Question Number 118230 by bobhans last updated on 16/Oct/20 $$\mathrm{If}\:\int\:\frac{\left(\sqrt{\mathrm{x}}\right)^{\mathrm{5}} }{\left(\sqrt{\mathrm{x}}\right)^{\mathrm{7}} +\mathrm{x}^{\mathrm{6}} }\:\mathrm{dx}\:=\:\mathrm{p}\:\mathrm{ln}\:\left(\frac{\mathrm{x}^{\mathrm{q}} }{\mathrm{x}^{\mathrm{q}} +\mathrm{1}}\right)\:+\:\mathrm{C}\: \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{p}\:\mathrm{and}\:\mathrm{q}. \\ $$ Answered by bemath last updated on…
Question Number 183761 by MikeH last updated on 29/Dec/22 $$\mathrm{Solve}\:\mathrm{the}\:\mathrm{differential}\:\mathrm{equation}\:\mathrm{for}\:\mathrm{the}\:\mathrm{function} \\ $$$$\mathrm{given}\:\mathrm{by}\:{U}\left({x},{t}\right). \\ $$$$\begin{cases}{\frac{\partial{U}}{\partial{t}}\:=\:\mathrm{2}\frac{\partial^{\mathrm{2}} {U}}{\partial{x}^{\mathrm{2}} }\:,\:\mathrm{0}\:<\:{x}\:<\:\pi}\\{{U}\left(\mathrm{0},{t}\right)\:=\:\mathrm{0},\:{U}\left(\pi,{t}\right)\:=\:\mathrm{0},\:{t}\:>\:\mathrm{0}}\end{cases} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{U}\left({x},\mathrm{0}\right)\:=\:\mathrm{25}{x} \\ $$ Answered by leodera last updated…
Question Number 118218 by bemath last updated on 16/Oct/20 $$\:\int\:\mathrm{sin}\:^{\mathrm{6}} \left(\mathrm{2}{x}\right){dx}\:=?\: \\ $$ Answered by bobhans last updated on 16/Oct/20 $$\:\mathrm{Solve}\:\int\:\mathrm{sin}\:^{\mathrm{6}} \left(\mathrm{2x}\right)\:\mathrm{dx}\:. \\ $$$$\mathrm{by}\:\mathrm{De}'\mathrm{moivre}\:\mathrm{theorem}\: \\…
Question Number 52683 by maxmathsup by imad last updated on 11/Jan/19 $${let}\:{f}\left(\lambda\right)\:=\int_{−\infty} ^{+\infty} \:\:\frac{{sin}\left(\lambda{x}\right)}{\left({x}^{\mathrm{2}} \:+\mathrm{2}\lambda{x}\:+\mathrm{1}\right)^{\mathrm{2}} }{dx}\:\:\:\:{with}\:\mid\lambda\mid<\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{the}\:{value}\:{of}\:{f}\left(\lambda\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{−\infty} ^{+\infty} \:\:\:\frac{{sin}\left(\frac{{x}}{\mathrm{2}\:}\right)}{\left({x}^{\mathrm{2}} \:\:+{x}+\mathrm{1}\right)^{\mathrm{2}} }{dx} \\…
Question Number 52680 by maxmathsup by imad last updated on 11/Jan/19 $${let}\:{f}_{{n}} \left({x}\right)=\frac{{sin}\left({nx}\right)}{{n}^{\mathrm{3}} }\:\:\:{and}\:{f}\left({x}\right)=\sum_{{n}=\mathrm{1}} ^{\infty} \:{f}_{{n}} \left({x}\right) \\ $$$${calculate}\:\int_{\mathrm{0}} ^{\pi} \:{f}\left({x}\right){dx}\:. \\ $$ Commented by…
Question Number 52667 by gunawan last updated on 11/Jan/19 $$\int\frac{{x}^{\mathrm{4}} +\mathrm{1}}{{x}^{\mathrm{2}} \sqrt{{x}^{\mathrm{4}} −\mathrm{1}}}\:{dx} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 11/Jan/19 $$\int\frac{{x}^{\mathrm{2}} +\frac{\mathrm{1}}{{x}^{\mathrm{2}} }}{\:\sqrt{{x}^{\mathrm{2}}…
Question Number 118188 by mnjuly1970 last updated on 16/Oct/20 Commented by MJS_new last updated on 16/Oct/20 $${f}\left({x}\right)=\mathrm{e}^{−\frac{\mathrm{4}}{{x}^{\mathrm{2}} }} \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:{f}\left({x}\right)\:=\mathrm{0} \\ $$$$\underset{{x}\rightarrow\pm\infty} {\mathrm{lim}}\:{f}\left({x}\right)\:=\mathrm{1} \\…
Question Number 52649 by Tawa1 last updated on 10/Jan/19 $$\int\:\frac{\mathrm{4x}^{\mathrm{2}} \:+\:\mathrm{3}}{\left(\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{x}\:+\:\mathrm{1}\right)^{\mathrm{2}} }\:\mathrm{dx} \\ $$ Commented by maxmathsup by imad last updated on 10/Jan/19 $${et}\:{I}\:=\int\:\:\frac{\mathrm{4}{x}^{\mathrm{2}}…
Question Number 183709 by Michaelfaraday last updated on 30/Dec/22 Commented by Michaelfaraday last updated on 29/Dec/22 $${please}\:{who}\:{can}\:{help}\:{me}\:{on}\:{this} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 183706 by cortano1 last updated on 29/Dec/22 $$\:\:\:\:{A}=\int\:\frac{\mathrm{1}+\mathrm{cos}\:^{\mathrm{2}} {x}}{\mathrm{1}+\mathrm{sin}\:^{\mathrm{4}} {x}}\:{dx} \\ $$ Answered by Ar Brandon last updated on 29/Dec/22 $${A}=\int\frac{\mathrm{1}+\mathrm{cos}^{\mathrm{2}} {x}}{\mathrm{1}+\mathrm{sin}^{\mathrm{4}} {x}}{dx}=\int\frac{\mathrm{sec}^{\mathrm{4}}…