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Mathematics
Mathematics
Problem
1. Write
2
x
+
5
x
2
−
x
−
2
\frac{2x + 5}{x^2 - x - 2}
x
2
−
x
−
2
2
x
+
5
in the form
A
x
−
2
−
B
x
+
1
\frac{A}{x - 2} - \frac{B}{x + 1}
x
−
2
A
−
x
+
1
B
. 2. Hence find the exact value of
∫
3
9
2
x
+
5
x
2
−
x
−
2
d
x
.
\int_{3}^{9} \frac{2x + 5}{x^2 - x - 2} dx.
∫
3
9
x
2
−
x
−
2
2
x
+
5
d
x
.
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