Week Number Four

This week we reviewed trig. substitution integration and we also learned how to solve integration using partial fractions.

You can actually use partial fractions to break up fractions even if you aren't using it for integration.

Some simple steps for partial fraction integration:
1) First of all, make sure it isn't any other type of integration.
2) If you can factor the top or bottom then do so (if you can cancel anything then do so).
3) Once you've ruled out everything else, you then split the bottom factors into A/(factor1) + B/(factor2) +... = original.
4) Get common denominators and add.
5) Pick a convenient value for x (one that would give you zero once plugged into a factor) and plug in.
6) Solve for A, B, ... .
7) You then take the values of your variables and plug back in to when you first broke up the fraction.
8)Integrate! It will almost always be natural log integration. Remember that any number in front of a natural log is also it's exponent.

Question:
For integration using charts like we did in class on friday, how exactly do I know which formula to plug in to if the problem I'm facing doesn't have all of the necessary components. I.e. if the formula has an x and my problem doesn't.