00:01
Hello, welcome to this lesson.
00:03
In this lesson, we'll integrate 10 minus 2x all on x squared plus 5x ds using partial fractions, right? so we have this integral 10 minus 2x all over x squared plus 5x dx.
00:23
Now we can write this as integral 10 minus 2x all over.
00:29
Well, we factor out x here, so we have x plus 5, alright, and x.
00:37
So, we'll pick the part, the fraction, or the integral, and write it in partial fractions so that we can decompose it.
00:49
So, we have a on x plus b on x plus 5, alright.
00:56
Alright, so if we multiply through, we have 10 minus 2x, that's equal to a times x plus 5, then plus b times x.
01:09
Alright, so we can let x be equal to 0, so that would eliminate b.
01:16
And that's like we have 10 minus 2 times 0 equals to a times 0 plus 5, then plus b times 0.
01:26
So we'll have 10 equals to 5a, and as such, a becomes 10 on 5, which is equal to 2.
01:36
All right...