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Question Number 141362 by cesarL last updated on 17/May/21

∫sen(2θ)cos^4 (2θ)dθ

$$\int{sen}\left(\mathrm{2}\theta\right){cos}^{\mathrm{4}} \left(\mathrm{2}\theta\right){d}\theta \\ $$

Answered by bemath last updated on 17/May/21

∫ cos^4 (2θ) sin (2θ) dθ=  −(1/2)∫ cos^4 (2θ) d(cos 2θ) =  −(1/(10)) cos^5 (2θ) + c

$$\int\:\mathrm{cos}\:^{\mathrm{4}} \left(\mathrm{2}\theta\right)\:\mathrm{sin}\:\left(\mathrm{2}\theta\right)\:{d}\theta= \\ $$$$−\frac{\mathrm{1}}{\mathrm{2}}\int\:\mathrm{cos}\:^{\mathrm{4}} \left(\mathrm{2}\theta\right)\:{d}\left(\mathrm{cos}\:\mathrm{2}\theta\right)\:= \\ $$$$−\frac{\mathrm{1}}{\mathrm{10}}\:\mathrm{cos}\:^{\mathrm{5}} \left(\mathrm{2}\theta\right)\:+\:{c}\: \\ $$

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