Question Number 109838 by mnjuly1970 last updated on 25/Aug/20 $$ \\ $$$$ \\ $$$$\:\:\:\:{please}\:{prove}::: \\ $$$$\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\mathrm{1}}{\:\sqrt{\mathrm{1}−{x}}}{log}\left(\frac{{x}}{\mathrm{1}−{x}}\right){dx}\:=\mathrm{4}{log}\left(\mathrm{2}\right)\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$ \\ $$$$ \\ $$ Answered…
Question Number 44302 by abdo.msup.com last updated on 26/Sep/18 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dx}}{\left({x}+\mathrm{1}\right)\left({x}+\mathrm{2}\right)\left({x}+\mathrm{3}\right)} \\ $$ Commented by maxmathsup by imad last updated on 28/Sep/18 $${let}\:{I}\:=\int_{\mathrm{0}} ^{\infty}…
Question Number 175351 by cortano1 last updated on 28/Aug/22 $$\:\:\underset{\mathrm{0}} {\overset{\pi/\mathrm{2}} {\int}}\:\frac{\mathrm{sin}\:^{\mathrm{3}} {x}}{\mathrm{sin}\:{x}+\mathrm{cos}\:{x}}\:{dx}\:=? \\ $$ Answered by som(math1967) last updated on 28/Aug/22 $${I}=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{{sin}^{\mathrm{3}}…
Question Number 175343 by rexford last updated on 27/Aug/22 $$\int_{\mathrm{0}} ^{\infty} \frac{{x}^{\mathrm{5}} }{\:\sqrt{\mathrm{3}−{x}}}{dx} \\ $$ Commented by BaliramKumar last updated on 28/Aug/22 $${I}\:{think}\:{Q}.\:{will}\:{be}\:\:\:\underset{\mathrm{0}} {\overset{\mathrm{3}} {\int}}\frac{\:{x}^{\mathrm{5}}…
Question Number 44264 by pramid last updated on 25/Sep/18 $$\int\frac{\mathrm{1}}{\left(\mathrm{x}^{\mathrm{2}} +\mathrm{2x}+\mathrm{5}\right)^{\mathrm{2}} }\mathrm{dx} \\ $$ Commented by maxmathsup by imad last updated on 25/Sep/18 $${let}\:{I}\:=\:\int\:\frac{{dx}}{\left({x}^{\mathrm{2}} \:+\mathrm{2}{x}\:+\mathrm{5}\right)^{\mathrm{2}}…
Question Number 109801 by mathmax by abdo last updated on 25/Aug/20 $$\mathrm{calculste}\:\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{6}} }\mathrm{dx} \\ $$ Commented by Dwaipayan Shikari last updated on 25/Aug/20…
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Question Number 44250 by pieroo last updated on 24/Sep/18 $$\mathrm{Evaliate}\:\int\mathrm{sin}^{\mathrm{4}} \mathrm{x}\:\mathrm{dx} \\ $$$$\mathrm{please}\:\mathrm{show}\:\mathrm{working}. \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 24/Sep/18 $$\int\left(\frac{\mathrm{1}−{cos}\mathrm{2}{x}}{\mathrm{2}}\right)^{\mathrm{2}} {dx} \\…
Question Number 175305 by cortano1 last updated on 26/Aug/22 Answered by mr W last updated on 27/Aug/22 $${let}\:{t}=\frac{{x}}{\mathrm{6}} \\ $$$$\mathrm{6}\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{36}}} \frac{\mathrm{1}−\mathrm{cos}\:\mathrm{2}{t}}{\mathrm{sin}\:\mathrm{3}{t}}{dt} \\ $$$$=\mathrm{12}\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{36}}}…
Question Number 44232 by LYCON TRIX last updated on 24/Sep/18 $$\int_{\mathrm{0}} ^{\pi} \mathrm{e}^{\mathrm{sin}^{\mathrm{2}} \mathrm{x}} \mathrm{Cos}^{\mathrm{3}} \mathrm{xdx} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 24/Sep/18…