Question Number 81165 by abdomathmax last updated on 09/Feb/20 $${let}\:{f}\left({x}\right)=\frac{\mathrm{1}}{{x}^{\mathrm{2}} −\mathrm{2}\left({cos}\theta\right){x}\:+\mathrm{1}} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}^{\left({n}\right)} \left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:\int_{\mathrm{0}} ^{\infty} \:{f}\left({x}\right){dx} \\ $$$$\left.\mathrm{3}\right)\:{find}\:\int_{\mathrm{0}} ^{\infty} \:{f}^{\left({n}\right)} \left({x}\right){dx} \\ $$…
Question Number 146697 by ArielVyny last updated on 15/Jul/21 $$\forall{t}\geqslant−\mathrm{1},{F}\left({t}\right)=\frac{\mathrm{2}}{\pi}\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \sqrt{\mathrm{1}+{tcos}^{\mathrm{2}} \varphi}{d}\varphi \\ $$$$\left.\mathrm{1}\right)\:{Show}\:{that}\:\forall{t}\leqslant−\mathrm{1}\:{F}\left({t}\right)=\sqrt{\mathrm{1}+{t}}{F}\left(−\frac{\mathrm{1}}{\mathrm{1}+{t}}\right) \\ $$$$\left.\mathrm{2}\right)\:{show}\:{that}\:{if}\:\mathrm{0}\leqslant{t}_{\mathrm{1}} \:, \\ $$$$\mathrm{0}\leqslant{F}\left({t}_{\mathrm{2}} \right)−{F}\left({t}_{\mathrm{1}} \right)\leqslant\frac{{t}_{\mathrm{2}} −{t}_{\mathrm{1}} }{\mathrm{4}} \\…
Question Number 146669 by Ar Brandon last updated on 14/Jul/21 $$\int_{\mathrm{0}} ^{\pi} \left(\mathrm{a}−\mathrm{e}^{−\mathrm{ix}} \right)^{\mathrm{n}} \left(\mathrm{a}−\mathrm{e}^{\mathrm{ix}} \right)^{\mathrm{n}} \mathrm{cos}\left(\mathrm{nx}\right)\mathrm{dx} \\ $$ Answered by mindispower last updated on…
Question Number 81100 by jagoll last updated on 09/Feb/20 $$\int\:\frac{{x}\:{dx}}{\left(\mathrm{tan}\:{x}+\mathrm{cot}\:{x}\right)^{\mathrm{2}} }\:=\:? \\ $$ Commented by mind is power last updated on 09/Feb/20 $${tan}\left({x}\right)+{cot}\left({x}\right)=\frac{\mathrm{1}}{{sin}\left({x}\right){cos}\left({x}\right)} \\ $$$$\Leftrightarrow\int{xsin}^{\mathrm{2}}…
Question Number 146619 by mnjuly1970 last updated on 14/Jul/21 $$ \\ $$$$\:\:\:\:{solve}\:::\:\:\:\left(\:{x}\:\in\:\mathbb{R}\:\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left[\:{x}\:\right]\:=\:\left[\:{x}^{\:\mathrm{2}} −\:{x}\:−\mathrm{6}\:\right] \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:{note}::\:\:\:\left[{x}\:\right]\::=\:{max}\:\left\{\:{q}\:\in\:\mathbb{Z}\:\mid\:{q}\:\leqslant\:{x}\:\right\} \\ $$ Answered by mindispower last…
Question Number 146597 by iloveisrael last updated on 14/Jul/21 $$\:\:\:\:\int\:\frac{\mathrm{cos}\:\mathrm{5x}+\mathrm{cos}\:\mathrm{4x}}{\mathrm{1}−\mathrm{2cos}\:\mathrm{3x}}\:\mathrm{dx}\:=?\: \\ $$$$\:\:\int\:\frac{\sqrt{\mathrm{tan}\:\mathrm{x}}}{\mathrm{sin}\:\mathrm{2x}}\:\mathrm{dx}\:=? \\ $$$$\:\:\int\:\frac{\mathrm{dx}}{\:\sqrt{\mathrm{cos}\:^{\mathrm{3}} \mathrm{x}\:\mathrm{sin}\:^{\mathrm{5}} \mathrm{x}}}\:=? \\ $$ Answered by gsk2684 last updated on 14/Jul/21…
Question Number 146584 by mnjuly1970 last updated on 14/Jul/21 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:……{nice}\:…\:…\:…\:{calculus}…… \\ $$$$\: \\ $$$$\Omega=\:\int_{\mathrm{0}} ^{\:\mathrm{4}} {x}^{\:\mathrm{2}} \:{d}\:\left(\lfloor{x}+\lfloor{x}\:+\lfloor{x}+\lfloor{x}\rfloor\rfloor\rfloor\right)=?\: \\ $$$$ \\ $$ Terms of…
Question Number 146582 by iloveisrael last updated on 14/Jul/21 $$\:\:\:\int\:\mathrm{tan}\:^{\mathrm{4}} \mathrm{x}\:\mathrm{cos}\:^{\mathrm{2}} \mathrm{x}\:\mathrm{dx}\:=? \\ $$ Answered by bobhans last updated on 14/Jul/21 $$\mathrm{I}=\int\:\left(\mathrm{sec}\:^{\mathrm{2}} \mathrm{x}−\mathrm{1}\right)^{\mathrm{2}} \mathrm{cos}\:^{\mathrm{2}} \mathrm{x}\:\mathrm{dx}…
Question Number 81043 by john santu last updated on 09/Feb/20 $$\int\:\frac{\mathrm{2}{e}^{\mathrm{2}{x}} −{e}^{{x}} }{\:\sqrt{\mathrm{3}{e}^{\mathrm{2}{x}} −\mathrm{6}{e}^{{x}} −\mathrm{1}}}\:{dx} \\ $$ Commented by john santu last updated on 09/Feb/20…
Question Number 146577 by bekzodjumayev last updated on 14/Jul/21 Commented by bekzodjumayev last updated on 14/Jul/21 $${Help} \\ $$$$ \\ $$ Answered by Ar Brandon…