Question Number 47540 by maxmathsup by imad last updated on 11/Nov/18 $${find}\:\int\:{arctan}\left(\sqrt{{x}}\right){dx}. \\ $$ Commented by maxmathsup by imad last updated on 16/Nov/18 $${let}\:{I}=\int\:{arctan}\left(\sqrt{{x}}\right){dx}\:{changement}\:\sqrt{{x}}={t}\:{give} \\…
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Question Number 178563 by zaheen last updated on 18/Oct/22 $$\int{e}^{{x}^{\mathrm{2}} } {dx}=? \\ $$ Answered by Acem last updated on 18/Oct/22 $$ \\ $$$${We}\:{have}\:\int{e}^{−{x}^{\mathrm{2}} }…
Question Number 178550 by cortano1 last updated on 18/Oct/22 Answered by Ar Brandon last updated on 18/Oct/22 $${I}=\int_{\frac{\pi}{\mathrm{12}}} ^{\frac{\pi}{\mathrm{8}}} \frac{\left(\mathrm{7}+\mathrm{cos4}\vartheta\right)\mathrm{cos2}\vartheta}{\mathrm{1}−\mathrm{cos4}\vartheta}\left(\frac{\mathrm{9}−\mathrm{cos4}\vartheta}{\mathrm{sin2}\vartheta}\right)^{\mathrm{2021}} {d}\vartheta \\ $$$$\:\:=\int_{\frac{\pi}{\mathrm{12}}} ^{\frac{\pi}{\mathrm{8}}} \frac{\left(\mathrm{6}+\mathrm{2cos}^{\mathrm{2}}…
Question Number 113004 by malwan last updated on 10/Sep/20 $${prove}\:{that} \\ $$$$\:_{\mathrm{0}} \int^{\:\infty} \:{cos}\left({x}^{\mathrm{2}} \right){dx}\:=\:\:_{\mathrm{0}} \int^{\:\infty} {sin}\left({x}^{\mathrm{2}} \right){dx}\:=\frac{\sqrt{\pi}}{\mathrm{2}\sqrt{\mathrm{2}}} \\ $$ Answered by mathdave last updated…
Question Number 112997 by malwan last updated on 10/Sep/20 $$\int\frac{\:{tan}\:{x}\:{dx}}{\:\sqrt{{sec}^{\mathrm{3}} \:{x}\:+\:\mathrm{1}}}\:=\:? \\ $$ Commented by MJS_new last updated on 10/Sep/20 $$\mathrm{sorry}\:\mathrm{I}\:\mathrm{haven}'\mathrm{t}\:\mathrm{got}\:\mathrm{the}\:\mathrm{time}\:\mathrm{to}\:\mathrm{finish}\:\mathrm{it}\:\mathrm{but} \\ $$$$\mathrm{the}\:\mathrm{path}\:\mathrm{is} \\ $$$$\int\frac{\mathrm{tan}\:{x}}{\:\sqrt{\mathrm{sec}^{\mathrm{3}}…
Question Number 112958 by mnjuly1970 last updated on 10/Sep/20 Commented by mathdave last updated on 11/Sep/20 Commented by mnjuly1970 last updated on 11/Sep/20 $${thank}\:{you}\:{sir}.. \\…
Question Number 178487 by cortano1 last updated on 17/Oct/22 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int\:\frac{{dx}}{\mathrm{cot}\:^{\mathrm{3}} {x}\:\mathrm{sin}\:^{\mathrm{7}} {x}}\:=? \\ $$ Answered by Frix last updated on 18/Oct/22 $$\int\frac{{dx}}{\mathrm{cot}^{\mathrm{3}} \:{x}\:\mathrm{sin}^{\mathrm{7}} \:{x}}=\int\frac{{dx}}{\mathrm{cos}^{\mathrm{3}} \:{x}\:\mathrm{sin}^{\mathrm{4}}…
Question Number 47387 by ARVIND DAYAMA last updated on 09/Nov/18 $$\mathscr{F}{ind}\int\sqrt{{sin}\mathrm{2}{x}}\:{dx}=?? \\ $$ Commented by MJS last updated on 09/Nov/18 $$\mathrm{look}\:\mathrm{at}\:\mathrm{the}\:\mathrm{comnents}\:\mathrm{to}\:\mathrm{question}\:\mathrm{42945},\:\mathrm{a} \\ $$$$\mathrm{path}\:\mathrm{is}\:\mathrm{given}\:\mathrm{there} \\ $$…
Question Number 47376 by vajpaithegrate@gmail.com last updated on 09/Nov/18 Answered by MJS last updated on 09/Nov/18 $${f}_{\mathrm{1}} :\:{y}={x}^{\mathrm{2}} −\mathrm{5}{x}+\mathrm{4} \\ $$$${f}_{\mathrm{2}} :\:{y}=\mathrm{1}−{x} \\ $$$${f}_{\mathrm{3}} :\:{y}=\mathrm{0}…