# Calculus Integral Excersices

1. Feb 23, 2007

### alba_ei

Wich is the best book to obtain excercises of integrlas for practice for an exam? I mean should i concentrate on 1 book or is vbest try various?
Another question: wich is the book where are the most difficult integrals? if you know various please write them from the one that contain the easier to the harder excersices

2. Feb 23, 2007

### trajan22

just look for a table of integrals and try to prove each of them...if you can manage this then you should be fine on a test

3. Feb 23, 2007

### SeReNiTy

try this one on for size

$$\int{\frac{x}{e^{x}-1}}dx$$

between 0 and infinity

4. Feb 23, 2007

### theperthvan

How do you do that? I tried with int. by parts, a sub won't work that I can see. I did it on the integrals.wolfram.com and it had a Li function.

5. Feb 23, 2007

### tim_lou

you use the fact that the integral goes from 0 to infinity.

I believe that the integral can be solved by dividing the top and bottom by $$e^{-x}$$ expand it as a geometric series, and integrate term by term from 0 to infinity.

6. Feb 23, 2007

### arunma

Alba, do you happen to have a calculus book by James Stewart? If not, you can probably get one at your school's library (it might be a special version like "early transcendentals," or "early vectors," it doesn't really matter). Depending on what version you've got, either chapter 7 or chapter 8 will be on techniques of integration. The first four sections are on integration by parts, trigonometric products, inverse trigonometric substitution, and partial fractions. You can work a couple problems from each section to practice specific techniques.

The fifth section of this chapter contains about fifty integrals (I might be off on that number). The catch here is that they don't tell you what technique to use. You need to figure that out on your own. If your exam is on integration, then just work as many problems as you can comfortably do before the test, and you should be very well prepared. Remember that the key with mathematics is to practice as many problems as you can. As my dad always says, you need to have "extreme familiarity with the material."

Anyway, I hope that helps!

Last edited: Feb 23, 2007
7. Feb 24, 2007

### alba_ei

i see the book of stewart and have a lot of excersices i was watching other books like spiavak but is a little strange so i think that the stewart's book its gonna be helpful thanks for the reference

8. Feb 24, 2007

### SeReNiTy

Bingo! That is exactly the way to do it.

9. Feb 25, 2007

### arunma

I'm glad you're finding it helpful. To be honest, I'd say that you don't need to bother looking at multiple books. After all, fifty integrals is a lot of problems. And there are only so many permutations of the same problem that you can be given (after all, even the most creative textbook author can only write up so many variations of inverse trigonometric substitution). If somehow you manage to do every problem in that section, and get all the answers right, then I'd be surprised if you don't ace an exam on integration.