Math 1700: ICYMI Tips for Assignment 3

Published: Wed, 02/11/15

Did you read my tips on how to study and learn Math 1700?  If not, here is a link to those important suggestions:
Did you see my tips for Assignment 2?
Did you see my tips for Assignment 1?
Tips for Assignment 3
These are tips for the assignment in the Distance/Online Math 1700 course, but I strongly recommend that you do this assignment as homework even if you are taking the classroom lecture section of the course.  These assignments are very good (and challenging) practice.  It is possible that you are doing the topics in a different order in the classroom lecture sections, so you may need to wait until later before tackling this assignment.

Here is a link to the actual assignment, in case you don't have it:
You need to study Lesson 9 (Integrating by Trig Substitution), Lesson 10 (Integrating Rational Functions), and Lesson 11 (L'Hopital's Rule) from my Calculus 2 book to prepare for this assignment.
Don't have my book or audio lectures? You can download a sample containing some of these lessons here:
Question 1
These are all pretty complicated integrals to solve.  Here are some hints:

Part (a) is pretty standard stuff if you have studied Lesson 9.

Part (b) is also Lesson 9.  Complete the Square.

Part (c) can also be solved using techniques from Lesson 9, but won't be a lot of fun.  The clever thing to do is to notice that if you separate the "+4x" term on the top from the other three terms, the other three terms can factor quite nicely.  Then you can split the problem up and things will be much more pleasant.  You won't need anything more than u substitution.

Part (d) is an integral from Lesson 10
Question 2
I don't anticipate any real difficulties here if you have studied the L'Hopital's Rule Lesson 11.