# Solve the indefinite integral of f(x)=(2x-5)/(x^2-5x+6) . Then solve the definite integral of f from x=0 to x=1.

f(x) = (2x-5) /(x^2 -5x + 6)

F(x)= intg f(x) = intg (2x-5)/(x^2 - 5x + 6)

Let u = x^2 - 5x + 6

==> du = (2x - 5) dx

F(x) = intg du/u

= ln u

= ln (x^2 -5x +6)

F(1) = ln (1-5+6) = ln 2

F(0) = ln (0-0+6) = ln 6

Then the definite intergral = ln 2 - ln 6

= ln 2/6

= ln 1/3

= -ln3

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