Integration by parts always evaluates an integral directly. You should always make u' simpler than u and v simpler than v'. 5. Integration by parts does not apply to definite integrals. It may be necessary to apply integration by parts more than once. 7.5 Tables of Integrals 1.
Most functions have elementary antiderivatives.
Partial fractions requires the decomposition of a quotient into two or more fractions and comes from the solution of several equations in several unknowns. 7.6 Approximating Definite Integrals 1. Riemann sums are only calculated using left sums and right sums. The midpoint rule is the average of the left and right sums. The trapezoid rule gives an over estimate if the integral is concave up.