Mathematics

Problem

During the evaluation of

I=\displaystyle\int e^{ax}\cos bx\,dx

, an intermediate step gives an equation of the form

I=P(x)+kI,

where

P(x)

is an elementary function of

x

and

k

depends only on

a

and

b

. (i) Write

k

in terms of

a

and

b

. (ii) In one sentence, state how this relation enables you to find the explicit expression for

I

. a. (i) Value of

k

b. (ii) Brief explanation