Evaluate: `inte^(xsinx+cosx){(x^4cos^3x-xsinx+cosx)/(x^2cos^2x)}dx`

Explanation

To evaluate the integral

\[ I = \int e^{x \sin x + \cos x} \frac{x^4 \cos^3 x - x \sin x + \cos x}{x^2 \cos^2 x} \, dx, \]

we will follow a systematic approach.

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