### Home > APCALC > Chapter 11 > Lesson 11.4.1 > Problem11-113

11-113.

Multiple Choice: $\int \frac { 3 } { ( 2 x - 1 ) ( x + 5 ) } d x=$ Homework Help ✎

1. $\frac { 3 } { 11 } \operatorname { ln } | \frac { 2 x - 1 } { x + 5 } |+ C$

1. $\frac { 6 } { 11 } \operatorname { ln } | 2 x - 1 | - \frac { 3 } { 11 } \operatorname { ln } | x + 5 |+ C$

1. $\frac { 1 } { 2 }\ln| ( 2 x - 1 ) ( x + 5 ) |+C$

1. $\operatorname { ln } | 2 x - 1 | + \operatorname { ln } | x + 5 |+C$

1. None of these

$\frac{3}{(2x-1)(x+5)}=\frac{a}{2x-1}+\frac{b}{x+5}$

$a(x+5)+b(2x-1)=3$

$a + 2b = 0$
$5a - b = 3$

Solve for $a$ and $b$ then rewrite the integrand and integrate.