Question

Evaluate the integral by particle fractions: integral from 3 to 4 of (x^3-2x^2-4)/x^3-2x^2 dx

Answer 1

\[
\int\frac{x^3-2x^2-4}{x^3-2x^2}\,dx=\int1-\frac{4}{x^3-2x^2}\,dx
\]

Answer 2

\[\frac{x^3-2 x^2-4}{x^3-2 x^2}=\frac{2}{x^2}+\frac{1}{x}-\frac{1}{x-2}+1 \]\[\int\limits_3^4 \left(\frac{2}{x^2}+\frac{1}{x}-\frac{1}{x-2}+1\right) \, dx=\frac{7}{6}-\log \left(\frac{3}{2}\right) \]