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Mathematics
Problem
Which of the following is an antiderivative of
6
x
+
5
3
x
2
+
5
x
+
7
\dfrac{6x+5}{3x^{2}+5x+7}
3
x
2
+
5
x
+
7
6
x
+
5
? a)
(
3
x
2
+
5
x
+
7
)
2
2
+
C
\dfrac{(3x^{2}+5x+7)^{2}}{2}+C
2
(
3
x
2
+
5
x
+
7
)
2
+
C
b)
1
3
ln
∣
3
x
2
+
5
x
+
7
∣
+
C
\dfrac13\,\ln|3x^{2}+5x+7|+C
3
1
ln
∣3
x
2
+
5
x
+
7∣
+
C
c)
ln
∣
3
x
2
+
5
x
+
7
∣
+
C
\ln|3x^{2}+5x+7|+C
ln
∣3
x
2
+
5
x
+
7∣
+
C
d)
arctan
(
3
x
+
5
3
)
+
C
\arctan\!\Bigl(\dfrac{3x+5}{\sqrt{3}}\Bigr)+C
arctan
(
3
3
x
+
5
)
+
C
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