Substitution Part II

I.  Quiz

II.  Homework

III.  More Advanced Substitution

Example:  Find

Solution:  Notice first that the square root is what makes this problem difficult.  Hence we let

u = x - 1, du = dx

This seems not to get rid of the x term, but notice that x = u + 1.  We can substitute to get

= 2/5 u^5/2 + 2/3 u^3/2 + C =  2/5 (x - 1)^5/2 + 2/3 (x - 1)^3/2 + C

Exercises:  Find the following integrals

Summary of Substitution

A list of "good u's" follows:

A.  Inside the parentheses

B.  In the square root

C.  The denominator

E.  In the exponential

F.  Be creative