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Mathematics
Mathematics
Problem
Let
f
(
x
)
=
x
2
+
4
x
+
1
x
+
2
f(x)=\frac{x^{2}+4x+1}{x+2}
f
(
x
)
=
x
+
2
x
2
+
4
x
+
1
for all
x
≠
−
2
x\neq-2
x
=
−
2
. (a) Rewrite
f
(
x
)
f(x)
f
(
x
)
as the sum of a polynomial and a proper rational expression. (b) Find an explicit antiderivative
F
(
x
)
F(x)
F
(
x
)
of
f
(
x
)
f(x)
f
(
x
)
. (c) Evaluate
∫
0
3
f
(
x
)
d
x
\displaystyle\int_{0}^{3} f(x)\,dx
∫
0
3
f
(
x
)
d
x
using the antiderivative from part (b).
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