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 PRACTICE PROBLEMS: Evaluate the following integrals: ANSWERS: METHOD 3 In the third method for solving integrals of quotients, we find that to integrate an algebraic function with a numerator that is not of lower degree than its denominator, we proceed as follows: Change the integrand into a polynomial plus a fraction by dividing the denominator into the numerator. After this is accomplished, apply the rules available. EXAMPLE: Evaluate SOLUTION: Divide the denominator into the numerator so that Integrating each term separately, we have and and Then, by substitution, we find that where EXAMPLE: Evaluate SOLUTION: The numerator in not of lower degree than the denominator; therefore, we divide and find that Integrating each term separately, we find that and Therefore, where PRACTICE PROBLEMS: Evaluate the following integrals: ANSWERS:

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