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.