Question Number 178922 by mnjuly1970 last updated on 22/Oct/22 Answered by ARUNG_Brandon_MBU last updated on 22/Oct/22 $$\frac{\mathrm{1}}{{n}\left({n}+\mathrm{1}\right)\left({n}+\mathrm{2}\right)}=\frac{\frac{\mathrm{1}}{\mathrm{2}}}{{n}}−\frac{\mathrm{1}}{{n}+\mathrm{1}}+\frac{\frac{\mathrm{1}}{\mathrm{2}}}{{n}+\mathrm{2}} \\ $$$$\left(\frac{\mathrm{1}}{{n}\left({n}+\mathrm{1}\right)\left({n}+\mathrm{2}\right)}\right)^{\mathrm{2}} =\frac{\mathrm{1}}{\mathrm{4}}\left(\frac{\mathrm{1}}{{n}}−\frac{\mathrm{2}}{{n}+\mathrm{1}}+\frac{\mathrm{1}}{{n}+\mathrm{2}}\right)^{\mathrm{2}} \\ $$$$=\frac{\mathrm{1}}{\mathrm{4}}\left(\frac{\mathrm{1}}{{n}^{\mathrm{2}} }+\frac{\mathrm{4}}{\left({n}+\mathrm{1}\right)^{\mathrm{2}} }+\frac{\mathrm{1}}{\left({n}+\mathrm{2}\right)^{\mathrm{2}} }+\mathrm{2}\left(\frac{−\mathrm{2}}{{n}\left({n}+\mathrm{1}\right)}+\frac{−\mathrm{2}}{\left({n}+\mathrm{1}\right)\left({n}+\mathrm{2}\right)}+\frac{\mathrm{1}}{{n}\left({n}+\mathrm{2}\right)}\right)\right)…
Question Number 178879 by mathlove last updated on 22/Oct/22 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 113323 by AbhishekBasnet last updated on 12/Sep/20 Answered by bemath last updated on 12/Sep/20 $$\mathrm{let}\:\mathrm{a}+\mathrm{bx}\:=\:\mathrm{u}\:,\:\mathrm{x}\:=\:\frac{\mathrm{u}−\mathrm{a}}{\mathrm{b}} \\ $$$$\int\:\left(\frac{\mathrm{u}−\mathrm{a}}{\mathrm{b}}\right)\mathrm{u}^{\mathrm{3}} \left(\frac{\mathrm{du}}{\mathrm{b}}\right)\:=\:\frac{\mathrm{1}}{\mathrm{b}^{\mathrm{2}} }\int\:\left(\mathrm{u}^{\mathrm{4}} −\mathrm{au}^{\mathrm{3}} \right)\mathrm{du} \\ $$$$=\frac{\mathrm{1}}{\mathrm{b}^{\mathrm{2}}…
Question Number 178832 by Spillover last updated on 22/Oct/22 Answered by ARUNG_Brandon_MBU last updated on 22/Oct/22 $${a}.\:\int\frac{\mathrm{y}\left(\mathrm{y}−\mathrm{8}\right)}{\left(\mathrm{y}−\mathrm{4}\right)^{\mathrm{2}} }{d}\mathrm{y}=\int\frac{\left(\left(\mathrm{y}−\mathrm{4}\right)+\mathrm{4}\right)\left(\left(\mathrm{y}−\mathrm{4}\right)−\mathrm{4}\right)}{\left(\mathrm{y}−\mathrm{4}\right)^{\mathrm{2}} }{d}\mathrm{y} \\ $$$$\:\:\:\:=\int\frac{\left(\mathrm{y}−\mathrm{4}\right)^{\mathrm{2}} −\mathrm{16}}{\left(\mathrm{y}−\mathrm{4}\right)^{\mathrm{2}} }{d}\mathrm{y}=\int\left(\mathrm{1}−\frac{\mathrm{16}}{\left(\mathrm{y}−\mathrm{4}\right)^{\mathrm{2}} }\right){d}\mathrm{y} \\…
Question Number 113275 by bemath last updated on 12/Sep/20 $$\:\int\:\frac{\mathrm{dx}}{\mathrm{3sin}\:\mathrm{x}+\mathrm{sin}\:^{\mathrm{3}} \mathrm{x}}\:? \\ $$ Answered by bemath last updated on 12/Sep/20 $$\mathrm{I}\:=\:\int\:\frac{\mathrm{dx}}{\mathrm{sin}\:\mathrm{x}\left(\mathrm{3}+\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}\right)} \\ $$$$\mathrm{I}=\int\:\frac{\mathrm{sin}\:\mathrm{x}\:\mathrm{dx}}{\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}\left(\mathrm{3}+\mathrm{sin}\:^{\mathrm{2}}…
Question Number 47737 by ajfour last updated on 14/Nov/18 $$\:\:{I}\:=\:\int_{\mathrm{0}} ^{\:\:{L}/\mathrm{2}} \frac{{Rz}^{\mathrm{2}} }{\left({d}^{\mathrm{2}} +{z}^{\mathrm{2}} \right)\sqrt{{d}^{\mathrm{2}} +{z}^{\mathrm{2}} −{R}^{\mathrm{2}} }}\:{dz} \\ $$$$\:{Find}\:{I}\:. \\ $$ Answered by MJS…
Question Number 47720 by maxmathsup by imad last updated on 13/Nov/18 $${find}\:\int\:{ln}\left(\mathrm{1}+{x}^{\mathrm{3}} \right){dx} \\ $$ Answered by MJS last updated on 14/Nov/18 $$\int\mathrm{ln}\:\left({x}^{\mathrm{3}} +\mathrm{1}\right)\:{dx}= \\…
Question Number 113218 by mnjuly1970 last updated on 11/Sep/20 Answered by mathdave last updated on 12/Sep/20 $${the}\:{integral}\:{doen}'{t}\:{converge} \\ $$$$\because{divergent} \\ $$ Commented by MJS_new last…
Question Number 47677 by vajpaithegrate@gmail.com last updated on 13/Nov/18 $$\int\mathrm{x}^{\mathrm{x}\:} \mathrm{dx}= \\ $$ Commented by maxmathsup by imad last updated on 13/Nov/18 $${at}\:{form}\:{of}\:{serie}\:\: \\ $$$$\int\:{x}^{{x}}…
Question Number 47675 by Rio Michael last updated on 13/Nov/18 $${A}\:{particle}\:{of}\:{mass}\:\mathrm{4}{kg}\:{was}\:{at}\:{rest}\:{a}\:{a}\:{point}\:{of}\:{position}\:{vector} \\ $$$${i}\:+\mathrm{4}{j}.\:{A}\:{force}\:{F}\:{was}\:{applied}\:{to}\:{it}\:{and}\:{it}\:{moved}\:{at}\:{a}\:{velocity} \\ $$$${of}\:\left(\mathrm{3}{i}\:+\:\mathrm{7}{j}\right){ms}^{−\mathrm{1}} \:\:\:{after}\:{a}\:{time}\:{of}\:\:\mathrm{5}{seconds}.\:{Find}\: \\ $$$$\left.{a}\right)\:{the}\:{magnitude}\:{of}\:{F} \\ $$$$\left.{b}\right)\:{The}\:{speed}\:{at}\:{which}\:{it}\:{moves},{Hence}, \\ $$$$\left.{c}\right)\:{The}\:{distance}\:{it}\:{covered}. \\ $$$$ \\…