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Partial Fractions with Distinct Linear Factors
Worksheet
Grade Level
Calculus II
CAL2.36 Partial Fractions with Distinct Linear Factors
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A student is integrating f(x)=(14x
2
- 78x - 378)/[(2x+7)(x)(x-6)]. Which option has the correct decomposition and logarithmic antiderivative?
A
f(x)=2/(2x+7) + 9/(x) - 3/(x-6); F(x)=ln(abs(2x+7)) + 9 ln(abs(x)) - 3 ln(abs(x-6)) + C
B
f(x)=9/(2x+7) + 2/(x) - 3/(x-6); F(x)=(9/2) ln(abs(2x+7)) + 2 ln(abs(x)) - 3 ln(abs(x-6)) + C
C
f(x)=2/(2x-7) + 9/(x) - 3/(x-6); F(x)=ln(abs(2x-7)) + 9 ln(abs(x)) - 3 ln(abs(x-6)) + C
D
f(x)=2/(2x+7) + 9/(x) + 3/(x-6); F(x)=ln(abs(2x+7)) + 9 ln(abs(x)) + 3 ln(abs(x-6)) + C
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