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Mathematics
Mathematics
Problem
Find
∫
4
x
−
1
x
2
+
4
d
x
\displaystyle \int \frac{4x-1}{x^{2}+4}\,dx
∫
x
2
+
4
4
x
−
1
d
x
. a)
ln
(
x
2
+
4
)
−
1
2
arctan
(
x
2
)
+
C
\ln\bigl(x^{2}+4\bigr)-\dfrac{1}{2}\arctan\!\left(\dfrac{x}{2}\right)+C
ln
(
x
2
+
4
)
−
2
1
arctan
(
2
x
)
+
C
b)
2
ln
(
x
2
+
4
)
−
1
2
arctan
(
x
2
)
+
C
2\ln\bigl(x^{2}+4\bigr)-\dfrac{1}{2}\arctan\!\left(\dfrac{x}{2}\right)+C
2
ln
(
x
2
+
4
)
−
2
1
arctan
(
2
x
)
+
C
c)
2
ln
(
x
2
+
4
)
+
1
2
arctan
(
x
2
)
+
C
2\ln\bigl(x^{2}+4\bigr)+\dfrac{1}{2}\arctan\!\left(\dfrac{x}{2}\right)+C
2
ln
(
x
2
+
4
)
+
2
1
arctan
(
2
x
)
+
C
d)
2
ln
(
x
2
+
4
)
−
arctan
(
x
2
)
+
C
2\ln\bigl(x^{2}+4\bigr)-\arctan\!\left(\dfrac{x}{2}\right)+C
2
ln
(
x
2
+
4
)
−
arctan
(
2
x
)
+
C
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