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Mathematics
Problem
Without carrying out any integration, explain why every antiderivative of the function
g
(
x
)
=
A
x
−
3
+
B
x
+
2
g(x)=\dfrac{A}{x-3}+\dfrac{B}{x+2}
g
(
x
)
=
x
−
3
A
+
x
+
2
B
(where
A
A
A
and
B
B
B
are nonzero constants) must contain logarithmic terms of the form
ln
∣
x
−
3
∣
\ln|x-3|
ln
∣
x
−
3∣
and
ln
∣
x
+
2
∣
\ln|x+2|
ln
∣
x
+
2∣
.
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