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Mathematics
Problem
Let
a
a
a
and
b
b
b
be distinct non-zero real numbers. Evaluate the integral
I
=
∫
2
x
−
a
−
b
(
x
−
a
)
(
x
−
b
)
d
x
,
I=\int \frac{2x-a-b}{(x-a)(x-b)}\,dx,
I
=
∫
(
x
−
a
)
(
x
−
b
)
2
x
−
a
−
b
d
x
,
and simplify the result to a single logarithmic expression plus the constant of integration.
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