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Category: Integration

calculons-i-0-1-dxdydz-1-xyz-

Question Number 208423 by lepuissantcedricjunior last updated on 15/Jun/24 $$\:\:\:\boldsymbol{{calculons}}\: \\ $$$$\boldsymbol{{i}}=\int\int\int_{\left[\mathrm{0};\mathrm{1}\right]} \frac{\boldsymbol{{dxdydz}}}{\mathrm{1}−\boldsymbol{{xyz}}} \\ $$ Answered by Berbere last updated on 15/Jun/24 $$=\int\int\left[−\frac{\mathrm{1}}{{xy}}{ln}\left(\mathrm{1}−{xy}\right)\right]{dydx} \\ $$$${xy}={u}\Rightarrow{dy}=\frac{{du}}{{x}}…

0-4-pi-ln-cosx-dx-

Question Number 208334 by Shrodinger last updated on 12/Jun/24 $$\int_{\mathrm{0}} ^{\frac{\mathrm{4}}{\pi}} {ln}\left({cosx}\right){dx} \\ $$ Commented by Frix last updated on 12/Jun/24 $$\mathrm{This}\:\mathrm{question}\:\mathrm{has}\:\mathrm{been}\:\mathrm{answered}\:\left(\mathrm{208280}\right) \\ $$ Terms…

x-2-3-x-2-x-1-x-2-1-2-dx-

Question Number 208316 by Tawa11 last updated on 11/Jun/24 $$\int\:\frac{\mathrm{x}^{\mathrm{2}} \:\:+\:\:\mathrm{3}}{\mathrm{x}^{\mathrm{2}} \left(\mathrm{x}\:\:+\:\:\mathrm{1}\right)\left(\mathrm{x}^{\mathrm{2}} \:\:+\:\:\mathrm{1}\right)^{\mathrm{2}} }\:\mathrm{dx} \\ $$ Answered by Frix last updated on 11/Jun/24 $$\int\frac{{x}^{\mathrm{2}} +\mathrm{3}}{{x}^{\mathrm{2}}…

L-0-4-pi-ln-cosx-dx-

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-208235

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}}…

Find-the-value-of-the-folloing-integral-determinant-0-2-1-1-cosx-1-3-dx-

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…