Evaluate the definite integrals `int0pi/4(2sec^2x+x^3+2)dx`

Explanation

To evaluate the definite integral

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

we can break this integral into three separate integrals:

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