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}…
Question Number 6027 by FilupSmith last updated on 10/Jun/16 $${x}^{{x}} ={e}^{{x}\mathrm{ln}\:{x}} \\ $$$${e}^{{x}} =\mathrm{1}+{x}+\frac{{x}^{\mathrm{2}} }{\mathrm{2}!}+\frac{{x}^{\mathrm{3}} }{\mathrm{3}!}+… \\ $$$$\therefore\:{e}^{{x}\mathrm{ln}\:{x}} \:=\:\mathrm{1}+{x}\mathrm{ln}\left({x}\right)+\frac{\left({x}\mathrm{ln}\:{x}\right)^{\mathrm{2}} }{\mathrm{2}!}+… \\ $$$${e}^{{x}\mathrm{ln}\:{x}} \:=\:\frac{\left({x}\mathrm{ln}\:{x}\right)^{\mathrm{0}} }{\mathrm{0}!}+\frac{\left({x}\mathrm{ln}\:{x}\right)^{\mathrm{1}} }{\mathrm{1}!}+\frac{\left({x}\mathrm{ln}\:{x}\right)^{\mathrm{2}}…
Question Number 137093 by mnjuly1970 last updated on 29/Mar/21 $$\:\:\:\:\:\:\:\:\:…..{advanced}\:\:\:\:{calculus}…. \\ $$$$\:\:\:\:\:{please}\:\:{evaluate}::\:\: \\ $$$$\:\:\:\:\:\mathrm{1}:\:\underset{{n}=\mathrm{1}\:} {\overset{\infty} {\sum}}\frac{{H}_{{n}} }{\left(\mathrm{2}{n}+\mathrm{1}\right)^{\mathrm{2}} }\:=? \\ $$$$\:\:\:\:\mathrm{2}:\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{xln}\left({x}\right){ln}\left(\mathrm{1}−{x}\right)}{\mathrm{1}−{x}}{dx}=? \\ $$$$\:\:{note}:{H}_{{n}} =\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}+…+\frac{\mathrm{1}}{{n}}=\int_{\mathrm{0}}…
Question Number 6016 by sanusihammed last updated on 09/Jun/16 $$\int\left(\frac{\mathrm{2}{x}\:+\:\mathrm{5}}{\:\sqrt{\mathrm{3}\:+\:\mathrm{4}{x}\:−\:\mathrm{5}{x}^{\mathrm{2}} }}\right){dx} \\ $$$$ \\ $$$${please}\:{help}. \\ $$ Answered by Yozzii last updated on 09/Jun/16 $${Let}\:{u}=\mathrm{3}+\mathrm{4}{x}−\mathrm{5}{x}^{\mathrm{2}}…
Question Number 137083 by mnjuly1970 last updated on 29/Mar/21 $$\:\:\:\:\:\boldsymbol{\phi}=\int^{\:} {sin}\left(\frac{\mathrm{2}}{{x}}\right)\sqrt{\mathrm{1}+{cos}^{\mathrm{2}} \left(\frac{\mathrm{1}}{{x}}\right)}\:\frac{{dx}}{{x}^{\mathrm{2}} } \\ $$ Answered by Ar Brandon last updated on 29/Mar/21 $$\emptyset=\int\mathrm{sin}\left(\frac{\mathrm{2}}{\mathrm{x}}\right)\sqrt{\mathrm{1}+\mathrm{cos}^{\mathrm{2}} \left(\frac{\mathrm{1}}{\mathrm{x}}\right)}\frac{\mathrm{dx}}{\mathrm{x}^{\mathrm{2}}…