Question Number 2526 by Filup last updated on 22/Nov/15 $$\mathrm{Evaluate}:\:\underset{−\infty} {\overset{\infty} {\int}}{e}^{−{x}^{\mathrm{2}} } {dx} \\ $$$$\mathrm{Please}\:\mathrm{show}\:\mathrm{and}\:\mathrm{explain}\:\mathrm{working} \\ $$ Commented by Filup last updated on 22/Nov/15…
Question Number 133591 by benjo_mathlover last updated on 23/Feb/21 $$\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\mathrm{x}^{\mathrm{2}} \:\sqrt{\mathrm{1}−\mathrm{x}^{\mathrm{2}} }\:\mathrm{dx}\:?\: \\ $$ Answered by EDWIN88 last updated on 23/Feb/21 $$\mathrm{by}\:\mathrm{Ostrogradsky}\:\mathrm{method} \\…
Question Number 68046 by mhmd last updated on 03/Sep/19 Answered by mind is power last updated on 03/Sep/19 $$\frac{{d}\left({e}^{\frac{{sin}\left(\mathrm{2}{x}\right)}{\mathrm{2}}} \right)}{{dx}}={cos}\left(\mathrm{2}{x}\right){e}^{{sin}\left({x}\right){cos}\left({x}\right)} \\ $$$$\int\frac{{e}^{{sin}\left({x}\right){cos}\left({x}\right)} {cos}\left(\mathrm{2}{x}\right)}{\mathrm{1}+{e}^{{sin}\left(\mathrm{2}{x}\right)} }{dx} \\…
Question Number 68043 by mhmd last updated on 03/Sep/19 $$\int_{\pi/\mathrm{2}} ^{\pi} {e}^{{cosx}} \sqrt{\mathrm{1}−{e}^{{cosx}} }\:{sinx}\:{dx} \\ $$ Commented by mathmax by abdo last updated on 03/Sep/19…
Question Number 68040 by mathmax by abdo last updated on 03/Sep/19 $${find}\:{f}\left({a}\right)\:=\int_{\mathrm{1}} ^{\mathrm{2}} {arctan}\left({x}+\frac{{a}}{{x}}\right){dx}\:\:{and} \\ $$$${calculate}\:{f}^{'} \left({a}\right)\:{at}\:{form}\:{of}\:{integral} \\ $$ Commented by mathmax by abdo last…
Question Number 68038 by mathmax by abdo last updated on 03/Sep/19 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{arctan}\left({x}^{\mathrm{2}} −\mathrm{1}\right)}{{x}^{\mathrm{2}} \:+\mathrm{4}}{dx} \\ $$ Commented by mathmax by abdo last updated…
Question Number 68039 by mathmax by abdo last updated on 03/Sep/19 $${find}\:\int\:\:{arctan}\left({x}+\frac{\mathrm{1}}{{x}}\right){dx} \\ $$ Commented by mathmax by abdo last updated on 04/Sep/19 $${let}\:{I}\:=\int\:{arctan}\left({x}+\frac{\mathrm{1}}{{x}}\right){dx}\:\:{by}\:{parts}\:{we}\:{have} \\…
Question Number 68037 by mathmax by abdo last updated on 03/Sep/19 $${find}\:\int\:\:\:\frac{{x}^{\mathrm{2}} {dx}}{\left({x}^{\mathrm{3}} −\mathrm{8}\right)\left({x}^{\mathrm{4}} \:+\mathrm{1}\right)} \\ $$ Answered by MJS last updated on 04/Sep/19 $$\int\frac{{x}^{\mathrm{2}}…
Question Number 68033 by mathmax by abdo last updated on 03/Sep/19 $${find}\:\int\:\:\frac{{dx}}{\mathrm{1}+{sinx}\:+{sin}\left(\mathrm{2}{x}\right)} \\ $$ Answered by MJS last updated on 04/Sep/19 $$\mathrm{I}\:\mathrm{think}\:\mathrm{I}\:\mathrm{did}\:\mathrm{this}\:\mathrm{before} \\ $$$$\mathrm{we}\:\mathrm{have}\:\mathrm{to}\:\mathrm{use}\:\mathrm{Weierstrass} \\…
Question Number 133563 by bemath last updated on 23/Feb/21 $$\:\underset{\mathrm{0}} {\overset{\infty} {\int}}\:\left[\mathrm{sin}\:\frac{\mathrm{1}}{\mathrm{x}}−\frac{\mathrm{1}}{\pi}\mathrm{sin}\:\left(\frac{\pi}{\mathrm{x}}\right)\right]\:\mathrm{dx} \\ $$ Answered by EDWIN88 last updated on 23/Feb/21 $$\:\mathrm{Calculate}\:\underset{\mathrm{0}} {\overset{\infty} {\int}}\left(\mathrm{sin}\left(\:\frac{\mathrm{1}}{\mathrm{x}}\right)−\frac{\mathrm{1}}{\pi}\:\mathrm{sin}\:\left(\frac{\pi}{\mathrm{x}}\:\right)\:\right)\mathrm{dx} \\…