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Mathematics
Mathematics
Problem
Calculate the exact value of
∫
1
4
5
x
+
1
x
2
+
3
x
d
x
\displaystyle \int_{1}^{4} \frac{5x+1}{x^{2}+3x}\,dx
∫
1
4
x
2
+
3
x
5
x
+
1
d
x
. a)
1
3
ln
4
+
14
3
ln
7
\dfrac{1}{3}\ln 4+\dfrac{14}{3}\ln 7
3
1
ln
4
+
3
14
ln
7
b)
13
3
ln
4
−
14
3
ln
7
\dfrac{13}{3}\ln 4-\dfrac{14}{3}\ln 7
3
13
ln
4
−
3
14
ln
7
c)
14
3
ln
4
+
1
3
ln
7
4
\dfrac{14}{3}\ln 4+\dfrac{1}{3}\ln\dfrac{7}{4}
3
14
ln
4
+
3
1
ln
4
7
d)
1
3
ln
4
+
14
3
ln
7
4
\dfrac{1}{3}\ln 4+\dfrac{14}{3}\ln\dfrac{7}{4}
3
1
ln
4
+
3
14
ln
4
7
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