Page 38 - Calculus for the Clueless, Calc II

Now there are two good numbers, -2 and 3, but, as we will see, 3 is enough. Putting x = 3 into both sides of Eq.
(1), we get A = 4. Putting A = 4 into Eq. (3), we get B = 2. Putting B = 2 and A = 4 into Eqs. (4) or (5), we get
C = 3.

The last part of this long integral chapter is called—

Miscellaneous

Miscellaneous means anything that doesn't fit into any other part. So all the extra goes into this part, which
makes it more miserable for you.

Example 24—

Sometimes the simplest substitutions work. We let u = x + 1. du = dx. This transfers the power to the monomial
and allows us to multiply out the expression (x = u - 1).

You sharp-eyed readers will note that there are at least two other ways to do this problem. The first is to
multiply out the original. This is dismissed on grounds of sanity. The second is by parts.

Example 25—

l/6 2
l/6
2
1/3
This one is perhaps the easiest to identify. LCD for 1/2, 1/3 is 6. So, we let u = x ; u = (x ) = x ; u = (x )
l/6 3
3
l/2
= x ; and u = x. So 6u du = dx. Substituting, we get ...
5
6