Let f(x)= x^ 2 +4x+1 x+2 for all .

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

Problem

Let

f(x)=\frac{x^{2}+4x+1}{x+2}

for all

x\neq-2

. (a) Rewrite

f(x)

as the sum of a polynomial and a proper rational expression. (b) Find an explicit antiderivative

F(x)

f(x)

. (c) Evaluate

\displaystyle\int_{0}^{3} f(x)\,dx

using the antiderivative from part (b).