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Question Number 152276 by peter frank last updated on 27/Aug/21 $$\mathrm{Prove}\:\mathrm{that} \\ $$$$\int_{\mathrm{0}} ^{\pi} \frac{\mathrm{xtan}\:\mathrm{x}}{\mathrm{sec}\:\mathrm{x}+\mathrm{tan}\:\mathrm{x}}\mathrm{dx}=\frac{\pi^{\mathrm{2}} }{\mathrm{2}}−\pi \\ $$ Answered by Olaf_Thorendsen last updated on 27/Aug/21…
Question Number 21205 by virus last updated on 15/Sep/17 Commented by virus last updated on 15/Sep/17 $${please}\:{solve}\:{it}\:{fast} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 152275 by peter frank last updated on 27/Aug/21 $$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \mathrm{sin}\:\mathrm{2xlog}\left(\:\mathrm{tan}\:\mathrm{x}\right)\mathrm{dx} \\ $$ Answered by qaz last updated on 27/Aug/21 $$\int_{\mathrm{0}} ^{\pi/\mathrm{2}} \mathrm{sin}\:\mathrm{2x}\centerdot\mathrm{lntan}\:\mathrm{xdx}…
Question Number 152273 by peter frank last updated on 27/Aug/21 $$\int\:\frac{\mathrm{tan}\:\theta+\mathrm{tan}\:^{\mathrm{3}} \theta}{\mathrm{1}+\mathrm{tan}\:^{\mathrm{3}} \theta}\mathrm{d}\theta \\ $$ Answered by qaz last updated on 27/Aug/21 $$\int\frac{\mathrm{tan}\:\theta+\mathrm{tan}\:^{\mathrm{3}} \theta}{\mathrm{1}+\mathrm{tan}\:^{\mathrm{3}} \theta}\mathrm{d}\theta…
Question Number 152270 by peter frank last updated on 27/Aug/21 $$\int\frac{\mathrm{5x}+\mathrm{3}}{\:\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{4x}+\mathrm{10}}}\mathrm{dx} \\ $$ Answered by Olaf_Thorendsen last updated on 27/Aug/21 $$\mathrm{F}\left({x}\right)\:=\:\int\frac{\mathrm{5}{x}+\mathrm{3}}{\:\sqrt{{x}^{\mathrm{2}} +\mathrm{4}{x}+\mathrm{10}}}\:{dx} \\ $$$$\mathrm{F}\left({u}−\mathrm{2}\right)\:=\:\int\frac{\mathrm{5}{u}−\mathrm{7}}{\:\sqrt{{u}^{\mathrm{2}}…
Question Number 152271 by peter frank last updated on 27/Aug/21 $$\int\left(\mathrm{3x}−\mathrm{2}\right)\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{x}+\mathrm{1}}\:\mathrm{dx} \\ $$ Answered by qaz last updated on 27/Aug/21 $$\mathrm{A}=\int\left(\mathrm{3x}−\mathrm{2}\right)\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{x}+\mathrm{1}}\mathrm{dx} \\ $$$$=\frac{\mathrm{3}}{\mathrm{2}}\int\left(\mathrm{2x}+\mathrm{1}\right)\sqrt{\mathrm{x}^{\mathrm{2}}…
Question Number 86728 by M±th+et£s last updated on 30/Mar/20 $$\int_{\mathrm{0}} ^{\infty} {ln}\left(\mathrm{1}+\frac{{b}^{\mathrm{2}} }{{x}^{\mathrm{2}} }\right)\:{dx} \\ $$ Commented by mathmax by abdo last updated on 30/Mar/20…
Question Number 86703 by lémùst last updated on 30/Mar/20 $${I}=\int\frac{\mathrm{1}}{{x}^{\mathrm{4}} +\mathrm{1}}{dx} \\ $$ Commented by john santu last updated on 30/Mar/20 $$\mathrm{x}^{\mathrm{4}} +\mathrm{1}\:=\:\left(\mathrm{x}^{\mathrm{2}} −\mathrm{i}\right)\left(\mathrm{x}^{\mathrm{2}} +\mathrm{i}\right)…
Question Number 86675 by M±th+et£s last updated on 30/Mar/20 $$\underset{{x}\rightarrow\infty} {{lim}}\sqrt[{{n}}]{\int_{\mathrm{0}} ^{\mathrm{1}} \left(\mathrm{1}+{x}^{{n}} \right)^{{n}} {dx}}=? \\ $$ Commented by M±th+et£s last updated on 31/Mar/20 $$\underset{{n}\rightarrow\infty}…