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:
