Let f(x)= 3x+4 (x+1)(x-2)

MATHEMATICS · Multi-part · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

Let

f(x)=\frac{3x+4}{(x+1)(x-2)}.

Consider the indefinite integral

\displaystyle\int f(x)\,dx

. (a) Rewrite

f(x)

in the form

\frac{A}{x+1}+\frac{B}{x-2},

where

A

and

B

are real numbers. Determine the values of

A

and

B

. (b) Evaluate

\displaystyle\int f(x)\,dx

and state the antiderivative in its simplest form, including an arbitrary constant of integration.