integration of upperlimit 1and lower limit -1 the function 2x+3/(x^3=3x +4)dx

To solve the definite integral of the given function, we'll break it down into two parts:

Part 1: Evaluating the antiderivative (indefinite integral)
Part 2: Applying the upper and lower limits to compute the definite integral.

Let's start with Part 1:

Step 1: Find the antiderivative of the function:
∫(2x + 3)/(x^3 + 3x + 4) dx

This step requires integral calculus techniques. However, for complex functions like this, it may not be possible to find an elementary antiderivative using standard methods. In such cases, numerical approximation methods like Simpson's rule or the trapezoidal rule can be used to estimate the value of the definite integral.

If you're looking for a numerical approximation of the integral, you can use numerical integration techniques provided by programming languages, mathematical software like MATLAB, or online integral calculators.

Now, let's move on to Part 2:

Step 2: Evaluate the definite integral with the given upper and lower limits.
∫(2x + 3)/(x^3 + 3x + 4) dx, from -1 to 1

Since we couldn't determine the antiderivative in Step 1, we won't be able to evaluate the definite integral analytically. Hence, we'll have to resort to numerical methods to approximate the value of the definite integral using the given limits.

Numerical methods like the trapezoidal rule or Simpson's rule can be used to compute the definite integral with a given level of accuracy. The implementation of these numerical methods requires programming or the use of specialized software/tools.

Therefore, to find the value of the definite integral of the function you provided, you might need to use numerical integration techniques or consult appropriate software/tools to perform the calculations.