Consider the rational function g(x)= 7-2x (x-5)(4-x)

MATHEMATICS · Multi-part · CBSE · Mathematics · Integrals · Integrals

Problem

Consider the rational function

g(x)=\frac{7-2x}{(x-5)(4-x)}.

Throughout this problem, treat

x\neq5

and

x\neq4

. (a) Rewrite

g(x)

in the form

\frac{A}{x-5}+\frac{B}{4-x},

where

A

and

B

are real constants. Solve for

A

and

B

. (b) Compute the indefinite integral

\displaystyle\int g(x)\,dx

and simplify your answer. Express the final result so that any logarithmic arguments are positive inside absolute value signs.