Question Number 128082 by liberty last updated on 04/Jan/21 $$\beta\:=\:\int\:\frac{\mathrm{1}+\mathrm{ln}\:\left(\mathrm{x}\right)}{\mathrm{x}.\mathrm{cos}\:^{\mathrm{2}} \left(\mathrm{x}\right)}\:\mathrm{dx}\: \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 128079 by liberty last updated on 04/Jan/21 $$\Omega\:=\:\int\:\mathrm{ln}\:\left(\mathrm{x}+\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{a}^{\mathrm{2}} }\:\right)\mathrm{dx} \\ $$ Answered by bemath last updated on 04/Jan/21 $$\Omega=\mathrm{x}\:\mathrm{ln}\:\left(\mathrm{x}+\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{a}^{\mathrm{2}} }\:\right)−\int\:\frac{\mathrm{x}\left(\mathrm{1}+\frac{\mathrm{x}}{\:\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{a}^{\mathrm{2}}…
Question Number 128073 by I want to learn more last updated on 04/Jan/21 $$\int\:\frac{\mathrm{sin}\left(\mathrm{2x}\right)}{\left(\mathrm{1}\:\:−\:\:\mathrm{x}\right)^{\mathrm{3}} }\:\:\mathrm{dx} \\ $$ Answered by mindispower last updated on 04/Jan/21 $$\Leftrightarrow{Im}\int\frac{{e}^{\mathrm{2}{ix}}…
Question Number 128057 by bramlexs22 last updated on 04/Jan/21 $$\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \int_{\mathrm{0}} ^{\:\mathrm{1}} \:\frac{\mathrm{1}}{\mathrm{1}−\mathrm{xy}^{\mathrm{2}} }\:\mathrm{dx}\:\mathrm{dy}\:=? \\ $$ Answered by liberty last updated on 04/Jan/21 $$\:\frac{\mathrm{1}}{\mathrm{1}−\mathrm{xy}^{\mathrm{2}}…
Question Number 128052 by bramlexs22 last updated on 04/Jan/21 $$\:\mathrm{I}\:=\:\int\:\mathrm{arctan}\:\left(\frac{\mathrm{x}−\mathrm{2}}{\mathrm{x}+\mathrm{2}}\right)\:\mathrm{dx}\: \\ $$ Answered by liberty last updated on 04/Jan/21 $$\mathrm{I}\:=\:\mathrm{x}\:\mathrm{arctan}\:\left(\frac{\mathrm{x}−\mathrm{2}}{\mathrm{x}+\mathrm{2}}\right)−\int\:\mathrm{x}\left(\frac{\mathrm{1}}{\mathrm{1}+\left(\frac{\mathrm{x}−\mathrm{2}}{\mathrm{x}+\mathrm{2}}\right)^{\mathrm{2}} }.\:\frac{\mathrm{4}}{\left(\mathrm{x}+\mathrm{2}\right)^{\mathrm{2}} }\right)\mathrm{dx} \\ $$$$\mathrm{I}=\mathrm{x}\:\mathrm{arctan}\:\left(\frac{\mathrm{x}−\mathrm{2}}{\mathrm{x}+\mathrm{2}}\right)−\int\:\frac{\mathrm{2x}}{\mathrm{x}^{\mathrm{2}} +\mathrm{4}}\:\mathrm{dx}…
Question Number 128026 by Ar Brandon last updated on 03/Jan/21 $$\int_{\frac{\pi}{\mathrm{2}}} ^{\frac{\mathrm{2}\pi}{\mathrm{3}}} \frac{\left(\mathrm{arcsinhx}\right)^{\mathrm{2}} }{\mathrm{2cosx}}\mathrm{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 128025 by Algoritm last updated on 03/Jan/21 Answered by Olaf last updated on 03/Jan/21 $$\mathrm{Let}\:\Phi_{{n}} \:=\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} {e}^{\mathrm{cos}\theta} \mathrm{cos}\left({n}\theta−\mathrm{sin}\theta\right){d}\theta \\ $$$$\mathrm{Let}\:\Omega_{{n}} \:=\:\int_{\mathrm{0}} ^{\mathrm{2}\pi}…
Question Number 128023 by mnjuly1970 last updated on 04/Jan/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:….{nice}\:\:{calculus}…= \\ $$$$\:\:{Titu}'{s}\:{lemma}:: \\ $$$$\:{for}\:{any}\:{positive}\:{numbers}\:: \\ $$$${a}_{\mathrm{1}} ,{a}_{\mathrm{2}} ,…,{a}_{{n}} \:,\:{b}_{\mathrm{1}} ,{b}_{\mathrm{2}} ,…,{b}_{{n}} \\ $$$$\:{we}\:{have}: \\ $$$$\:\frac{\left({a}_{\mathrm{1}}…
Question Number 62453 by Tawa1 last updated on 21/Jun/19 $$\int\:\frac{\mathrm{x}}{\mathrm{e}^{\mathrm{x}} \:−\:\mathrm{1}}\mathrm{dx},\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{for}\:\:\mathrm{x}\:>\:\mathrm{0} \\ $$ Commented by mathmax by abdo last updated on 21/Jun/19 $$\int\:\:\frac{{x}}{{e}^{{x}} −\mathrm{1}}{dx}\:=\int\:\:\frac{{x}\:{e}^{−{x}} }{\mathrm{1}−{e}^{−{x}}…
Question Number 62455 by aliesam last updated on 21/Jun/19 Commented by mathmax by abdo last updated on 22/Jun/19 $${S}\:=\sum_{{n}=\mathrm{1}} ^{\infty} \:{A}_{{n}} \:\:\:{with}\:{A}_{{n}} =\int_{{n}−\frac{\pi}{\mathrm{2}}} ^{{n}+\frac{\pi}{\mathrm{2}}} \:{e}^{−{x}}…