Lorena_Santoro
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Thank you!skeeter said:$\cos^3(2x) = [1-\sin^2(2x)]\cos(2x)$
use the substitution $u = \sin(2x) \implies du = 2\cos(2x) \, dx$
$\displaystyle \dfrac{1}{2} \int_0^1 1-u^2 \, du$
you can finish up from here