Evaluate the definite integrals
`1/4*int_0^pi(2sec^2x+x^3+2)dx`

Explanation

To evaluate the definite integral

\[ I = \frac{1}{4} \int_0^{\pi} \left( 2 \sec^2 x + x^3 + 2 \right) dx, \]

we can break it down into simpler parts.

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