Evaluate Definite Integral

[akistar]

Need help on this one..really stuck this time:-(

Evaluate Definite Integral

 

[stapel]

Need help on this one..really stuck this time:-(

Evaluate Definite Integral

\(\displaystyle \displaystyle{\int_{-2}^{-1}}\, \frac{-3x^2\, +\, 6x\, -\, 2}{3x^2\, -\, 2x}\, dx\)

One possible first step might be to do the long polynomial division, to convert this "fraction" into "mixed-number" form. Then integrate the terms....

 

[HallsofIvy]

Need help on this one..really stuck this time:-(

Evaluate Definite Integral
View attachment 4114

\(\displaystyle \frac{-3x^2+ 6x- 2}{3x^2- 2x}= -1+ \frac{4x+ 2}{x(3x- 2)}\)
Use "partial fractions" to integrate the remaining fraction.