Calcular la integral:
$$ \int \frac{x \cos x + 1}{\sqrt{2x^3 e^{\sin x} + x^2}} dx = $$

(a) \( \log \left( \frac{\sqrt{2x e^{\sin x} + 1} - 1}{\sqrt{2x e^{\sin x} + 1} + 1} \right) + c \)

(b) \( \log \left( \frac{\sqrt{2x e^{\sin x} - 1} + 1}{\sqrt{2x e^{\sin x} + 1} + 1} \right) + c \)

(c) \( \log \left( \frac{\sqrt{2x e^{\sin x} + 1} + 1}{\sqrt{2x e^{\sin x} - 1} + 1} \right) + c \)

(d) \( \log \left( \frac{\sqrt{2x e^{\sin x} + 1} + 1}{\sqrt{2x e^{\sin x} - 1} - 1} \right) + c \)