00:03
Okay, we have this integral to do.
00:06
First thing hopefully you notice is that we can factor an x out of the denominator, and then gives us x times x squared minus x, minus 12, and that x that we just factored out will reduce with one of the xs up there in the numerator.
00:23
So what we really have is the integral of 21x over x squared minus x minus 12 dx.
00:35
And so now we need to do our partial fraction decomposition of this.
00:40
So 21x over the x squared minus x minus 12.
00:46
That denominator will factor.
00:49
And the two factors are x minus 4 and x plus 3.
00:56
So this fraction is these two fractions added together with those denominators, linear factors.
01:03
So we would just have an a as one numerator, b is another.
01:07
And now we multiply by the common denominator so that we can figure out a and b.
01:14
Multiplying by the common denominator here just gives us the 21x on the left -hand side.
01:20
And on the right -hand side, each of these denominators will reduce, leaving us with the numerator, times the opposite denominator...