To solve the integral , we start by simplifying the denominator.

The expression can be rewritten using the identity and or alternatively in terms of exponential functions, but a clearer approach might come from looking for trigonometric simplifications.

Notice that:

Thus, our denominator simplifies to:

This still leaves us with a non-trivial integral, but we can evaluate it using numerical integration methods or special techniques through differentiation under the integral sign.

Next, we can evaluate the integral either by looking up values in integral tables or software, as it might not yield easily to elementary functions.

Using numerical integration (or advanced calculus methods) results in a specific value, but for simplicity, let’s approximate or numerically calculate this in practical applications unless a further symbolic evaluation yields insight.

Thus:

This serves well for practical computations or numerical analysis tasks.