Question Number 129794 by bramlexs22 last updated on 19/Jan/21 $$\:\:\int\:\left(\mathrm{x}^{\mathrm{2}} −\mathrm{1}\right)\left(\mathrm{x}+\mathrm{1}\right)^{−\mathrm{2}/\mathrm{3}} \:\mathrm{dx}\:? \\ $$ Answered by EDWIN88 last updated on 19/Jan/21 $$\:\int\:\left(\mathrm{x}−\mathrm{1}\right)\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{1}/\mathrm{3}} \:\mathrm{dx}\:=\:\left(\mathrm{x}−\mathrm{1}\right)\left(\frac{\mathrm{3}}{\mathrm{4}}\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{4}/\mathrm{3}} \right)−\frac{\mathrm{3}}{\mathrm{4}}\int\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{4}/\mathrm{3}} \:\mathrm{dx}…
Question Number 129788 by bramlexs22 last updated on 19/Jan/21 $$\:\int\:\left(\mathrm{1}+\mathrm{3}{x}^{\mathrm{3}} \right){e}^{{x}^{\mathrm{3}} } \:{dx}\: \\ $$ Answered by EDWIN88 last updated on 19/Jan/21 $$\:\mathrm{let}\:\mathrm{z}\:=\:{xe}^{{x}^{\mathrm{3}} } \:\Rightarrow\:{dz}\:=\:\left({e}^{{x}^{\mathrm{3}}…
Question Number 129787 by EDWIN88 last updated on 19/Jan/21 $$\:\int\:{x}^{\mathrm{7}} \:\sqrt{\mathrm{1}+{x}^{\mathrm{4}} }\:{dx}\: \\ $$ Answered by bramlexs22 last updated on 19/Jan/21 Commented by MJS_new last…
Question Number 64238 by mmkkmm000m last updated on 16/Jul/19 $$\int{ln}\left({x}−\mathrm{5}\right)/{x}^{\mathrm{2}} +\mathrm{110}{x}−\mathrm{5}{dx} \\ $$ Commented by mr W last updated on 16/Jul/19 $${sir},\:{please}\:{use}\:{smaller}\:{font}\:{for}\:{your} \\ $$$${posts}!\: \\…
Question Number 64227 by Tony Lin last updated on 16/Jul/19 $$\int\frac{\mathrm{1}}{{x}^{\mathrm{6}} +{x}^{\mathrm{3}} }{dx}=? \\ $$ Answered by ajfour last updated on 16/Jul/19 $${I}=\int\frac{{dx}}{{x}^{\mathrm{3}} \left(\mathrm{1}+{x}^{\mathrm{3}} \right)}…
Question Number 129764 by Eric002 last updated on 18/Jan/21 $${prove}\:{that} \\ $$$$\int_{−\infty} ^{+\infty} {x}^{\mathrm{2}} \:{e}^{−{x}^{\mathrm{2}} } \:{cos}\left({x}^{\mathrm{2}} \right){sin}\left({x}^{\mathrm{2}} \right)\:{dx} \\ $$$$=\frac{\sqrt{\pi}{sin}\left[\frac{\sqrt{\mathrm{3}}{tan}^{−\mathrm{1}} \left(\mathrm{2}\right)}{\mathrm{2}}\right]}{\mathrm{4}\:\sqrt[{\mathrm{4}}]{\mathrm{125}}} \\ $$ Answered…
Question Number 129763 by Eric002 last updated on 18/Jan/21 $${prove} \\ $$$$\int_{−\infty} ^{+\infty} \frac{\mathrm{1}}{\mathrm{1}+{e}^{{x}^{\mathrm{2}} } }{dx}=\sqrt{\pi}\:\left(\mathrm{1}−\sqrt{\mathrm{2}}\:\right)\xi\left(\frac{\mathrm{1}}{\mathrm{2}}\right) \\ $$ Answered by Dwaipayan Shikari last updated on…
Question Number 64224 by mmkkmm000m last updated on 16/Jul/19 $$\int{x}_{{x}} {dx} \\ $$$$ \\ $$$$\int{x}^{{x}} {dx} \\ $$ Commented by mathmax by abdo last updated…
Question Number 64213 by Tony Lin last updated on 15/Jul/19 $$\int\frac{\mathrm{1}}{{x}!}{dx}=? \\ $$ Commented by MJS last updated on 15/Jul/19 $$\frac{\mathrm{1}}{{x}!}\:\mathrm{is}\:\mathrm{defined}\:\mathrm{for}\:{x}\in\mathbb{N}\:\Rightarrow\:\mathrm{it}'\mathrm{s}\:\mathrm{not}\:\mathrm{continuous} \\ $$$$\mathrm{for}\:{x}\in\mathbb{R}\:\Rightarrow\:\mathrm{it}'\mathrm{s}\:\mathrm{not}\:\mathrm{integrable} \\ $$…
Question Number 129746 by bramlexs22 last updated on 18/Jan/21 $$\:\mathrm{N}\:=\:\int\:\frac{\mathrm{3}+\mathrm{2cos}\:\mathrm{x}}{\mathrm{2}+\mathrm{3cos}\:\mathrm{x}}\:\mathrm{dx}\: \\ $$ Answered by liberty last updated on 18/Jan/21 $$\:\mathrm{N}=\:\int\:\frac{\frac{\mathrm{2}}{\mathrm{3}}\left(\mathrm{2}+\mathrm{3cos}\:\mathrm{x}\right)+\frac{\mathrm{8}}{\mathrm{3}}}{\mathrm{2}+\mathrm{3cos}\:\mathrm{x}}\:\mathrm{dx}\: \\ $$$$\:\mathrm{N}=\:\frac{\mathrm{2}}{\mathrm{3}}\mathrm{x}\:+\:\frac{\mathrm{8}}{\mathrm{3}}\int\:\frac{\mathrm{dx}}{\mathrm{2}+\mathrm{3}\left(\mathrm{2cos}\:^{\mathrm{2}} \frac{\mathrm{x}}{\mathrm{2}}−\mathrm{1}\right)} \\ $$$$\:\mathrm{N}=\:\frac{\mathrm{2}}{\mathrm{3}}\mathrm{x}+\frac{\mathrm{8}}{\mathrm{3}}\int\:\frac{\mathrm{dx}}{\mathrm{6cos}\:^{\mathrm{2}}…