Question Number 102138 by Dwaipayan Shikari last updated on 06/Jul/20 $$\int_{\mathrm{0}} ^{\mathrm{1}} \int_{\sqrt{{y}}} ^{\mathrm{0}} \sqrt{{x}^{\mathrm{3}} +\mathrm{1}+{ax}^{\mathrm{2}} +{bx}+{c}}\:\:{dx}\:{dy} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 36595 by rahul 19 last updated on 03/Jun/18 $$\int\:\frac{{x}\:{dx}}{\:\sqrt{\mathrm{1}+{x}^{\mathrm{2}} +\sqrt{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\mathrm{3}} }}}\:=\:? \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 03/Jun/18 $${t}=\mathrm{1}+{x}^{\mathrm{2}} \\…
Question Number 36597 by rahul 19 last updated on 03/Jun/18 $$\int\frac{\mathrm{d}{x}}{{x}^{\frac{\mathrm{2}}{\mathrm{3}}} \left(\mathrm{1}+{x}^{\frac{\mathrm{2}}{\mathrm{3}}} \right)}\:=\:? \\ $$ Commented by rahul 19 last updated on 03/Jun/18 $$\mathrm{I}\:\mathrm{tried}\:\mathrm{by}\:\mathrm{taking}\:{x}^{\frac{\mathrm{2}}{\mathrm{3}}} \:{common}\:{from}…
Question Number 102128 by Study last updated on 06/Jul/20 $$\:\int\frac{{x}+\mathrm{1}}{\:\sqrt{{x}}\:+\mathrm{1}}{dx}=? \\ $$ Answered by Dwaipayan Shikari last updated on 06/Jul/20 $$\int\frac{{x}}{\:\sqrt{{x}}+\mathrm{1}}+\frac{\mathrm{1}}{\:\sqrt{{x}}+\mathrm{1}}=\int\frac{\mathrm{2}{u}^{\mathrm{3}} }{{u}+\mathrm{1}}{du}+\int\frac{\mathrm{2}{u}}{{u}+\mathrm{1}}{du}\:\:\:\:\left\{\:\:\:{take}\:{x}\:\:{as}\:{u}^{\mathrm{2}} \right. \\ $$$$=\mathrm{2}\int\frac{{u}^{\mathrm{3}}…
Question Number 102127 by Study last updated on 06/Jul/20 $$\int_{\mathrm{0}} ^{\mathrm{2}} \left(\mathrm{1}−{x}^{\mathrm{2}} \right)^{\mathrm{3}} {dx}=? \\ $$$$\:{and}\:{write}\:{the}\:{furmollah} \\ $$ Answered by abdomathmax last updated on 06/Jul/20…
Question Number 102121 by Rohit@Thakur last updated on 06/Jul/20 $$\int_{−\infty} ^{\infty} \frac{{sin}\left({x}+\frac{\pi}{\mathrm{2}}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }\:{dx}\:\:{By}\:{real}\:{analysis} \\ $$ Commented by prakash jain last updated on 06/Jul/20 https://youtu.be/YWBdwYr6PGg Solution video. Answered…
Question Number 102115 by Dwaipayan Shikari last updated on 06/Jul/20 $$\Gamma\left({s}\right)\zeta\left({s}\right)=\int_{\mathrm{0}} ^{\infty} \frac{{x}^{{s}−\mathrm{1}} }{{e}^{{x}} +\mathrm{1}}{dx}\:\:\left({Prove}\:{that}\right) \\ $$$${And}\:{prove}\:\mathrm{1}+\mathrm{2}+\mathrm{3}+\mathrm{4}+\mathrm{5}+\mathrm{6}+\mathrm{7}+….\infty=−\frac{\mathrm{1}}{\mathrm{12}} \\ $$$$ \\ $$ Commented by mr W…
Question Number 167644 by MJS_new last updated on 22/Mar/22 $$\mathrm{find}\:\mathrm{the}\:\mathrm{exact}\:\mathrm{value}\:\mathrm{of} \\ $$$$\underset{\mathrm{0}} {\overset{\mathrm{2}\pi} {\int}}\frac{{dx}}{\:\sqrt{\mathrm{1}+\mathrm{sin}\:{x}}+\sqrt{\mathrm{1}+\mathrm{cos}\:{x}}} \\ $$ Commented by cortano1 last updated on 23/Mar/22 $${i}\:{got}\mathrm{3}.\mathrm{962}\: \\…
Question Number 167647 by mathlove last updated on 22/Mar/22 Answered by RoswelCod2003 last updated on 22/Mar/22 $$\mathrm{Using}\:“\mathrm{Feynman}'\mathrm{s}\:\mathrm{Rule}\:\mathrm{of}\:\mathrm{Integration}'' \\ $$$$\: \\ $$$${I}\left({k}\right)\:=\:\int_{\mathrm{0}} ^{\:\infty} {e}^{−{x}^{\mathrm{2}} } \mathrm{cos}\:\left({kx}\right)\:{dx}\:\therefore\:\mathrm{where}\:{k}\:=\:\mathrm{2}…
Question Number 102099 by Study last updated on 06/Jul/20 $$\int{sinx}\:\centerdot\:{cosx}\:\centerdot{cos}\mathrm{2}{x}\:\centerdot\:{cos}\mathrm{4}{x}\:{dx}=? \\ $$ Answered by PRITHWISH SEN 2 last updated on 06/Jul/20 $$\frac{\mathrm{1}}{\mathrm{2}}\int\mathrm{sin}\:\mathrm{2xcos}\:\mathrm{2xcos}\:\mathrm{4x}\:\mathrm{dx}=\frac{\mathrm{1}}{\mathrm{4}}\int\mathrm{sin}\:\mathrm{4xcos}\:\mathrm{4xdx} \\ $$$$=\frac{\mathrm{1}}{\mathrm{8}}\int\mathrm{sin}\:\:\mathrm{8xdx}=−\frac{\mathrm{cos}\:\:\mathrm{8x}}{\mathrm{64}}\:+\mathrm{C} \\…