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Mathematics
Problem
Determine
∫
6
x
−
2
3
x
2
−
2
x
+
7
d
x
\displaystyle \int \dfrac{6x-2}{3x^{2}-2x+7}\,dx
∫
3
x
2
−
2
x
+
7
6
x
−
2
d
x
. a)
arctan
(
3
x
−
1
7
)
+
C
\arctan\!\left(\dfrac{3x-1}{\sqrt{7}}\right)+C
arctan
(
7
3
x
−
1
)
+
C
b)
(
3
x
2
−
2
x
+
7
)
2
4
+
C
\dfrac{(3x^{2}-2x+7)^{2}}{4}+C
4
(
3
x
2
−
2
x
+
7
)
2
+
C
c)
ln
∣
3
x
2
−
2
x
+
7
∣
+
C
\ln|3x^{2}-2x+7|+C
ln
∣3
x
2
−
2
x
+
7∣
+
C
d)
1
2
ln
∣
3
x
2
−
2
x
+
7
∣
+
C
\tfrac12\,\ln|3x^{2}-2x+7|+C
2
1
ln
∣3
x
2
−
2
x
+
7∣
+
C
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