7.4- Integration by Partial Fractions, 7.5 Strategies for Integration

If a rational function is improper:

Do Long Division First

Then Pick a Case

Integrate Partial Fractions

Integral of 1/(x²+a²)

1/a [tan^-1 (x/a)] + C

Integral of 1/x²-a²

1/(2a) [ln(abs([x-a]/[x+a]))] +C

Rationalizing Substitutions

Some nonrational functions can be changed into rational functions by means of appropriate substitutions. In particular, when an integrand contains an expression of the form nth root of g(x) , then the substitution may be effective.

Strategy for Integration

1. Simplify the Integrand if Possible

2. Look for an Obvious Substitution

3. Classify the Integrand According to Its Form

4. TRY AGAIN

Facto