1. 8.1 Fitting Integration Rules

2. Ex. 1 Compare each of the following similar integrals:b) a) c)
Notice this fits the arctan rule: a) b)
Notice this is a simple u-substitution:

3. Degrees of num and denom are the same, so let’s use
long division to simplify: c)

4. Ex.2 Evaluate:
Arcsin rule
U-sub

5. Still fits the arcsin rule!
Ex. 3

6. Ex. 4 Because of the fraction, this may be a log rule in disguise…
Need an to make the substitution.

7. Ex. 5

8. Ex. 6
First, take care of the 2x:
Notice this is a trig identity!

9. Strategies for Fitting Integrands to Basic Rules:
1) Expand (multiply out) the numerator.
2) Separate numerators into separate fractions.
3) Complete the square.
4) Divide the rational function.
5) Add and subtract terms in the numerator.
6) Use trig identities.
7) Multiply numerator and denominator by a conjugate.