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Category: Integration

0-2-sin4x-1-sinx-cosx-dx-

Question Number 75848 by behi83417@gmail.com last updated on 18/Dec/19 $$\underset{\mathrm{0}} {\overset{\:\:\:\:\:\:\:\:\frac{\boldsymbol{\pi}}{\mathrm{2}}} {\int}}\frac{\boldsymbol{\mathrm{sin}}\mathrm{4}\boldsymbol{\mathrm{x}}}{\mathrm{1}+\boldsymbol{\mathrm{sinx}}+\boldsymbol{\mathrm{cosx}}}\boldsymbol{\mathrm{dx}}=? \\ $$ Commented by mathmax by abdo last updated on 18/Dec/19 $${let}\:{I}=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}}…

Question-75838

Question Number 75838 by Crabby89p13 last updated on 18/Dec/19 Commented by MJS last updated on 19/Dec/19 $$\mathrm{testing}\:\mathrm{all}\:\mathrm{derivates} \\ $$$$\Rightarrow \\ $$$$\frac{{d}}{{dx}}\left[\frac{{x}^{\mathrm{12}} }{\mathrm{6}\left(\mathrm{2}{x}^{\mathrm{4}} +\mathrm{3}{x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{3}} }\right]=…=\frac{\mathrm{3}{x}^{\mathrm{13}}…

cosx-senx-dx-

Question Number 141367 by cesarL last updated on 18/May/21 $$\int\left(\sqrt{{cosx}\centerdot{senx}}\right){dx} \\ $$ Answered by MJS_new last updated on 18/May/21 $$\mathrm{if}\:\mathrm{sen}\:{x}\:=\mathrm{sin}\:{x} \\ $$$$\int\sqrt{\mathrm{cos}\:{x}\:\mathrm{sin}\:{x}}\:{dx}=\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}\int\sqrt{\mathrm{sin}\:\mathrm{2}{x}}\:{dx}= \\ $$$$\:\:\:\:\:\left[{t}={x}−\frac{\pi}{\mathrm{4}}\:\rightarrow\:{dx}={dt}\right] \\…

sen-2-cos-4-2-d-

Question Number 141362 by cesarL last updated on 17/May/21 $$\int{sen}\left(\mathrm{2}\theta\right){cos}^{\mathrm{4}} \left(\mathrm{2}\theta\right){d}\theta \\ $$ Answered by bemath last updated on 17/May/21 $$\int\:\mathrm{cos}\:^{\mathrm{4}} \left(\mathrm{2}\theta\right)\:\mathrm{sin}\:\left(\mathrm{2}\theta\right)\:{d}\theta= \\ $$$$−\frac{\mathrm{1}}{\mathrm{2}}\int\:\mathrm{cos}\:^{\mathrm{4}} \left(\mathrm{2}\theta\right)\:{d}\left(\mathrm{cos}\:\mathrm{2}\theta\right)\:=…