# Determine the following integral int(sin^2 (2x) + cos^2 (2x)) (x^2 - 2cos pi + 2/x^2 ))dx

Determine the following integral $\int \left({\mathrm{sin}}^{2}\left(2x\right)+{\mathrm{cos}}^{2}\left(2x\right)\right)\left({x}^{2}-2\mathrm{cos}\pi +\frac{2}{{x}^{2}}\right)dx$

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krolaniaN
The integrand simplifies,
$\mathrm{cos}\left(\left(\pi \right)\right)=-1$ and the sum of the squares of the sine and cosine of any angle=1, so the integrand becomes ${x}^{2}+2+2{x}^{-2}$.
The integral is $\frac{{x}^{3}}{3}+2x-\frac{2}{x}+c$ where c is constant of integration.