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Mathematics
Problem
Evaluate the integral
∫
d
x
x
2
+
6
x
+
13
\displaystyle\int \frac{dx}{x^{2}+6x+13}
∫
x
2
+
6
x
+
13
d
x
. a. (i) Express the denominator
x
2
+
6
x
+
13
x^{2}+6x+13
x
2
+
6
x
+
13
in completed–square form. b. (ii) Hence, find the indefinite integral
∫
d
x
x
2
+
6
x
+
13
\displaystyle\int \frac{dx}{x^{2}+6x+13}
∫
x
2
+
6
x
+
13
d
x
, simplifying your final answer as far as possible.
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