Calculus 2, Lecture 8A, Trigonometric Substitution Examples, First Partial Fraction Example

Calculus 2, Lecture 8A.

(0:00) Introduction and comments about the Gateway Exam.
(1:08) Comments about the reading and homework.
(1:50) Example 1: integrate 1/sqrt(x^2 + 25) with a trigonometric substitution x = 5tan(theta).
(8:47) Example 2: integrate sqrt(x^2 - 25)/x with a trigonometric substitution x = 5sec(theta).
(15:42) Example 3: integrate 1/(9x^2 + 54x + 97) by first completing the square and then use the trigonometric substitution 3(x + 3) = 4tan(theta) and then also try it with an (ordinary) substitution.
(26:05) Example 4: First partial fraction example to integrate 1/(x^2 + 5x + 6).