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…
Question Number 33257 by prof Abdo imad last updated on 14/Apr/18 $${let}\:{g}\left({x}\right)=\:\frac{\mathrm{1}}{\mathrm{1}+{x}^{\mathrm{4}} } \\ $$$$\left.\mathrm{1}\right)\:{find}\:{g}^{\left({n}\right)} \left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{g}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{3}\right)\:{if}\:{g}\left({x}\right)=\Sigma\:{u}_{{n}} \:{x}^{{n}} \:\:\:{find}\:{the}\:{sequence}\:{u}_{{n}} \\ $$…
0-x-1-ln-F-x-5-cos-pix-x-1-F-x-5-cos-pix-x-1-dx-F-x-Fib-x-xth-Extended-fibonacci-number-f-R-R-1-5-2-
Question Number 98776 by M±th+et+s last updated on 16/Jun/20 $$\int_{\mathrm{0}} ^{\infty} \frac{\left({x}−\mathrm{1}\right)}{{ln}\left({F}\left({x}\right)\sqrt{\mathrm{5}}+{cos}\left(\pi{x}\right)\left(\varphi\right)^{−{x}} −\mathrm{1}\right)\sqrt{{F}\left({x}\right)\sqrt{\mathrm{5}}+{cos}\left(\pi{x}\right)\left(\varphi\right)^{−{x}} −\mathrm{1}}}{dx} \\ $$$$ \\ $$$${F}\left({x}\right)={Fib}\left({x}\right)={xth}\:{Extended}\:{fibonacci}\:{number} \\ $$$${f}:\mathbb{R}\rightarrow\mathbb{R} \\ $$$$\varphi=\frac{\mathrm{1}+\sqrt{\mathrm{5}}}{\mathrm{2}} \\ $$ Terms…
Question Number 33232 by prof Abdo imad last updated on 13/Apr/18 $${find}\:{the}\:{value}\:{of}\:\:\:\int_{−\infty} ^{+\infty} \:\:\:\frac{{x}\:{sin}\left(\mathrm{2}{x}\right)}{\left(\mathrm{1}+\mathrm{4}{x}^{\mathrm{2}} \right)^{\mathrm{2}} }\:{dx}\:. \\ $$ Commented by prof Abdo imad last updated…
Question Number 33223 by prof Abdo imad last updated on 13/Apr/18 $${let}\:\:{A}_{{n}} \:=\int_{−\infty} ^{+\infty} \:\:\:\frac{{e}^{{i}\pi{x}} }{\mathrm{1}+{x}+{x}^{\mathrm{2}} \:+…{x}^{{n}−\mathrm{1}} }\:\:{with}\:{n}\geqslant\mathrm{3}\:{integr} \\ $$$${find}\:{the}\:{value}\:{of}\:{A}_{{n}} \:. \\ $$ Terms of…
Question Number 33222 by prof Abdo imad last updated on 13/Apr/18 $${let}\:{give}\:{n}\:\geqslant\mathrm{3}\:{integr}\:\:{calculate} \\ $$$${I}_{{n}} =\:\int_{−\infty} ^{+\infty} \:\:\:\:\:\frac{{dx}}{\mathrm{1}+{x}\:+{x}^{\mathrm{2}} \:+….+{x}^{{n}−\mathrm{1}} } \\ $$ Terms of Service Privacy…