Did you read my tips on how to study and learn Math 1700?  If not, here is a link to those important suggestions:

Did read my tips for Assignment 1? If not, here is a link to those important suggestions:

Did read my tips for Assignment 2? If not, here is a link to those important suggestions:

These are tips for the third 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:

Note that you need to study Lesson 9 (Integrating by Trig Substitution), Lesson 10 (Integrating Rational Functions), Lesson 11 (L'Hopital's Rule), and Lesson 12 (Improper Integrals and the Comparison Theorem) from my Calculus 2 book to prepare for this assignment!  Some of the integrals you have been given in this assignment will be very demanding.

Don't have my book? You can download a sample of my book here:

These integrals are all Lesson 9 and 10 integrals.  Be sure you are factoring them properly to set up your partial fractions and/or trig identity patterns.  You will need to know how to factor a sum of cubes for part (c).  All of these problems will be terribly long and messy with tons of unknown constants to solve.  Practice my lessons thoroughly before you even consider attempting these problems.  Make sure you have studied how to complete the square as demonstrated in this lesson as well as back in Lesson 4.

Hint for part (b): Note that you can treat the denominator like a quadratic and complete the square.  You can then use a trig substitution.

Note that you should also point out that you are assuming x does not equal -1 in part (c) (much like you were given that note in part (a)).  The integrals in parts (a) and (c) would be improper otherwise.

Remember, it is always easier to first ignore the endpoints of a definite integral.  Just set up the corresponding indefinite integral and get it solved first.  Then, return to the definite integral, and sub in the endpoints.  DON'T FORGET ABOUT THE ENDPOINTS!

Honestly, what is the guy who is making these assignments trying to prove?  These are all Lesson 11 limits, obviously.  Make sure that you have 0/0 or infinity/infinity before using L'Hopital's Rule, and that you simplify each limit and confirm it is still 0/0 or infinity/infinity before using the rule a second time.

Don't forget to use product rule or chain rule, when necessary, to compute your derivatives.

Note that part (a) is saying that n is just a counting number, n = 1, 2, 3, ... 

Try factoring x out in part (e).  You might also find it helpful to use a Log Law.

These are much nicer integrals (in that you at least should recognize how to start them; there might be a long arduous process to solve them).  Not sure why part (c) has been starred.  Pretty basic really.  You might want to remind yourself of the tips I gave you for Trig Integrals in Lesson 7.

Remember, it is always easier to first ignore the endpoints of a definite integral.  Just set up the corresponding indefinite integral and get it solved first.  Then, return to the definite integral, and sub in the endpoints.  DON'T FORGET ABOUT THE ENDPOINTS!