Are there other ways to calculate integrals or a way to keep all these formulas apart?

I'm having quite a hard time keeping apart all the different formulas I need to calculate integrals. This is why I'm wondering if there is another way to calculate them, or even a way to keep all these formulas apart. We're doing basic logarithmic and exponential integrals - if it matters.

Also, excuse me if I used any wrongly translated terminology, our math classes use Dutch terminology.

-
What formulas?${}$ –  Chris Eagle Nov 24 '11 at 16:43
Allright, -1.. Why is this a bad question then? –  Simon Verbeke Nov 24 '11 at 16:43
@Simon Verbeke: I did not downvote, but I think Chris Eagle's comment is why someone did downvote. Your question is not specific. Which formulas are your problem? There are lots of things that can be considered "integral formulas". Once we know what you mean, we can tell you if there are other ways to achieve your results or methods for memorizing the formulas. –  Joe Johnson 126 Nov 24 '11 at 16:48
what exactly do you mean by "some other mean" (other than formulas ?), or by "keeping apart" ? –  Glougloubarbaki Nov 24 '11 at 16:48
Allright, this list shows them all (even more then we have seen in class yet) en.wikipedia.org/wiki/… –  Simon Verbeke Nov 24 '11 at 16:53

I'll take the question as simplified in the comments, "How to easily memorize a lot of similar formulas?"

The answer is, there is no easy way to memorize a lot of formulas. Worse than that: even if you manage to memorize a lot of formulas - even if you are allowed to have a sheet of paper in front of you with all the formulas you've ever seen - you will find that the real problem is deciding which formula(s) will be useful when you are faced with an integral that isn't on your list.

The good news is, there is a way to get to where you want to go; it just isn't easy. The way to get to where you want to go is to do a few dozen problems. A few hundred would be even better. The more problems you do, the more formulas you will find you have memorized, and the better you will become at judging which formula(s) to use on a given problem.

It's like that old joke:

Tourist: How do I get to Het Muziektheater?

Native: Practice, practice, practice.

-
Was the Tourist the same one trying to get to Carnegie Hall in New York City? –  Asaf Karagila Nov 25 '11 at 0:01
@AsafKaragila, she has also been seen asking for directions to 19 Shaul Hamelech St. –  Gerry Myerson Nov 25 '11 at 0:15

There is no general method to compute any integral, if it's your question. Actually, there are lots of primitives of simple functions that cannot be expressed using usual functions (rational fractions, log, exp and trigonometric functions).

Furthermore, it has even been shown that there is no general algorithm (i.e., method) to determine systematically if an integral is finite or not.

So the only way to go is to learn to use "recipes" that only work in some special (but often used) cases.

-