Partial Fractions

Evaluate $\int_6^{18}\frac{6x^2}{x^3+15x^2+72x+108}dx.$

What is $\int\frac{1}{x^2+7x+6}dx?$

-\ln\left|x^2+7x+6\right|+C

\frac{1}{5}\ln\left|\frac{x+1}{x+6}\right|+C

\frac{1}{5}\ln\left|\frac{x+6}{x+1}\right|+C

\ln\left|x^2+7x+6\right|+C

Suppose that $f(x)$ is a function whose derivative is $f'(x)=\frac{1}{x^2-2x}$ and that $f(-2)=\frac{1}{2}\ln2.$ What is the value of $f(8)?$

What is $\int\frac{x+6}{x^2-9x+20}dx?$

11\ln\lvert x-5\rvert-10\ln\lvert x-4\rvert-\ln\lvert x+6\rvert+C

11\ln\lvert x-5\rvert-10\ln\lvert x-4\rvert+C

10\ln\lvert x-4\rvert-11\ln\lvert x-5\rvert+C

10\ln\lvert x-4\rvert-11\ln\lvert x-5\rvert+\ln\lvert x+6\rvert+C

What is $\int\frac{1}{x^2-16}dx?$

\frac{1}{8}\ln\left|\frac{x-4}{x+4}\right|+C

-\frac{1}{2}\ln\left|x^2-16\right|+C

\frac{1}{8}\ln\left|\frac{x+4}{x-4}\right|+C

\frac{1}{2}\ln\left|x^2-16\right|+C

Partial Fractions - Application to Integration