Question Number 74224 by mathmax by abdo last updated on 20/Nov/19 $${find}\:\int\:\:\:\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\frac{\mathrm{1}}{\mathrm{4}}} \:{cos}\left(\frac{\mathrm{1}}{\mathrm{2}}{arctan}\left(\frac{\mathrm{1}}{{x}}\right)\right){dx}\:\:{and} \\ $$$$\int\:\:\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\frac{\mathrm{1}}{\mathrm{4}}} {sin}\left(\frac{\mathrm{1}}{\mathrm{2}}{arctan}\left(\frac{\mathrm{1}}{{x}}\right)\right){dx} \\ $$ Commented by mathmax by abdo…
Question Number 139762 by mathdanisur last updated on 01/May/21 $${x};{y};{z}>\mathrm{0},\:\gamma\geqslant\mathrm{0},\:{x}^{\mathrm{3}} +{y}^{\mathrm{3}} +{z}^{\mathrm{3}} +{xyz}=\mathrm{4} \\ $$$${proof}:\:\left({x}+{y}+{z}\right)^{\mathrm{3}} +\gamma\left({x}^{\mathrm{3}} +{y}^{\mathrm{3}} +{z}^{\mathrm{3}} \right)\geqslant\mathrm{27}+\mathrm{3}\gamma \\ $$ Answered by mindispower last…
Question Number 74225 by mathmax by abdo last updated on 20/Nov/19 $${let}\:{p}\left({x}\right)=\left(\mathrm{1}+{jx}\right)^{{n}} −\left(\mathrm{1}−{jx}\right)^{{n}} \:\:{with}\:{j}={e}^{\frac{{i}\mathrm{2}\pi}{\mathrm{3}}} \\ $$$$\left.\mathrm{1}\right)\:{determine}\:{the}\:{roots}\:{of}\:{p}\left({x}\right)\:{and}\:{factorize}\:{P}\left({x}\right)\:{inside}\:{C}\left[{x}\right] \\ $$$$\left.\mathrm{2}\right)\:{decompose}\:{the}\:{fraction}\:{F}\left({x}\right)=\frac{\mathrm{1}}{{p}\left({x}\right)} \\ $$ Answered by mind is power…
Question Number 139756 by cherokeesay last updated on 01/May/21 Answered by mr W last updated on 01/May/21 Commented by mr W last updated on 01/May/21…
Question Number 74223 by mathmax by abdo last updated on 20/Nov/19 $${calculate}\:\:{f}\left({a}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{{x}^{\mathrm{2}} +{ax}+\mathrm{1}}{dx}\:\:\:{and}\:{g}\left({a}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{xdx}}{\:\sqrt{{x}^{\mathrm{2}} +{ax}+\mathrm{1}}} \\ $$$${with}\:\:\mid{a}\mid<\mathrm{2} \\ $$$$\left.\mathrm{2}\right){find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{{x}^{\mathrm{2}} +\sqrt{\mathrm{2}}{x}+\mathrm{1}}{dx}\:{and}\:\int_{\mathrm{0}}…
Question Number 8685 by Rasheed Soomro last updated on 23/Oct/16 $$\mathrm{Divide}\:\mathrm{a}\:\mathrm{circle}\:\mathrm{in}\:\mathrm{two}\:\mathrm{equal}\:\mathrm{parts} \\ $$$$\mathrm{by}\:\mathrm{drawing}\:\mathrm{an}\:\mathrm{arc}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 74218 by malikmasood3535@gmail.com last updated on 20/Nov/19 $${verify}\:{that}\:{y}\left({x}\right)={e}^{{x}} \left(\mathrm{cos}\:{e}^{{x}} −{e}^{{x}} \mathrm{sin}\:{e}^{{x}} \right)\:{is}\:{the}\:{solution}\:{of}\:{integral}\:{equation}\:{y}\left({x}\right)=\left(\mathrm{1}−{xe}^{\mathrm{2}{x}} \right)\mathrm{cos}\:\mathrm{1}−{e}^{\mathrm{2}{x}} \mathrm{sin}\:\mathrm{1}+\underset{\mathrm{0}} {\overset{{x}} {\int}}\left\{\mathrm{1}−\left({x}−{t}\right){e}^{\mathrm{2}{x}} \right\}{y}\left({t}\right){dt} \\ $$ Answered by mind is…
Question Number 8683 by 314159 last updated on 21/Oct/16 Commented by prakash jain last updated on 21/Oct/16 $${x}^{\mathrm{4}} −\mathrm{4}{cx}^{\mathrm{2}} +\mathrm{6}{x}^{\mathrm{2}} +{x}+\mathrm{1}=\left({x}−{p}\right)^{\mathrm{2}} \left({x}−{a}\right)\left({x}−{b}\right) \\ $$$$={x}^{\mathrm{4}} −\left(\mathrm{2}{p}+{a}+{b}\right){x}^{\mathrm{3}}…
Question Number 74219 by MASANJAJ last updated on 20/Nov/19 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 8681 by arinto27 last updated on 21/Oct/16 Terms of Service Privacy Policy Contact: info@tinkutara.com