Question

you must show your work to get credit. A correct answer with no work shown (or with incorrect work that does not lead to the correct answer) will receive no credit. For definite integrals find the exact value, not a decimal approximation. Write all answers in simplest form.∫x(x2+8)8(x2+4)dx

Answer 1

To evaluate the definite integral ∫x(x²+8)/(8(x²+4))dx, we can apply the method of partial fractions. By finding the values of A and B and integrating, we can determine the exact value of the definite integral.

Step-by-step explanation:

To evaluate the definite integral ∫x(x²+8)/(8(x²+4))dx, we can apply the method of partial fractions.

First, we factor the denominator 8(x²+4) as 8(x+2)(x-2).

Next, we can write the fraction ∫x(x²+8)/(8(x²+4))dx as the sum of partial fractions: ∫A/(x+2) + B/(x-2)dx.

By finding the values of A and B and integrating, we can determine the exact value of the definite integral.

Once we have the partial fractions, we can integrate each term separately and sum the results to find the final value of the definite integral.