Question Number 130528 by mathmax by abdo last updated on 26/Jan/21 $$\mathrm{calculate}\:\int_{\mathrm{2}} ^{\infty} \:\:\:\:\frac{\mathrm{dx}}{\left(\mathrm{x}^{\mathrm{2}} −\mathrm{1}\right)^{\mathrm{5}} } \\ $$ Answered by mathmax by abdo last updated…
Question Number 64994 by aliesam last updated on 23/Jul/19 $$\int\sqrt{{tanh}\left({x}\right)}\:{dx} \\ $$ Commented by zakaria elghaouti last updated on 24/Jul/19 Answered by zakaria elghaouti last…
Question Number 130529 by mathmax by abdo last updated on 26/Jan/21 $$\mathrm{calvulste}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\frac{\mathrm{cos}\left(\mathrm{2x}\right)}{\mathrm{3}+\mathrm{cosx}}\mathrm{dx} \\ $$ Answered by mathmax by abdo last updated on 27/Jan/21…
Question Number 64993 by mathmax by abdo last updated on 23/Jul/19 $${let}\:{f}\left({a}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{cos}\left({x}^{\mathrm{2}} \right)−{sin}\left({x}^{\mathrm{2}} \right)}{\left({x}^{\mathrm{2}} +{a}^{\mathrm{2}} \right)^{\mathrm{2}} }{dx}\:\:{with}\:{a}>\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}\left({a}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{values}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{cos}\left({x}^{\mathrm{2}}…
Question Number 130512 by MJS_new last updated on 26/Jan/21 $$\int{x}\mathrm{e}^{\frac{\mathrm{1}}{\mathrm{2}{x}}} {dx}=? \\ $$ Commented by Dwaipayan Shikari last updated on 26/Jan/21 $$\frac{\mathrm{1}}{\mathrm{2}{x}}=−{t}\Rightarrow\frac{\mathrm{1}}{\mathrm{2}{x}^{\mathrm{2}} }=\frac{{dt}}{{dx}} \\ $$$$=−\mathrm{2}\int{x}^{\mathrm{3}}…
Question Number 64975 by Tawa1 last updated on 23/Jul/19 Commented by Prithwish sen last updated on 23/Jul/19 $$\int\mathrm{x}^{\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{2}} .\mathrm{2}!}\:+\:\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{3}} .\mathrm{3}!}+….} \mathrm{dx}\:=\int\mathrm{x}^{\sqrt{\mathrm{e}}−\mathrm{1}} \mathrm{dx}\:\mathrm{and}\:\mathrm{proceed} \\ $$ Terms…
Question Number 64970 by mathmax by abdo last updated on 23/Jul/19 $${let}\:{f}\left({a}\right)=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{cos}\left({x}^{\mathrm{2}} \right)\:+{sin}\left({x}^{\mathrm{2}} \right)}{\left({x}^{\mathrm{2}} \:+{a}^{\mathrm{2}} \right)^{\mathrm{2}} }\:{dx}\:\:\:{with}\:{a}>\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}\left({a}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{values}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{cos}\left({x}^{\mathrm{2}}…
Question Number 130486 by benjo_mathlover last updated on 26/Jan/21 $$\:\int_{\mathrm{0}} ^{\:{x}} \:\frac{\mathrm{cos}\:{t}\:\sqrt[{\mathrm{4}}]{\mathrm{sin}^{\mathrm{3}} \:{t}}}{\left(\mathrm{sin}\:{x}−\mathrm{sin}\:{t}\right)^{\mathrm{3}/\mathrm{4}} }\:{dt}\:? \\ $$ Answered by MJS_new last updated on 26/Jan/21 $$\int\mathrm{cos}\:{t}\:\left(\frac{\mathrm{sin}\:{t}}{\mathrm{sin}\:{x}\:−\mathrm{sin}\:{t}}\right)^{\mathrm{3}/\mathrm{4}} {dt}=…
Question Number 130485 by benjo_mathlover last updated on 26/Jan/21 $$\:\digamma\:=\:\int_{\mathrm{0}} ^{\:\infty} {x}^{\mathrm{5}\:} \mathrm{ln}\:\left({x}\right)\mathrm{cos}\:\left({x}\right){e}^{−{x}} \:{dx}\:? \\ $$ Answered by Dwaipayan Shikari last updated on 26/Jan/21 $${I}\left({a}\right)=\int_{\mathrm{0}}…
Question Number 130478 by liberty last updated on 26/Jan/21 $$\:{Integrate}\:{the}\:{function}\:{f}\left({x},{y}\right)={xy}\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right) \\ $$$${over}\:{the}\:{domain}\:{R}=\left\{−\mathrm{3}\leqslant{x}^{\mathrm{2}} −{y}^{\mathrm{2}} \leqslant\mathrm{3},\:\mathrm{1}\leqslant{y}\leqslant\mathrm{4}\:\right\} \\ $$ Answered by EDWIN88 last updated on 26/Jan/21…