During the evaluation of

MATHEMATICS · Multi-part · A Level · Mathematics · Integration · Integration

Problem

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) Value of

k

(ii) Brief explanation