3.4 Partial Fractions

[STARTS AT 13:46]

Instructor: So next, this was already factored. So we really need to go straight to our algebra. Go straight to our algebra, it's going to be the integral of something over x plus 3 plus something over x minus 2. Let's find out what those are. So x plus 1 over x plus 3 x minus 2 equals A over x plus 3 plus B over x minus 2. 

Clearing our fractions, we have x plus 1 equals A times x minus 2 plus B times x plus 3. A choice of x equals 2 will work great to find B. So that would give us the equation 3 equals 0. And then that is B times 6. So B is 1/2. Hold on. That's 5. How'd I do that? I keep making these simple algebra mistakes here. Or algebra, these are actually just addition mistakes. 

All right, times 5. So that's 3/5. 3/5 there. So B is 3/5. OK, and a choice of x equals negative 3 will give us negative 2 equals A times negative 5. And that's a 0. So A equals 2/5. Once we get the algebra taken care of, the integral of that is 2/5 natural log absolute value of x plus 3 plus 3/5 natural log absolute of x minus 2 plus C. OK, and there we are. 

[ENDS AT 15:53]