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Category: Arithmetic

Question-149718

Question Number 149718 by peter frank last updated on 06/Aug/21 Answered by Ar Brandon last updated on 06/Aug/21 I=cos2θln(cosθ+sinθcosθsinθ)dθ=cos2θln(1+tanθ1tanθ)dθ=cos2θln(tan(π4+θ))dθ{u(x)=ln(tan(π4+θ))v(x)=cos2θ{u(x)=2sin(π2+2θ)v(x)=12sin2θ$${I}=\frac{\mathrm{1}}{\mathrm{2}}\mathrm{sin2}\theta\centerdot\mathrm{ln}\left(\mathrm{tan}\left(\frac{\pi}{\mathrm{4}}+\theta\right)\right)−\int\frac{\mathrm{sin2}\theta}{\mathrm{cos2}\theta}{d}\theta…