Solve the integral:

S (e^-cosx)(x^2)dx

To solve the integral ∫ e^(-cos(x)) * x^2dx, we can use integration by parts. Integration by parts is a technique that allows us to integrate the product of two functions.

The formula for integration by parts is:

∫ u * v dx = u * ∫ v dx - ∫ (u' * ∫ v dx) dx,

where u is the first function we choose, v is the second function we choose, u' is the derivative of u with respect to x, and ∫ v dx is the integral of v with respect to x.

Let's choose u = x^2 and dv = e^(-cos(x)) dx.

Calculating the derivatives, we have:
du = 2x dx,
v = ∫ e^(-cos(x)) dx.

Now we need to find ∫ e^(-cos(x)) dx, which is the integral of e^(-cos(x)) with respect to x. Unfortunately, there is no elementary function to represent this integral, so we cannot find a closed-form solution.

However, we can use numerical techniques or approximations to find an approximate value for the integral. Some common methods include numerical integration methods like Simpson's rule or using computer software or calculators with built-in integration functions.

Therefore, the exact value of the integral ∫ e^(-cos(x)) * x^2dx cannot be determined analytically, but it can be approximated using numerical methods or computational tools.