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Mathematics
Mathematics
Problem
Find
∫
d
x
x
2
+
6
x
+
10
\displaystyle\int \frac{dx}{x^{2}+6x+10}
∫
x
2
+
6
x
+
10
d
x
. a)
1
2
arctan
(
x
+
3
)
+
C
\dfrac{1}{2}\arctan(x+3)+C
2
1
arctan
(
x
+
3
)
+
C
b)
ln
∣
x
2
+
6
x
+
10
∣
+
C
\ln|x^{2}+6x+10|+C
ln
∣
x
2
+
6
x
+
10∣
+
C
c)
arctan
(
x
+
3
)
+
C
\arctan(x+3)+C
arctan
(
x
+
3
)
+
C
d)
arctan
(
x
+
3
2
)
+
C
\arctan\!\left(\dfrac{x+3}{2}\right)+C
arctan
(
2
x
+
3
)
+
C
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