Evaluate $\int \frac { 3 x + 2 } { x - 1 } d x$
A) $5 \ln | x - 1 | + 3 x + C$
B) $5 \ln | x - 1 | + C$
C) $3 \ln | x - 1 | + 3 x + C$
D) $3 x + C$
E) $3 \ln | x - 1 | + 5 x + C$
F) $5 x + C$
G) $2 \ln | x - 1 | + 3 x + C$
H) $2 \ln | x | + C$

Question

Evaluate $\int \frac { 3 x + 2 } { x - 1 } d x$ 
A) $5 \ln | x - 1 | + 3 x + C$ 
B) $5 \ln | x - 1 | + C$ 
C) $3 \ln | x - 1 | + 3 x + C$ 
D) $3 x + C$ 
E) $3 \ln | x - 1 | + 5 x + C$ 
F) $5 x + C$ 
G) $2 \ln | x - 1 | + 3 x + C$ 
H) $2 \ln | x | + C$

Quizplus · Accepted Answer

To solve $\int \frac { 3 x + 2 } { x - 1 } d x$, first divide the numerator by the denominator to simplify the expression. This yields $3 + \frac{5}{x-1}$. Integrating term by term gives $3x + 5 \ln |x - 1| + C$, which matches option A.

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