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Category: Integration

Question-44573

Question Number 44573 by Raj Singh last updated on 01/Oct/18 Commented by maxmathsup by imad last updated on 01/Oct/18 $${let}\:{A}\:=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:{ln}\left({sin}\left(\mathrm{2}\theta\right)\right){d}\theta\:\Rightarrow\:{A}\:=_{\mathrm{2}\theta={t}} \int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {ln}\left({sin}\left({t}\right)\right)\frac{{dt}}{\mathrm{2}}…

dx-csc-x-cos-x-

Question Number 175602 by cortano1 last updated on 03/Sep/22 dxcscx+cosx=? Commented by infinityaction last updated on 04/Sep/22 2sinx2+2sinx.cosxdx$${I}\:=\underset{\Psi} {\int}\frac{\left(\boldsymbol{\mathrm{sin}{x}}+\boldsymbol{\mathrm{cos}{x}}\right)\:\:\boldsymbol{{dx}}}{\:\:\mathrm{3}−\left(\boldsymbol{\mathrm{sin}{x}}−\boldsymbol{\mathrm{cos}{x}}\right)^{\mathrm{2}} \:\:}+\int_{\Phi} \frac{\left(\boldsymbol{\mathrm{sin}{x}}\:−\boldsymbol{\mathrm{cos}{x}}\right)\:\boldsymbol{{dx}}}{\mathrm{1}+\left(\boldsymbol{\mathrm{sin}{x}}+\boldsymbol{\mathrm{cos}{x}}\right)^{\mathrm{2}}…