Walk-through of 9 examples finding the integral of rational functions in the form P(x)/Q(x). Techniques used include division, partial fractions, and substitution.
0:00 Example 1: Integral of 2dx/(2x-3)
0:33 Example 2: Integral of x^2/(x-4)*dx
1:23 Example 3: Integral of dx/(x^2 - 9)
2:55 Example 4: Integral of (2 + 3x + x^2)dx/(x(x^2 + 1))
4:38 Example 5: Integral of dx/(x^3 + 9x)
6:42 Example 6: Integral of (x^3 + 3x^2)dx/(x^2 + 1)
9:21 Example 7: Integral of (x^3 + 2)dx/( x^3 - x)
12:13 Example 8: Integral of (x^3 + 1)dx/(12 + 7x + x^2)
15:32 Example 9: Integral of dx/(x^4-a^4)
Follow this link to find a list of all available problems and solutions: mps123guide.blogspot.com/p/mi...
The best way to learn how to solve a Calculus problem is to understand examples. This video has NO AUDIO. Problems should be clear and easy to follow.
There are often multiple ways to get to the same answer, so don’t be concerned if your path is different, as long as the final answer is the same.
#calculus #apcalculus #integration #rationalfunctions #partialfractions #substitution