Question Number 123674 by mathmax by abdo last updated on 27/Nov/20 $$\mathrm{find}\:\int_{\mathrm{0}} ^{\infty} \:\:\mathrm{e}^{−\mathrm{2x}} \mathrm{ln}\left(\mathrm{1}+\mathrm{e}^{\mathrm{x}} \right)\mathrm{dx} \\ $$ Answered by Dwaipayan Shikari last updated on…
Question Number 123673 by mathmax by abdo last updated on 27/Nov/20 $$\mathrm{find}\:\int_{\mathrm{0}} ^{\infty} \:\:\left(\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{x}+\mathrm{1}}−\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{x}}\right)^{\mathrm{4}} \mathrm{dx} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 189189 by MikeH last updated on 13/Mar/23 Answered by cortano12 last updated on 13/Mar/23 $$\mathrm{it}\:\mathrm{should}\:\mathrm{be}\:\underset{−\mathrm{1}/\mathrm{2}} {\overset{\mathrm{1}/\mathrm{2}} {\int}}\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{1}+\sqrt{\mathrm{x}^{\mathrm{4}} +\mathrm{x}^{\mathrm{2}} +\mathrm{1}}}\:\mathrm{dx} \\ $$$$=\:\underset{−\mathrm{1}/\mathrm{2}} {\overset{\mathrm{1}/\mathrm{2}}…
Question Number 123639 by benjo_mathlover last updated on 26/Nov/20 $$\:\:\:\underset{\mathrm{0}} {\overset{\infty} {\int}}\:\sqrt{\mathrm{tan}^{−\mathrm{1}} \left({x}\right)}\:{dx}\:? \\ $$ Answered by MJS_new last updated on 27/Nov/20 $${x}\rightarrow+\infty\:\Rightarrow\:\mathrm{arctan}\:{x}\:\rightarrow\:\frac{\pi}{\mathrm{2}}\:\Rightarrow \\ $$$$\mathrm{integral}\:\mathrm{doesn}'\mathrm{t}\:\mathrm{converge}…
Question Number 189144 by talminator2856792 last updated on 12/Mar/23 $$\: \\ $$$$\: \\ $$$$\:\:\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \int_{\mathrm{0}} ^{\:\mathrm{1}} \int_{\mathrm{0}} ^{\:\mathrm{1}} \:\frac{\sqrt{{x}\:+\:{y}\:+\:{z}}}{\:\sqrt{{x}}\:+\:\sqrt{{y}}\:+\:\sqrt{{z}}\:}\:{dxdydz} \\ $$$$\: \\ $$$$\: \\…
Question Number 123552 by Lordose last updated on 26/Nov/20 $$\int_{\:\mathrm{0}} ^{\:\frac{\pi}{\mathrm{4}}} \mathrm{tan}^{\mathrm{n}} \left(\mathrm{x}\right)\mathrm{dx} \\ $$ Answered by Adeleke last updated on 26/Nov/20 Answered by TANMAY…
Question Number 123550 by mnjuly1970 last updated on 26/Nov/20 $$\:\:\:\:\:\:\:\:\:\:\:….{nice}\:\:\:\:{mathematics}… \\ $$$$\:\:\:\:\:\:{evaluate}\::::: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Omega=\int_{\mathrm{0}} ^{\:\infty} \left(\sqrt{{x}+\mathrm{1}}\:−\sqrt{{x}}\:\right)^{\mathrm{10}} {dx}=? \\ $$ Answered by Olaf last updated on…
Question Number 189066 by cortano12 last updated on 11/Mar/23 $$\:\mathrm{Given}\:\mathrm{f}\left(\mathrm{x}\right)+\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\left(\mathrm{x}+\mathrm{y}\right)^{\mathrm{2}} \:\mathrm{f}\left(\mathrm{y}\right)\:\mathrm{dy}=\mathrm{2x}^{\mathrm{2}} −\mathrm{3x}+\mathrm{1} \\ $$$$\:\mathrm{find}\:\mathrm{f}\left(\mathrm{x}\right). \\ $$ Answered by horsebrand11 last updated on 11/Mar/23…
Question Number 123526 by bramlexs22 last updated on 26/Nov/20 $$\:\:\underset{\mathrm{0}} {\overset{\infty} {\int}}\:\frac{{x}\:\mathrm{arctan}\:{x}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\mathrm{2}} }\:{dx}\:? \\ $$ Commented by liberty last updated on 26/Nov/20 $$\frac{\pi}{\mathrm{8}}\:? \\…
Question Number 57992 by Tinkutara last updated on 15/Apr/19 Answered by MJS last updated on 16/Apr/19 $$\underset{\mathrm{1}} {\overset{{c}} {\int}}\left(−{x}^{\mathrm{5}} +\mathrm{8}{x}^{\mathrm{2}} \right){dx}=\frac{\mathrm{16}}{\mathrm{3}} \\ $$$$−\frac{\mathrm{1}}{\mathrm{6}}{c}^{\mathrm{6}} +\frac{\mathrm{8}}{\mathrm{3}}{c}^{\mathrm{3}} −\frac{\mathrm{5}}{\mathrm{2}}=\frac{\mathrm{16}}{\mathrm{3}}…