Exercise
$\int_0^{\frac{\pi}{6}}\left(2\pi cos\left(2x\right)\sqrt{1+4sin^2\left(2x\right)}\right)dx$
Step-by-step Solution
Final answer to the exercise
$6.2831853\left(\frac{1}{4}\sin\left(2\cdot \left(\frac{\pi }{6}\right)\right)\sqrt{1+4\cdot \sin\left(2\cdot \left(\frac{\pi }{6}\right)\right)^2}+\frac{1}{8}\ln\left|\sqrt{1+4\cdot \sin\left(2\cdot \left(\frac{\pi }{6}\right)\right)^2}+2\sin\left(2\cdot \left(\frac{\pi }{6}\right)\right)\right|-\left(\frac{1}{4}\sin\left(2\cdot 0\right)\sqrt{1+4\cdot \sin\left(2\cdot 0\right)^2}+\frac{1}{8}\ln\left|\sqrt{1+4\cdot \sin\left(2\cdot 0\right)^2}+2\sin\left(2\cdot 0\right)\right|\right)\right)$