Integrate.

Answer

We didn't do this one yet. The denominator factors into

-2*x*^{2} + 3*x* – 1 = (-2*x* + 1)(*x* – 1)

so the partial fraction decomposition will look like

Add the partial fractions and set the resulting numerator equal to the original numerator:

-3*x* + 1 = *A*(*x* – 1) + *B*(-2*x* + 1).

Set *x* = 1 and solve for *B*:

-3*x* + 1 = *A*(*x* – 1) + *B*(-2*x* + 1)

-3(1) + 1 = *A*(1 – 1) + *B*(-2(1) + 1)

-2 = -*B*

2 = *B*

Then set *x* = 0 and solve for *A*:

-3*x* + 1 = *A*(*x* – 1) + *B*(-2*x* + 1)

-3(0) + 1 = *A*(0 – 1) + (2)(-2(0) + 1)

1 = -*A* + 2

*A* = 1

The partial fraction decomposition is

Now we can evaluate the integral: