AP Calculus BC Quiz
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INTEGRATION AND ACCUMULATION OF CHANGE
Question 1
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In an RC circuit, compute
∫
2
x
+
1
(
x
−
1
)
(
x
+
4
)
d
x
\int \frac{2x+1}{(x-1)(x+4)}\,dx
∫
(
x
−
1
)
(
x
+
4
)
2
x
+
1
d
x
by decomposing into linear fractions.
A
3
5
ln
∣
x
−
1
∣
+
7
5
ln
∣
x
+
4
∣
+
C
\frac{3}{5}\ln|x-1|+\frac{7}{5}\ln|x+4|+C
5
3
ln
∣
x
−
1∣
+
5
7
ln
∣
x
+
4∣
+
C
B
3
5
ln
∣
x
−
1
∣
−
7
5
ln
∣
x
+
4
∣
+
C
\frac{3}{5}\ln|x-1|-\frac{7}{5}\ln|x+4|+C
5
3
ln
∣
x
−
1∣
−
5
7
ln
∣
x
+
4∣
+
C
C
7
5
ln
∣
x
−
1
∣
+
3
5
ln
∣
x
+
4
∣
+
C
\frac{7}{5}\ln|x-1|+\frac{3}{5}\ln|x+4|+C
5
7
ln
∣
x
−
1∣
+
5
3
ln
∣
x
+
4∣
+
C
D
7
5
ln
∣
x
−
1
∣
−
3
5
ln
∣
x
+
4
∣
+
C
\frac{7}{5}\ln|x-1|-\frac{3}{5}\ln|x+4|+C
5
7
ln
∣
x
−
1∣
−
5
3
ln
∣
x
+
4∣
+
C
E
ln
∣
x
−
1
∣
+
ln
∣
x
+
4
∣
+
C
\ln|x-1|+\ln|x+4|+C
ln
∣
x
−
1∣
+
ln
∣
x
+
4∣
+
C
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