x}\right)\:={e}^{{x}} \\ $$$$\left.\mathrm{1}\right)\:{developp}\:{f}\:{at}\:{fourier}\:{serie} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\:\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}^{\mathrm{2}} \:+\mathrm{1}} \\ $$ Terms of Service Privacy…
Question Number 33311 by abdo imad last updated on 14/Apr/18 $${let}\:\:{f}\left({x}\right)\:=\mid{sinx}\mid\:\:\left(\mathrm{2}\pi\:{periodic}\:{even}\right) \\ $$$${developp}\:{f}\:{at}\:{fourier}\:{serie} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 33297 by abdo imad last updated on 14/Apr/18 $${find}\:\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:{ln}\left(\mathrm{1}+{x}\:{sin}\theta\right){d}\theta\:\:\:{with}\:\:\mathrm{0}<{x}<\mathrm{1} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:{ln}\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}{sin}\theta\right){d}\theta \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 98831 by bramlex last updated on 16/Jun/20 Commented by john santu last updated on 16/Jun/20 $$\int\:\frac{\mathrm{2}\:\mathrm{dx}}{\mathrm{x}^{\mathrm{8}} \left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{7}} }\right)}\:=\:\int\:\frac{\mathrm{2d}\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{7}} }\right)}{\mathrm{7}\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{7}} }\right)} \\ $$$$=\:\frac{\mathrm{2}}{\mathrm{7}}\:\mathrm{ln}\:\left(\frac{\mathrm{x}^{\mathrm{7}} −\mathrm{1}}{\mathrm{x}^{\mathrm{7}}…
Question Number 98826 by bramlex last updated on 16/Jun/20 $${Given}\:\underset{\mathrm{0}} {\overset{\infty} {\int}}\:\frac{{dx}}{{a}^{\mathrm{2}} +{x}^{\mathrm{2}} }\:=\:\frac{\pi}{\mathrm{2}{a}} \\ $$$${find}\:\underset{\mathrm{0}} {\overset{\infty} {\int}}\:\frac{{dx}}{\left({a}^{\mathrm{2}} +{x}^{\mathrm{2}} \right)^{\mathrm{3}} }\:? \\ $$ Commented by…
Question Number 98821 by bramlex last updated on 16/Jun/20 $$\int\overset{\infty} {\:}_{\mathrm{0}} \frac{{dx}}{{a}^{\mathrm{2}} +{x}^{\mathrm{2}} }\:=\:? \\ $$ Answered by Ar Brandon last updated on 16/Jun/20 $$\left.\mathcal{I}=\frac{\mathrm{1}}{\mathrm{a}}\left[\mathrm{arctan}\left(\frac{\mathrm{x}}{\mathrm{a}}\right)\right]_{\mathrm{0}}…
Question Number 33259 by prof Abdo imad last updated on 14/Apr/18 $${find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{arctan}\left(\mathrm{2}{x}\right)}{{a}^{\mathrm{2}} \:+{x}^{\mathrm{2}} }\:{dx}\:{with}\:{a}\neq\mathrm{0} \\ $$ Commented by prof Abdo imad last updated…
Question Number 33258 by prof Abdo imad last updated on 14/Apr/18 $${if}\:\:\:\frac{\mathrm{1}}{\mathrm{1}+{cosx}}\:=\:\frac{{a}_{\mathrm{0}} }{\mathrm{2}}\:+\sum_{{n}\geqslant\mathrm{1}} {a}_{{n}} {cos}\left({nx}\right)\:{calculate}\:{a}_{\mathrm{0}} \\ $$$${and}\:{a}_{{n}} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 164328 by mnjuly1970 last updated on 16/Jan/22 $$ \\ $$$$\:\:\:\:\:{solve} \\ $$$$\:\:\:\:\:\:\:\:\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\:{cos}^{\mathrm{2}{n}} \left({x}\right)}{{n}!}\:=\:\sqrt[{\mathrm{4}}]{{e}}\:\:\:\:\:\:\:\:\:\:\:\blacksquare\: \\ $$$$\:\:\:\:\:\:\:\:−−−−−−− \\ $$$$\:\: \\ $$ Answered by…