1. Understanding the integration of parts
Integration by parts for indefinite integrals
Integration by parts for definite integrals
Integration by parts for definite integrals


2. Indefinite integrals and rational functions
Special cases
Arbitrary rational functions


3. Using integrals for trigonometric and hyperbolic functions
Products of sin(x) and cos(x) or sinh(x) and cosh(x)
Special integrals that involve sin (mx) and cos (nx)
Rational functions of sin(x) and cos(x) or sinh(x) and cosh(x)


4. Integrations using trigonometric and hyberbolic substitutions
The substitution x = a sin (u)
The substitution x = a sinh (u)
The substitution x = a cosh (u)


5. Approximations in numerical integration
Riemann sums
The trapezoid rule
Simpson's rule
The derivation of Simpson's rule


6. Improper integrals: unbounded intervals and discontinuities
Improper integrals on unbounded intervals
Improper integrals that involve discontinuous functions


7. Improper integrals: using convergence tests
Improper integrals on unbounded intervals
Improper integrals that involve discontinuous functions


Index.