Question Number 6107 by gourav~ last updated on 14/Jun/16 $$\int\frac{{x}}{{x}^{\mathrm{3}} +{x}+\mathrm{2}}{dx}\:=? \\ $$ Commented by Yozzii last updated on 14/Jun/16 $${x}^{\mathrm{3}} +{x}+\mathrm{2}={x}^{\mathrm{3}} +\mathrm{1}+{x}+\mathrm{1} \\ $$$$=\left({x}+\mathrm{1}\right)\left({x}^{\mathrm{2}}…
Question Number 137171 by mnjuly1970 last updated on 30/Mar/21 Answered by Dwaipayan Shikari last updated on 30/Mar/21 $${log}\left(\mathrm{2}\right)=\mathrm{1}+\mathrm{1}\left(−\frac{\mathrm{1}}{\mathrm{2}}\right)+\mathrm{1}\left(−\frac{\mathrm{1}}{\mathrm{2}}\right)\left(−\frac{\mathrm{2}}{\mathrm{3}}\right)+… \\ $$$$=\frac{\mathrm{1}}{\mathrm{1}+\frac{\frac{\mathrm{1}}{\mathrm{2}}}{\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}}+\frac{\frac{\mathrm{2}}{\mathrm{3}}}{\mathrm{1}−\frac{\mathrm{2}}{\mathrm{3}}+\frac{\frac{\mathrm{3}}{\mathrm{4}}}{\mathrm{1}−\frac{\mathrm{3}}{\mathrm{4}}+..}}}}=\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{2}^{\mathrm{2}} }{\mathrm{1}+\frac{\mathrm{3}^{\mathrm{2}} }{\mathrm{1}+\frac{\mathrm{4}^{\mathrm{2}} }{\mathrm{1}+…}}}}} \\ $$$$\frac{\mathrm{1}}{{log}\left(\mathrm{2}\right)}=\mathrm{1}+\frac{\mathrm{1}^{\mathrm{2}}…
Question Number 137156 by adhigenz last updated on 30/Mar/21 $$\underset{\mathrm{1}} {\overset{\infty} {\int}}\frac{\sqrt{\mathrm{3}{x}^{\mathrm{4}} +\mathrm{5}{x}^{\mathrm{3}} +\mathrm{1}}}{\mathrm{4}{x}^{\mathrm{3}} +{x}^{\mathrm{2}} +\mathrm{2}}\:{dx}\:=\:… \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 137155 by mnjuly1970 last updated on 30/Mar/21 $$\:\:\:\:\:\:\:\:……{nice}\:\:\:\:{calculus}\:…… \\ $$$$\:\:\:\:\:\:{evaluate}\::: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\mathrm{2}\pi} \frac{\mathrm{1}}{\mathrm{1}+{cos}^{\mathrm{4}} \left({x}\right)}{dx}=??? \\ $$ Answered by Ar Brandon last updated…
Question Number 6079 by gourav~ last updated on 12/Jun/16 $$\int\frac{{x}+\mathrm{cos}\:\mathrm{2}{x}}{{x}+\mathrm{sin}\:\mathrm{2}{x}}{dx}=? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 137141 by Ar Brandon last updated on 30/Mar/21 $$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{t}^{\mathrm{4}} \left(\mathrm{1}−\mathrm{t}\right)^{\mathrm{4}} }{\mathrm{1}+\mathrm{t}^{\mathrm{2}} }\mathrm{dt} \\ $$ Answered by Ar Brandon last updated on…
Question Number 137139 by peter frank last updated on 30/Mar/21 Answered by Dwaipayan Shikari last updated on 30/Mar/21 $$\int_{\mathrm{1}} ^{{e}} \frac{\mathrm{1}}{\left(\mathrm{1}+{log}\left({x}\right)\right)}−\frac{\mathrm{1}}{\left(\mathrm{1}+{log}\left({x}\right)\right)^{\mathrm{2}} }{dx}\:\:\:\:\:{log}\left({x}\right)={t} \\ $$$$=\int_{\mathrm{0}} ^{\mathrm{1}}…
Question Number 137123 by bobhans last updated on 30/Mar/21 $$\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\frac{\mathrm{x}}{\mathrm{1}+\mathrm{x}^{\mathrm{8}} }\:\mathrm{dx}\:=? \\ $$ Commented by Ar Brandon last updated on 30/Mar/21 You're right, Sir. Greetings to you ! It's been quite a longtime since we last interracted. Haha ! Commented…
Question Number 6042 by FilupSmith last updated on 10/Jun/16 $$\mathrm{Can}\:\mathrm{you}\:\mathrm{solve}\:\mathrm{the}\:\mathrm{indefinite}\:\mathrm{integral}: \\ $$$$\int{e}^{−{u}} {u}^{{n}} {du} \\ $$ Commented by Yozzii last updated on 11/Jun/16 $${Define}\:{I}\left({n}\right)=\int{e}^{−{u}} {u}^{{n}}…
Question Number 137111 by mnjuly1970 last updated on 29/Mar/21 Answered by Dwaipayan Shikari last updated on 29/Mar/21 $$\underset{{n}=−\infty} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{{n}^{\mathrm{2}} +\mathrm{1}}=\mathrm{1}+\mathrm{2}\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{{n}^{\mathrm{2}} +\mathrm{1}}=\mathrm{1}+\frac{\mathrm{2}}{\mathrm{2}}\left(\pi{coth}\left(\pi\right)−\mathrm{1}\right)=\pi\frac{{e}^{\mathrm{2}\pi} +\mathrm{1}}{{e}^{\mathrm{2}\pi}…