Answer
$$\int_a^b {u\left( x \right)} v'\left( x \right)dx = \left. {u\left( x \right)v\left( x \right)} \right|_a^b - \int_a^b {v\left( x \right)u'\left( x \right)} dx$$
Work Step by Step
$$\eqalign{
& {\text{The integration by parts for definite integrals still has the form}} \cr
& \int {udv} = uv - \int {vdu} \cr
& {\text{Therefore, the integration by parts for Definite Integrals is:}} \cr
& \int_a^b {u\left( x \right)} v'\left( x \right)dx = \left. {u\left( x \right)v\left( x \right)} \right|_a^b - \int_a^b {v\left( x \right)u'\left( x \right)} dx \cr
& {\text{Where }}u{\text{ and }}v{\text{ are differentiable}}{\text{. }} \cr} $$
