Integration of Rational Functions by Partial Fractions

$$\frac{1}{8}\ln\left|x-3\right|-\frac{1}{8}\ln\left|x+5\right|+c$$  

$$\frac{1}{4}\ln\left|x-3\right|-\frac{1}{8}\ln\left|x+5\right|+c$$  

$$\frac{1}{8}\ln\left|x+5\right|-\frac{1}{8}\ln\left|x-3\right|+c$$  

$$\frac{1}{4}\ln\left|x+5\right|-\frac{1}{4}\ln\left|x-3\right|+c$$  

$$\frac{2}{9}\ln\left|x-2\right|-\frac{2}{9}\ln\left|x+1\right|+\frac{1}{3\left(x+1\right)}+c$$  

$$\frac{2}{9}\ln\left|x+1\right|-\frac{2}{9}\ln\left|x-2\right|-\frac{1}{3\left(x+1\right)}+c$$  

$$\frac{2}{9}\ln\left|x-2\right|-\frac{2}{9}\ln\left|x+1\right|-\frac{1}{3\left(x+1\right)}+c$$  

$$\frac{2}{9}\ln\left|x-2\right|+\frac{2}{9}\ln\left|x+1\right|+\frac{1}{3\left(x+1\right)}+c$$  

$$3x+11=A\left(x-2\right)-B\left(x-3\right)$$

$$3x+11\left(x^2-x-6\right)=A\left(x^2-x-6\right)+B\left(x^2-x-6\right)$$

$$3x+11=A\left(x+2\right)+B\left(x-3\right)$$

$$3x+11=A\left(x+2\right)-B\left(x-3\right)$$

$$x^2+9x+60$$

$$x^2+9x+60-\frac{424}{x-7}$$

$$x^2+9x+60+\frac{424}{x-7}$$

$$x^2+9x+60+\frac{424}{x^2+9x+60}$$

$$x+\frac{1}{2}\ln\left|x-1\right|-\frac{1}{2}\ln\left|x+1\right|+C$$

$$x+\frac{1}{2}\ln\left|x-1\right|+\frac{1}{2}\ln\left|x+1\right|+C$$

$$x+\ln\left|x-1\right|+C$$

$$x^2+\frac{1}{2}\ln\left|x^2-1\right|-\frac{1}{2}\ln\left|x^2+1\right|+C$$