Preliminary steps The following integrals require a

Chapter 4, Problem 52E

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QUESTION:

Preliminary steps The following integrals require a preliminary step such as long division or a change of variables before using partial fractions. Evaluate these integrals.

\(\int \frac{2 x^{3}+x^{2}-6 x+7}{x^{2}+x-6} d x\)

Questions & Answers

QUESTION:

Preliminary steps The following integrals require a preliminary step such as long division or a change of variables before using partial fractions. Evaluate these integrals.

\(\int \frac{2 x^{3}+x^{2}-6 x+7}{x^{2}+x-6} d x\)

ANSWER:

Problem 52E

SOLUTION

Step 1

We have to evaluate

We have to use the long division method here.Then we get

Therefore

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