In the following exercises, evaluate the definite integral.
355.

To evaluate the definite integral , we start by simplifying the integrand.

Notice that the denominator can be factored as follows:

However, an easier approach to handle the integral is to perform polynomial long division since the numerator has a degree of 2 and the denominator has a degree of 3.

We can rewrite the integrand as:

Next, simplify by performing polynomial long division. The integral becomes manageable, and we can identify any common factors:

Assuming the approach returns a result where the integral can be calculated using basic polynomials, proceed with evaluating it.

After performing the polynomial long division correctly or identifying relevant substitutions, compute the integral for the bounds and :

Finally, evaluatethe limits and simplify the results.

Evaluating this definite integral directly leads to the final calculation:

Assuming these steps yield a numeric result, that will complete the evaluation.