Question Number 118476 by mathmax by abdo last updated on 17/Oct/20 $$\mathrm{find}\:\int_{−\infty} ^{\infty} \:\frac{\mathrm{arctan}\left(\mathrm{1}+\mathrm{2x}\right)}{\mathrm{x}^{\mathrm{2}} \:+\mathrm{1}}\mathrm{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 183977 by cortano1 last updated on 01/Jan/23 $$\:\int_{\mathrm{0}} ^{\:\infty} \:\frac{{dx}}{{x}^{\mathrm{8}} +{x}^{\mathrm{4}} +\mathrm{1}}\:=?\: \\ $$ Answered by ARUNG_Brandon_MBU last updated on 01/Jan/23 $$\Omega=\int_{\mathrm{0}} ^{\infty}…
Question Number 183976 by cortano1 last updated on 01/Jan/23 $$\:\:\int\:\frac{\mathrm{sin}\:{x}−\sqrt{\mathrm{1}+\mathrm{sin}\:{x}}}{\mathrm{cos}\:{x}−\sqrt{\mathrm{1}+\mathrm{cos}\:{x}}}\:{dx}\:=? \\ $$ Answered by MJS_new last updated on 01/Jan/23 $${t}=\frac{\mathrm{1}+\mathrm{sin}\:\frac{{x}}{\mathrm{2}}}{\mathrm{cos}\:\frac{{x}}{\mathrm{2}}}\Leftrightarrow{x}=\mathrm{2arctan}\:\frac{{t}^{\mathrm{2}} −\mathrm{1}}{\mathrm{2}{t}}\:\rightarrow\:{dx}=\frac{\mathrm{4}{dt}}{{t}^{\mathrm{2}} −\mathrm{1}} \\ $$$$\Rightarrow \\…
Question Number 118436 by bramlexs22 last updated on 17/Oct/20 $$\:\:\int\:\mathrm{cos}\:^{\mathrm{4}} \left({x}\right)\:\mathrm{cos}\:^{\mathrm{4}} \left(\mathrm{2}{x}\right)\:{dx}\: \\ $$ Answered by benjo_mathlover last updated on 17/Oct/20 $$\left(\mathrm{1}\right)\:\mathrm{cos}\:^{\mathrm{4}} \left({x}\right)=\:\left(\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{2}}\mathrm{cos}\:\left(\mathrm{2}{x}\right)\right)^{\mathrm{2}} \\ $$$$\:\:=\frac{\mathrm{1}}{\mathrm{4}}+\frac{\mathrm{1}}{\mathrm{2}}\mathrm{cos}\:\left(\mathrm{2}{x}\right)+\frac{\mathrm{1}}{\mathrm{4}}\left(\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{2}}\mathrm{cos}\:\left(\mathrm{4}{x}\right)\right)…
Question Number 118438 by mnjuly1970 last updated on 17/Oct/20 $$\:\:\:\:\:\:…\:\:{nice}\:\:{calculus}… \\ $$$$ \\ $$$$\:\:\:\:\:{evaluate}\::: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$${lim}_{{s}\rightarrow\mathrm{0}} \frac{\zeta\left(\:\mathrm{1}+{s}\:\right)+\zeta\left(\mathrm{1}−{s}\right)}{\mathrm{2}}\:\overset{?} {=}\gamma \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\gamma:\:{euler}−{mascheroni}\:{constant} \\ $$$$\:\:\:{m}.{n}.\mathrm{1970}. \\…
Question Number 52900 by MJS last updated on 15/Jan/19 $$\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\mathrm{sin}\:{x}\:\sqrt{\mathrm{sin}\:\mathrm{2}{x}}\:{dx}=? \\ $$$$\underset{−\frac{\pi}{\mathrm{4}}} {\overset{\frac{\pi}{\mathrm{4}}} {\int}}\mathrm{cos}\:{x}\:\sqrt{\mathrm{cos}\:\mathrm{2}{x}}\:{dx}=? \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 15/Jan/19…
Question Number 52898 by MJS last updated on 14/Jan/19 $$\int\mathrm{arcsin}\:{x}\:\mathrm{arccos}\:{x}\:{dx}=? \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 15/Jan/19 $${a}={sin}^{−} {x} \\ $$$${sina}={x} \\ $$$${sin}^{−\mathrm{1}}…
Question Number 52893 by dwdkswd last updated on 14/Jan/19 $$\int\mathrm{sin}\:{x}×\mathrm{cos}\:{x}\:{dx} \\ $$ Answered by MJS last updated on 14/Jan/19 $$\int\mathrm{sin}\:{x}\:\mathrm{cos}\:{x}\:{dx}=\frac{\mathrm{1}}{\mathrm{2}}\int\mathrm{sin}\:\mathrm{2}{x}\:{dx}=−\frac{\mathrm{1}}{\mathrm{4}}\mathrm{cos}\:\mathrm{2}{x}\:+{C}= \\ $$$$=\frac{\mathrm{1}}{\mathrm{4}}−\frac{\mathrm{1}}{\mathrm{2}}\mathrm{cos}^{\mathrm{2}} \:{x}\:+{C}=−\frac{\mathrm{1}}{\mathrm{2}}\mathrm{cos}^{\mathrm{2}} \:{x}\:+{C} \\…
Question Number 118419 by bramlexs22 last updated on 17/Oct/20 $$\:\:\:\int\:\frac{\mathrm{2sin}\:\mathrm{2}{x}}{\mathrm{4cos}\:{x}+\mathrm{sin}\:\mathrm{2}{x}}\:{dx}\: \\ $$ Commented by bramlexs22 last updated on 17/Oct/20 $${yes}…{thank}\:{you}\:{all}\:{master}\: \\ $$ Answered by peter…
Question Number 118395 by TANMAY PANACEA last updated on 17/Oct/20 $$\int_{{a}} ^{{b}} \frac{{f}\left({x}\right)}{{f}\left({x}\right)+{f}\left({a}+{b}−{x}\right)}{dx} \\ $$ Commented by Dwaipayan Shikari last updated on 17/Oct/20 $$\frac{{b}−{a}}{\mathrm{2}} \\…