Question Number 45600 by maxmathsup by imad last updated on 14/Oct/18 $${find}\:{f}\left({x},{y}\right)\:=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {ln}\left({x}+{y}\:{sin}\theta\right){d}\theta\:\:{with}\:\:\mid{y}\mid<\mid{x}\mid \\ $$$$\left.\mathrm{2}\right)\:{find}\:{f}\left(\mathrm{2},\mathrm{3}\right) \\ $$$$\left.\mathrm{3}\right){find}\:{f}\left(\sqrt{\mathrm{2}},\sqrt{\mathrm{3}}\right)\:. \\ $$ Commented by maxmathsup by imad…
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Question Number 111104 by Lordose last updated on 02/Sep/20 Commented by mathdave last updated on 02/Sep/20 $${the}\:{question}\:{is}\:{not}\:{integradable} \\ $$ Commented by Dwaipayan Shikari last updated…
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Question Number 45561 by Sanjarbek last updated on 14/Oct/18 Commented by tanmay.chaudhury50@gmail.com last updated on 14/Oct/18 $${x}={sin}\theta\:\:\:\:{dx}={cos}\theta{d}\theta \\ $$$$\int\frac{{cos}\theta{d}\theta}{\:\sqrt{{cos}\theta}} \\ $$$$\int\sqrt{{cos}\theta}\:{d}\theta \\ $$$${wait}… \\ $$…
Question Number 111082 by john santu last updated on 02/Sep/20 $$\:\:\:\left[\int_{\mathrm{0}} ^{\infty} {JS}\:{dx}\:\right] \\ $$$$\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\:\frac{\mathrm{sin}\:\left({x}\right)\left(\mathrm{4}+\mathrm{sin}\:^{\mathrm{2}} \left({x}\right)\right)}{\left(\mathrm{4}−\mathrm{sin}\:^{\mathrm{2}} \left({x}\right)\right)^{\mathrm{2}} }\:{dx}\:? \\ $$ Commented by mathdave…
Question Number 111083 by bemath last updated on 02/Sep/20 $$\:\:\:\sqrt{\mathrm{bemath}} \\ $$$$\left(\mathrm{1}\right)\int\:\frac{\mathrm{dx}}{\mathrm{3sin}\:\mathrm{x}+\mathrm{sin}\:^{\mathrm{3}} \mathrm{x}} \\ $$$$\left(\mathrm{2}\right)\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\mathrm{x}\left(\mathrm{5}^{\frac{\mathrm{1}}{\mathrm{x}}} \:−\mathrm{1}\right)\: \\ $$$$\left(\mathrm{3}\right)\:\mathrm{find}\:\mathrm{the}\:\mathrm{asymptotes}\:\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{a}^{\mathrm{2}} }\:−\:\frac{\mathrm{y}^{\mathrm{2}} }{\mathrm{b}^{\mathrm{2}} }\:=\:\mathrm{1}\: \\ $$…
Question Number 45520 by maxmathsup by imad last updated on 14/Oct/18 $${let}\:{a}>\mathrm{0}\:{and}\:{b}>\mathrm{0}\:{calculate}\:\int\:\sqrt{{acos}^{\mathrm{2}} \theta\:+{bsin}^{\mathrm{2}} \theta}{d}\pi \\ $$$$\left.\mathrm{2}\right)\:{find}\:\int_{\frac{\pi}{\mathrm{4}}} ^{\frac{\pi}{\mathrm{2}}} \sqrt{\mathrm{2}{cos}^{\mathrm{2}} \theta\:+\mathrm{3}\:{sin}^{\mathrm{2}} \theta}{d}\theta\:. \\ $$ Commented by Meritguide1234…
Question Number 176594 by mnjuly1970 last updated on 22/Sep/22 $$ \\ $$$$\:\:\:\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\:\left(\:{tanh}^{\:−\mathrm{1}} \left({x}\right)\right)^{\mathrm{2}} }{\left(\mathrm{1}+{x}\:\right)^{\:\mathrm{2}} }\:{dx}\:=\:?\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\prec\:\:\:{solution}\:\:\succ \\ $$$$\:\:\:\:\:{note}\::\:\:{tanh}^{\:−\mathrm{1}} \left({x}\right)=−\:\frac{\mathrm{1}}{\mathrm{2}}\:{ln}\left(\frac{\mathrm{1}−{x}}{\mathrm{1}+{x}}\right) \\ $$$$\:\:\:\:\:\boldsymbol{\phi}=\:\frac{\mathrm{1}}{\mathrm{4}}\int_{\mathrm{0}} ^{\:\mathrm{1}}…
Question Number 45519 by maxmathsup by imad last updated on 14/Oct/18 $${find}\:\:\int\:\sqrt{\mathrm{2}+{tan}^{\mathrm{2}} \theta}{d}\theta \\ $$ Commented by Meritguide1234 last updated on 14/Oct/18 Commented by maxmathsup…