Question Number 48040 by maxmathsup by imad last updated on 18/Nov/18 $${let}\:{f}\left(\alpha\right)=\int_{−\infty} ^{+\infty} \:\:\frac{{xsin}\left(\alpha{x}\right)}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\mathrm{2}} }{dx} \\ $$$${calculate}\:{f}\left(\alpha\right)\:{and}\:{f}^{'} \left(\alpha\right).\left(\alpha\:{from}\:{R}\right)\:. \\ $$ Commented by Abdo msup.…
Question Number 179107 by Acem last updated on 25/Oct/22 $${I}=\:\int\:\frac{{x}^{\mathrm{2}} }{\mathrm{sin}\:\left(\mathrm{2arctan}\:\left({e}^{{x}} \right)\right)}\:{dx}\:\:,\:{Find}\:{I} \\ $$ Answered by MJS_new last updated on 25/Oct/22 $$\int\frac{{x}^{\mathrm{2}} }{\mathrm{sun}\:\mathrm{2arctan}\:\mathrm{e}^{{x}} }{dx}=\int{x}^{\mathrm{2}} \mathrm{cosh}\:{x}\:{dx}=…
Question Number 113564 by bemath last updated on 14/Sep/20 $$\:\:\int_{\mathrm{1}} ^{\mathrm{2}} {f}\left(\mathrm{2}{x}+\mathrm{1}\right)\:{dx}\:=\:\mathrm{3}\:{and}\: \\ $$$$\:\:\int_{\mathrm{1}} ^{\mathrm{2}} \left({x}^{\mathrm{2}} \:{f}\left({x}^{\mathrm{3}} +\mathrm{2}\right)\right){dx}\:=\:\mathrm{5} \\ $$$${then}\:\int_{\mathrm{5}} ^{\mathrm{10}} {f}\left({x}\right)\:{dx}\:=\:? \\ $$ Answered…
Question Number 113562 by mathmax by abdo last updated on 14/Sep/20 $$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{dx}}{\mathrm{x}^{\mathrm{4}} +\mathrm{ix}^{\mathrm{2}} \:+\mathrm{2}} \\ $$ Answered by Olaf last updated on 14/Sep/20…
Question Number 113565 by bemath last updated on 14/Sep/20 Answered by bobhans last updated on 14/Sep/20 $$\int\left(\mathrm{5x}^{\mathrm{2}} +\mathrm{10}\right)\left(\mathrm{x}^{\mathrm{3}} +\mathrm{6x}\right)^{\mathrm{3}} \mathrm{dx}\:= \\ $$$$\int\mathrm{5}\left(\mathrm{x}^{\mathrm{2}} +\mathrm{2}\right)\left(\mathrm{x}^{\mathrm{3}} +\mathrm{6x}\right)^{\mathrm{3}} \mathrm{dx}=…
Question Number 48027 by ajfour last updated on 18/Nov/18 Commented by ajfour last updated on 18/Nov/18 $${If}\:{OP}\:=\:\mathrm{1}\:{and}\:{all}\:{areas}\:{like} \\ $$$${ABPA}\:\:{are}\:{equal}\:{to}\:{all}\:{areas}\: \\ $$$${like}\:{OBPCO}\:\:{then}\:{find}\:{ellipse} \\ $$$${parameters}\:\boldsymbol{{a}}\:{and}\:\boldsymbol{{b}}. \\ $$…
Question Number 179066 by cortano1 last updated on 24/Oct/22 $$\:\:\:\:\:\mathrm{If}\:\mathrm{f}\left(\mathrm{x}\right)=\int\:\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{x}^{\mathrm{2}} +\mathrm{tan}\:\mathrm{x}}\:\mathrm{dx}\: \\ $$$$\:\:\:\:\mathrm{then}\:\int\:\frac{\mathrm{tan}\:\mathrm{x}}{\mathrm{x}^{\mathrm{2}} +\mathrm{tan}\:\mathrm{x}}\:\mathrm{dx}\:=? \\ $$ Answered by Ar Brandon last updated on 24/Oct/22…
Question Number 47985 by maxmathsup by imad last updated on 17/Nov/18 $${calculate}\:{I}=\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\mathrm{1}+\mathrm{2}\sqrt{{x}−{x}^{\mathrm{2}} }}{dx}\:\:{and}\:{J}\:=\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\mathrm{1}−\mathrm{2}\sqrt{{x}−{x}^{\mathrm{2}} }}{dx} \\ $$ Commented by MJS last updated…
Question Number 179042 by mnjuly1970 last updated on 23/Oct/22 Answered by Ar Brandon last updated on 23/Oct/22 $${I}=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{\mathrm{cos}^{\mathrm{2}} {x}}{\mathrm{sin}^{\mathrm{4}} {x}+\mathrm{cos}^{\mathrm{2}} {x}}{dx}=\int_{\mathrm{0}} ^{\infty} \frac{{dt}}{{t}^{\mathrm{4}}…
Question Number 47967 by Rio Michael last updated on 17/Nov/18 $${A}\:{particle}\:{moves}\:{in}\:{a}\:{linear}\:{scare}\:{such}\:{that}\:{acceleration} \\ $$$${after}\:{t}\:{seconds}\:{is}\:{a}\:{ms}^{−\mathrm{2}} \:{where}\:{a}=\:\mathrm{2}{t}^{\mathrm{2}} +\:{t}.{If}\:{its}\:{initial}\: \\ $$$${velocity}\:{was}\:\mathrm{3}{ms}^{−\mathrm{1}} \:{find}\:{an}\:{expression}\:{for}\:{S},{the}\:{distance}\:{in}\:{meters} \\ $$$${traveled}\:{from}\:{start}\:{t}\:{seconds}. \\ $$ Answered by ajfour…