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Mathematics
Problem
Calculate
∫
2
x
+
6
x
2
+
6
x
+
13
d
x
\displaystyle \int \frac{2x+6}{x^{2}+6x+13}\,dx
∫
x
2
+
6
x
+
13
2
x
+
6
d
x
. a)
1
2
ln
(
x
2
+
6
x
+
13
)
+
C
\dfrac{1}{2}\ln\left(x^{2}+6x+13\right)+C
2
1
ln
(
x
2
+
6
x
+
13
)
+
C
b)
2
tan
−
1
(
x
+
3
2
)
+
C
2\tan^{-1}\left(\dfrac{x+3}{2}\right)+C
2
tan
−
1
(
2
x
+
3
)
+
C
c)
ln
(
x
2
+
6
x
+
13
)
+
C
\ln\left(x^{2}+6x+13\right)+C
ln
(
x
2
+
6
x
+
13
)
+
C
d)
ln
(
x
+
3
)
+
C
\ln\left(x+3\right)+C
ln
(
x
+
3
)
+
C
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