01
Distinct linear factors
Compute the integral:
02
Long division first
Compute the integral:
03
Repeated factor
Compute the integral:
04
Partial fractions - irreducible quadratic
Compute the integral:
05
Partial fractions - long division
Compute the integral:
06
Partial fractions - big generic
Give the generic partial fraction decomposition (no need to solve for the constants):
07
Partial fractions - linear and quadratic
Compute the integral:
08
Partial fractions - repeated factor
Compute the integral:
09
Partial fractions - rationalize first
For each of these integrals, make a
-substitution that changes the integrand into a rational function. Write the integral in terms of for your answer. You do not have to compute the -integral. (a)
(b)