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Mathematics
Mathematics
Problem
Evaluate
∫
3
x
+
2
x
2
+
1
d
x
\displaystyle \int \frac{3x+2}{x^{2}+1}\,dx
∫
x
2
+
1
3
x
+
2
d
x
. a)
3
2
ln
∣
x
∣
+
2
arctan
x
+
C
\dfrac{3}{2}\ln|x|+2\arctan x + C
2
3
ln
∣
x
∣
+
2
arctan
x
+
C
b)
3
ln
(
x
2
+
1
)
+
2
arctan
x
+
C
3\ln(x^{2}+1)+2\arctan x + C
3
ln
(
x
2
+
1
)
+
2
arctan
x
+
C
c)
3
2
ln
(
x
2
+
1
)
+
2
arctan
x
+
C
\dfrac{3}{2}\ln(x^{2}+1)+2\arctan x + C
2
3
ln
(
x
2
+
1
)
+
2
arctan
x
+
C
d)
3
2
ln
(
x
2
+
1
)
−
2
arctan
x
+
C
\dfrac{3}{2}\ln(x^{2}+1)-2\arctan x + C
2
3
ln
(
x
2
+
1
)
−
2
arctan
x
+
C
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