### Home > APCALC > Chapter 7 > Lesson 7.4.2 > Problem7-192

7-192.

Demonstrate that $\frac { x + 11 } { x ^ { 2 } - 3 x - 4 } = \frac { 3 } { x - 4 } - \frac { 2 } { x + 1 }$. Then, use this fact to integrate $\int \frac { x + 11 } { x ^ { 2 } - 3 x - 4 } d x$.

Manipulate the right side of the equation by finding a common denominator and subtracting.

Before integrating, rewrite the integrand as a subtraction problem.

$\int \frac{x+11}{x^{2}-3x-4}dx=\int \left ( \frac{3}{x-4}-\frac{2}{x+1} \right )dx$