Integration by parts formula the product rule of differentiation, this means Integration by parts formula

Example Ex. Find Sol. (1) Choose then

Example Ex. Find Sol. (1) Choose then

Example Ex. Find Sol.

Example Ex. Find Sol. This gives an equation of I. Solving the equation, we find I:

Example Ex. Evaluate Sol.

Example Ex. Evaluate Sol.

Example Ex. Find Sol.

Integration by parts for definite integrals Integration by parts formula for definite integral Ex. Evaluate Sol.

Example Ex. Evaluate Sol.

Trigonometric integrals Ex. Find Sol. Ex. Evaluate

Question Ex. Find Sol.

General strategy Strategy for evaluating (a) If either power is odd, say, m=2k+1, then (b) If both power are even, use the half-angle identities

Trigonometric integrals Similar strategy applies to the integrals of the form Ex. Find Sol.

Example Ex. Find Sol.

Example Ex. Find Sol.

A systematic method There is a systematic method: substitution then Ex. Find Sol. Let then