$\text { Use partial fractions to find the integral } \int \frac { 16 x - 136 } { x ^ { 2 } - 16 x + 60 } d x \text {. }$
A) $10 x + 60 \ln | 6 - x | + 6 \ln | 10 - x | + C$
B) $10 x + 60 \ln | 6 - x | + 6 x + 60 \ln | 10 - x | + C$
C) $10 \ln | x - 6 | - 6 \ln | x - 10 | + C$
D) $10 \ln | x - 6 | + 6 \ln | x - 10 | + C$
E) $10 x + 60 \ln | 6 - x | - 6 x + 60 \ln | 10 - x | + C$

Question

$\text { Use partial fractions to find the integral } \int \frac { 16 x - 136 } { x ^ { 2 } - 16 x + 60 } d x \text {. }$ 
A) $10 x + 60 \ln | 6 - x | + 6 \ln | 10 - x | + C$
B) $10 x + 60 \ln | 6 - x | + 6 x + 60 \ln | 10 - x | + C$
C) $10 \ln | x - 6 | - 6 \ln | x - 10 | + C$
D) $10 \ln | x - 6 | + 6 \ln | x - 10 | + C$
E) $10 x + 60 \ln | 6 - x | - 6 x + 60 \ln | 10 - x | + C$

Quizplus · Accepted Answer

The integral can be solved by first factoring the denominator as $(x-6)(x-10)$ and then using partial fractions to decompose the integrand. After finding the coefficients for the partial fractions and integrating, the result involves natural logarithms of the factors $|x-6|$ and $|x-10|$, leading to the correct answer.

Use partial fractions to find the integral ∫16x−136x2−16x+60dx. \text { Use partial fractions to find the integral } \int \frac { 16 x - 136 } { x ^ { 2 } - 16 x + 60 } d x \text {. } Use partial fractions to find the integral ∫x2−16x+6016x−136​dx.

$\text { Use partial fractions to find the integral } \int \frac { 16 x - 136 } { x ^ { 2 } - 16 x + 60 } d x \text {. }$