Question Number 39336 by rahul 19 last updated on 05/Jul/18 Commented by ajfour last updated on 05/Jul/18 $$−\mathrm{2}\:{is}\:{even}\:{or}\:{odd}\:? \\ $$ Commented by rahul 19 last…
Question Number 104871 by I want to learn more last updated on 24/Jul/20 Answered by mathmax by abdo last updated on 24/Jul/20 $$\mathrm{A}_{\mathrm{p}} =\int_{\mathrm{0}} ^{\mathrm{1}}…
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Question Number 104851 by bemath last updated on 24/Jul/20 $$\int\:\frac{\sqrt{{x}^{\mathrm{2}} −\mathrm{9}}}{{x}^{\mathrm{3}} }\:{dx}\: \\ $$ Answered by Dwaipayan Shikari last updated on 24/Jul/20 $$\int\frac{{t}^{\mathrm{2}} {dt}}{{x}^{\mathrm{4}} }\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{x}^{\mathrm{2}}…
Question Number 170384 by amin96 last updated on 22/May/22 $$\boldsymbol{\mathrm{Prove}}\:\boldsymbol{\mathrm{that}} \\ $$$$\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \boldsymbol{\mathrm{ln}}\left(\boldsymbol{\mathrm{a}}−\boldsymbol{\mathrm{sin}}^{\mathrm{2}} \left(\boldsymbol{\mathrm{x}}\right)\right)\boldsymbol{\mathrm{dx}}=\pi\boldsymbol{\mathrm{ln}}\left(\sqrt{\frac{\boldsymbol{\mathrm{a}}−\mathrm{1}}{\boldsymbol{\mathrm{a}}}}+\mathrm{1}\right)+\frac{\pi}{\mathrm{2}}\boldsymbol{\mathrm{ln}}\left(\frac{\boldsymbol{\mathrm{a}}}{\mathrm{4}}\right) \\ $$$$\boldsymbol{\mathrm{a}}>\mathrm{0}\:\:\:\:\boldsymbol{\mathrm{I}{m}}\left\{\boldsymbol{{a}}\right\}\neq\mathrm{0}\:\: \\ $$ Terms of Service Privacy Policy Contact:…
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Question Number 39292 by math khazana by abdo last updated on 04/Jul/18 $${let}\:{f}\left({x}\right)=\:{arctan}\left(\mathrm{2}{x}\right) \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}^{\left({n}\right)} \left({x}\right)\:{then}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right)\:{developp}\:{f}\:{at}\:{integr}\:{serie} \\ $$$$\left.\mathrm{3}\right)\:{let}\:{F}\left({t}\right)=\:\int_{\mathrm{0}} ^{{t}} \:\:{arctan}\left(\mathrm{2}{x}\right){dx} \\ $$$${developp}\:{F}\:{at}\:{integr}\:{serie}…
Question Number 104826 by Study last updated on 24/Jul/20 $$\int\mathrm{3}^{{x}+\mathrm{2}} \centerdot{lnsin}\mathrm{3}^{{x}} {dx}=??? \\ $$ Commented by Study last updated on 24/Jul/20 $${help}\:{me} \\ $$ Answered…
Question Number 170349 by antoineop last updated on 21/May/22 $$ \\ $$$${help}\:{please}\:\: \\ $$$$\overset{\infty} {\int}_{\mathrm{1}} \left(\frac{\mathrm{1}}{{t}}−\mathrm{sin}^{−\mathrm{1}} \left(\frac{\mathrm{1}}{{t}}\right)\right)\:{dt} \\ $$$${I}\:{can}\:{show}\:{that}\:{it}\:{is}\:{equal}\:{to} \\ $$$$−\underset{{n}\geqslant\mathrm{0}} {\sum}\left(−\mathrm{1}\right)^{{n}} \frac{\left(\mathrm{2}{n}−\mathrm{1}\right)!}{\mathrm{4}^{{n}} \left({n}!\right)^{\mathrm{2}} \left(\mathrm{2}{n}+\mathrm{1}\right)}…
Question Number 39280 by rahul 19 last updated on 04/Jul/18 $$\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\mathrm{cos}\:^{\mathrm{10}} {x}.\mathrm{sin}\:\mathrm{12}{x}\:{dx}\:=\:? \\ $$$$\mathrm{Given} \\ $$$$\mathrm{reduction}\:\mathrm{formula}\:: \\ $$$$\int\:\mathrm{cos}^{\mathrm{m}} {x}\:{sin}\:{nx}\:{dx}\: \\ $$$$\:\mathrm{I}_{\mathrm{m},\mathrm{n}} =\:−\frac{\mathrm{cos}\:^{\mathrm{m}} {x}\:.\:{cosnx}}{{m}+{n}}\:+\:\frac{{m}}{{m}+{n}}\:\mathrm{I}_{\mathrm{m}−\mathrm{1},\mathrm{n}−\mathrm{1}}…