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} \\ $$$${i}\:+\mathrm{4}{j}.\:{A}\:{force}\:{F}\:{was}\:{applied}\:{to}\:{it}\:{and}\:{it}\:{moved}\:{at}\:{a}\:{velocity} \\ $$$${of}\:\left(\mathrm{3}{i}\:+\:\mathrm{7}{j}\right){ms}^{−\mathrm{1}} \:\:\:{after}\:{a}\:{time}\:{of}\:\:\mathrm{5}{seconds}.\:{Find}\: \\ $$$$\left.{a}\right)\:{the}\:{magnitude}\:{of}\:{F} \\ $$$$\left.{b}\right)\:{The}\:{speed}\:{at}\:{which}\:{it}\:{moves},{Hence}, \\ $$$$\left.{c}\right)\:{The}\:{distance}\:{it}\:{covered}. \\ $$$$ \\…
Question Number 113203 by abdomsup last updated on 11/Sep/20 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dx}}{{x}^{\mathrm{4}} \:+\mathrm{2}{x}^{\mathrm{2}} +\mathrm{3}} \\ $$ Answered by 1549442205PVT last updated on 11/Sep/20 $$\mathrm{Consider}\:\mathrm{f}\left(\mathrm{z}\right)=\frac{\mathrm{1}}{\mathrm{z}^{\mathrm{4}} +\mathrm{2z}^{\mathrm{2}}…
Question Number 113198 by mnjuly1970 last updated on 11/Sep/20 $$\:\:\:\:\:\:\:\:\:….\:{calculus}…. \\ $$$$\:\:\:\:\:\:\mathscr{E}{valuate}\:::: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\mathrm{I}\::=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\mathrm{1}}{\:\sqrt{{x}\left({x}+\mathrm{1}\right)\left({x}+\mathrm{2}\right)\left({x}+\mathrm{3}\right)+\mathrm{1}}−\mathrm{3}{x}}{dx}=??? \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\mathscr{M}.\mathscr{N}.{july}\:\mathrm{1970}# \\ $$$$\:\: \\…
Question Number 47651 by prof Abdo imad last updated on 12/Nov/18 $${calculate}\:\:{A}_{{n}} =\int_{\mathrm{0}} ^{\mathrm{1}} \:\:{sin}\left(\left[{nx}\right]\right){e}^{−\mathrm{2}{x}} {dx}\:{with}\:{n} \\ $$$${integr}\:{natural}\:. \\ $$ Commented by maxmathsup by imad…
Question Number 178712 by mnjuly1970 last updated on 20/Oct/22 Answered by mr W last updated on 20/Oct/22 $$\frac{\mathrm{1}}{{n}}\left(\frac{\mathrm{1}}{\mathrm{4}{n}^{\mathrm{2}} −\mathrm{1}}\right)=\frac{\mathrm{1}}{\mathrm{2}{n}}\left(\frac{\mathrm{1}}{\mathrm{2}{n}−\mathrm{1}}−\frac{\mathrm{1}}{\mathrm{2}{n}+\mathrm{1}}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\frac{\mathrm{1}}{\mathrm{2}{n}−\mathrm{1}}+\frac{\mathrm{1}}{\mathrm{2}{n}+\mathrm{1}}−\frac{\mathrm{1}}{{n}} \\ $$$$ \\ $$$$\underset{{n}=\mathrm{1}}…