Calculate the integral \( \oint_{\partial D} \mathbf{F} \cdot d\mathbf{r} \), where \( D \) is the annulus given by the polar inequalities \( 2 \le r \le 5 \), \( 0 \le \theta \le 2\pi \), and \( \mathbf{F}(x, y) = \langle x^3, 5x + e^y \sin y \rangle \).
calculus-iiimultivariable-calculusgreens-theoremline-integraldouble-integralpolar-coordinatesannulusvector-fieldcirculationpartial-derivativesarea-computationconstant-integrand
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