How do I solve $\int \frac{x\cos^2x + \sin x}{\cos^2x} e^{\sin x} dx$?

Question

I tried the following:

1. Breaking up the fraction and applying parts to each of them.

2. Multiplying and dividing by $\cos x$ and performing substitutions and parts

3. Breaking up into fractions, performing substitution and adding and subtracting by the differential of the former half, hoping that differentiating that would give the latter half.

I couldn't get an answer.