AP Calculus AB Quiz
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INTEGRATION AND ACCUMULATION OF CHANGE
Question 1
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During a lab, the accumulated charge is modeled by
∫
x
2
+
1
x
−
1
d
x
\int \frac{x^2+1}{x-1}\,dx
∫
x
−
1
x
2
+
1
d
x
. Which is an antiderivative?
A
x
2
+
1
x
−
1
+
C
\frac{x^2+1}{x-1}+C
x
−
1
x
2
+
1
+
C
B
x
2
2
+
x
+
ln
∣
x
−
1
∣
+
C
\frac{x^2}{2}+x+\ln|x-1|+C
2
x
2
+
x
+
ln
∣
x
−
1∣
+
C
C
x
2
2
+
x
+
2
ln
∣
x
−
1
∣
+
C
\frac{x^2}{2}+x+2\ln|x-1|+C
2
x
2
+
x
+
2
ln
∣
x
−
1∣
+
C
D
x
2
2
+
x
+
2
x
−
1
+
C
\frac{x^2}{2}+x+\frac{2}{x-1}+C
2
x
2
+
x
+
x
−
1
2
+
C
E
x
2
2
+
x
+
ln
∣
x
+
1
∣
+
C
\frac{x^2}{2}+x+\ln|x+1|+C
2
x
2
+
x
+
ln
∣
x
+
1∣
+
C
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