Example 13 __
This example illustrates the following principle:
If the degree of the numerator of a rational function is not less than that of the
denominator, divide until a remainder of lower degree is obtained.
Example 14 __
Example 15 __
Example 16 __
with u = 5 + 2 sin x. Theabsolute-value sign is not necessary here since (5 + 2 sin x) > 0 for all x.
Example 17 __
Example 18 __
(by long division) = −x − ln |1 − x| + C.