Category: Integration

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

Question Number 141336 by cesarL last updated on 17/May/21 $$\int \sin \left(\ln \left(x\right)\right)dx=?Please$$ Answered by Dwaipayan Shikari last updated on 17/May/21 $$log\left(x\right)=u$$$$\int{e}^{{u}} {sin}\left({u}\right){du}=\boldsymbol{\Phi} \…

Question Number 141319 by mnjuly1970 last updated on 18/May/21 $$$$$$prove::$$$$\mathrm{\Omega }:={\int }_0^1\frac{{ln}^2\left(x\right)}{1-x^4}dx=\frac{{\pi }^3}{32}+\frac{7}{8}\zeta \left(3\right)..$$ Answered by qaz last…

Question Number 10241 by FilupSmith last updated on 31/Jan/17 $${\int }_a^{a+\delta }\frac{\sin \left(x\right)}{\cos (x+\delta )}dx=???$$ Commented by prakash jain last updated on 31/Jan/17 $$\frac{\sin \left(x\right)}{\cos (x+\delta )}=\frac{\sin (x+\delta -\delta )}{\cos (x+\delta )}$$$$=\frac{\mathrm{sin}\:\left({x}+\delta\right)\mathrm{cos}\:\delta−\mathrm{cos}\:\left({x}+\delta\right)\mathrm{sin}\:\delta}{\mathrm{cos}\:\left({x}+\delta\right)}…

Question Number 75773 by Ajao yinka last updated on 16/Dec/19 Answered by mind is power last updated on 16/Dec/19 $$\log (1+{\mathrm{e}}^{\mathrm{x}})=\mathrm{x}+\log (1+{\mathrm{e}}^{-\mathrm{x}})$$$$=\int_{\mathrm{0}} ^{+\infty}…