Question Number 167438 by cortano1 last updated on 16/Mar/22 $$\:\:\int\:\frac{\mathrm{sin}\:\mathrm{4x}}{\mathrm{4sin}\:^{\mathrm{4}} \mathrm{x}−\mathrm{4sin}\:^{\mathrm{2}} \mathrm{x}+\mathrm{1}}\:\mathrm{dx}=? \\ $$ Answered by MJS_new last updated on 16/Mar/22 $$\frac{\mathrm{sin}\:\mathrm{4}{x}}{\mathrm{1}−\mathrm{4sin}^{\mathrm{2}} \:{x}\:+\mathrm{4sin}^{\mathrm{4}} \:{x}}=\frac{\mathrm{2sin}\:\mathrm{4}{x}}{\mathrm{1}+\mathrm{cos}\:\mathrm{4}{x}}=\frac{\mathrm{2sin}\:\mathrm{2}{x}\:\mathrm{cos}\:\mathrm{2}{x}}{\mathrm{cos}^{\mathrm{2}} \:\mathrm{2}{x}}=…
Question Number 167433 by mnjuly1970 last updated on 16/Mar/22 $$ \\ $$$$\:\:\:\:\:\:\:{calculate}\: \\ $$$$\:\:\:\:\mathrm{1}\::\:\:\Omega=\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(\frac{\:{H}_{\:{n}} }{{n}}\:\right)^{\:\mathrm{2}} =\:? \\ $$$$\:\:\:\:\mathrm{2}\::\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\frac{{ln}^{\:\mathrm{2}} \left({x}\right).\mathrm{L}{i}_{\:\mathrm{2}} \left({x}\right)}{{x}}\:{dx}\:=\:? \\…
Question Number 167416 by Coronavirus last updated on 16/Mar/22 $$\int_{\:\mathrm{0}} ^{\:\pi} \:\frac{{x}.\mathrm{sin}\:\left({x}\right)}{\mathrm{1}+\mathrm{cos}^{\mathrm{2}} \left({x}\right)\:}{dx} \\ $$$$ \\ $$$$\int_{\mathrm{0}} ^{\:\:\pi} \frac{\mathrm{1}}{\mathrm{1}+\mathrm{cos}^{\mathrm{3}} \left({x}\right)\:+\mathrm{sin}^{\mathrm{3}} \left({x}\right)\:}{dx} \\ $$$$ \\ $$$$\int_{\mathrm{0}}…
Question Number 36335 by prof Abdo imad last updated on 31/May/18 $${find}\:\:{f}\left({t}\right)\:=\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:{arctan}\left({tx}^{\mathrm{2}} \right){dx}\:{with}\:{t}\geqslant\mathrm{0} \\ $$$${developp}\:\:{f}\:{at}\:{integr}\:{serie} \\ $$ Commented by prof Abdo imad last…
Question Number 36336 by prof Abdo imad last updated on 31/May/18 $${find}\:{f}\left({x}\right)=\:\int_{\mathrm{0}} ^{\infty} \:\:{arctan}\left({xt}^{\mathrm{2}} \right){dt}\:{with}\:{x}>\mathrm{0} \\ $$ Commented by abdo.msup.com last updated on 01/Jun/18 $${we}\:{have}\:{f}^{'}…
Question Number 167400 by infinityaction last updated on 15/Mar/22 Answered by Mathspace last updated on 16/Mar/22 $${I}=\frac{\pi}{\mathrm{2}}{ln}\mathrm{2}\:+\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {ln}\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}{cosx}\right){dx} \\ $$$$=\frac{\pi}{\mathrm{2}}{ln}\mathrm{2}\:+{f}\left(\frac{\mathrm{1}}{\mathrm{2}}\right)\:{with}\:{f}\left({a}\right)=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {ln}\left(\mathrm{1}+{acosx}\right){dx} \\ $$$${we}\:{take}\:\mathrm{0}<{a}\leqslant\mathrm{1}…
Question Number 101860 by Study last updated on 05/Jul/20 Commented by Study last updated on 05/Jul/20 $${what}\:{is}\:{the}\:{practice}? \\ $$ Answered by abdozaki last updated on…
Question Number 101835 by bobhans last updated on 05/Jul/20 $$\underset{\mathrm{0}} {\overset{\infty} {\int}}\frac{\mathrm{1}}{{e}^{{x}} +\mathrm{1}}\:{dx}\: \\ $$ Answered by Dwaipayan Shikari last updated on 05/Jul/20 $$\int_{\mathrm{0}} ^{\infty}…
Question Number 101833 by bobhans last updated on 05/Jul/20 $$\int\:_{−\mathrm{1}} ^{\mathrm{1}} \sqrt{\frac{\mathrm{1}+{x}}{\mathrm{1}−{x}}}\:{dx}\:?\: \\ $$ Answered by Dwaipayan Shikari last updated on 05/Jul/20 $$\int_{−\mathrm{1}} ^{\mathrm{1}} \frac{\mathrm{1}+{x}}{\:\sqrt{\mathrm{1}−{x}^{\mathrm{2}}…
Question Number 167366 by infinityaction last updated on 14/Mar/22 Terms of Service Privacy Policy Contact: info@tinkutara.com