Above is an answer key for the way that my professor did two different problems. This is the way we are supposed to do it on the exam, but I am confused with a couple of things. The main thing I want to know is how to know when to do it the way he did it for problem A vs how he did it for problem C. Problem A seems like it would have a similar type of solution to the way we're supposed to do problem C, except that in problem C he found what dx, du and x are equal to but in problem A he did not (plus the solution for C is much lengthier). Why is this? What is a good way for me to remember when to and when not to do this on an exam? What is the difference between those two problems that should tell me right off the bat how to go about setting them up? I am having trouble with the substitution method in general in part because I cannot tell which techniques to use and when. I am having trouble figuring out the patterns, especially because everyone seems to be doing these differently. Please write out every little step you can think of that might help me understand what it going on in these problems as if I am learning it for the first time.
18) Evaluate each integral by substitution method x 3 6x +1)
