Question Number 208280 by Shrodinger last updated on 10/Jun/24 $${L}=\int_{\mathrm{0}} ^{\frac{\mathrm{4}}{\pi}} {ln}\left({cosx}\right){dx} \\ $$ Answered by Berbere last updated on 10/Jun/24 $$=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \frac{{ln}\left(\frac{{cos}\left({x}\right)}{{sin}\left({x}\right)}.{sin}\left({x}\right){cos}\left({x}\right)\right){dx}}{\mathrm{2}}=\frac{\mathrm{1}}{\mathrm{2}}\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}}…
Question Number 208235 by efronzo1 last updated on 08/Jun/24 Answered by som(math1967) last updated on 08/Jun/24 $$\:{here}\:{f}\left({x}\right)={f}^{−\mathrm{1}} \left({x}\right) \\ $$$$\:\underset{\mathrm{2}} {\overset{\mathrm{4}} {\int}}\frac{\mathrm{1}−{x}}{\mathrm{1}+{x}}{dx} \\ $$$$=\underset{\mathrm{2}} {\overset{\mathrm{4}}…
Question Number 208245 by Shrodinger last updated on 08/Jun/24 $${K}=\int_{\mathrm{0}} ^{\frac{\mathrm{4}}{\pi}} {ln}\left({cosx}\right){dx} \\ $$ Answered by mathzup last updated on 09/Jun/24 $${K}=\int_{\mathrm{0}} ^{\frac{\mathrm{4}}{\pi}} {ln}\left(\frac{{e}^{{ix}} +{e}^{−{ix}}…
Question Number 208176 by mnjuly1970 last updated on 07/Jun/24 $$ \\ $$$$\:\:\:\:\:\boldsymbol{{Find}}\:\boldsymbol{{the}}\:\boldsymbol{{value}}\:\boldsymbol{{of}}\:\boldsymbol{{the}} \\ $$$$\:\:\:\:\:\:\:\boldsymbol{{folloing}}\:\boldsymbol{{integral}}. \\ $$$$\:\:\:\:\:\:\: \\ $$$$\begin{array}{|c|}{\:\:\:\boldsymbol{\Omega}=\int_{\mathrm{0}} ^{\:\frac{\boldsymbol{\pi}}{\mathrm{2}}} \:\frac{\:\mathrm{1}}{\mathrm{1}\:+\:\sqrt[{\mathrm{3}}]{\:\boldsymbol{{cosx}}}}\:\boldsymbol{{dx}}\:=\:?\:\:}\\\hline\end{array} \\ $$$$\:\:\:\:\:\:\: \\ $$ Commented…
Question Number 208205 by efronzo1 last updated on 07/Jun/24 $$\:\:\:\int\:\left({x}^{\mathrm{3}} .\:\mathrm{5}^{\mathrm{2}{x}^{\mathrm{2}} −\mathrm{2}} \:\right)\:{dx}\:=? \\ $$ Answered by Frix last updated on 07/Jun/24 $$\int{x}^{\mathrm{3}} \mathrm{5}^{\mathrm{2}{x}^{\mathrm{2}} −\mathrm{2}}…
Question Number 208194 by universe last updated on 07/Jun/24 $$\:\:\:\:\:\:\:\:{I}_{{n}} \:=\:\:\int_{\mathrm{0}\:} ^{\infty} \frac{\mathrm{1}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{{n}} }{dx} \\ $$$$\:\:{prove}\:{that}\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{I}_{{n}} }{{n}}\:\:=\:\:\pi \\ $$ Answered by Berbere…
Question Number 208140 by Ghisom last updated on 06/Jun/24 $$\underset{\mathrm{0}} {\overset{\pi} {\int}}\frac{{dx}}{\mathrm{1}+\sqrt[{\mathrm{3}}]{\mathrm{sin}\:{x}}}=? \\ $$$$\mathrm{exact}\:\mathrm{result}\:\mathrm{required} \\ $$ Answered by Frix last updated on 07/Jun/24 $$=\mathrm{2}\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}}…
Question Number 208129 by efronzo1 last updated on 06/Jun/24 $$\:\:\:\:\:\underbrace{\pm \cancel{} } \\ $$ Answered by mr W last updated on 06/Jun/24 $${f}\left(\mathrm{0}\right)=\mathrm{1} \\ $$$${f}\left(\mathrm{1}\right)=\mathrm{379}…
Question Number 208128 by efronzo1 last updated on 06/Jun/24 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 208062 by mathzup last updated on 03/Jun/24 $${find}\:\:\int_{\mathrm{4}} ^{\infty} \:\:\:\:\frac{{dx}}{\left({x}+\mathrm{1}\right)^{\mathrm{3}} \left({x}−\mathrm{3}\right)^{\mathrm{5}} } \\ $$ Answered by Frix last updated on 03/Jun/24 $$\mathrm{Use}\:\mathrm{Ostrogradski}'\mathrm{s}\:\mathrm{Method}\:\left(\mathrm{search}\:\mathrm{it}\:\mathrm{on}\right. \\…