Answer
$$\ln \left| {{x^2} - 3x - 10} \right| + C$$
Work Step by Step
$$\eqalign{
& \int {\frac{{2x - 3}}{{{x^2} - 3x - 10}}} dx \cr
& {\text{Integrate by the substitution method}} \cr
& {\text{Let }}u = {x^2} - 3x - 10,\,\,\,du = \left( {2x - 3} \right)dx,\,\,\,\,\,\,\,dx = \frac{{du}}{{2x - 3}} \cr
& {\text{write in terms of }}u \cr
& \int {\frac{{2x - 3}}{{{x^2} - 3x - 10}}} dx = \int {\frac{{2x - 3}}{u}} \left( {\frac{{du}}{{2x - 3}}} \right) \cr
& = \int {\frac{{du}}{u}} \cr
& = \ln \left| u \right| + C \cr
& {\text{write in terms of }}x \cr
& = \ln \left| {{x^2} - 3x - 10} \right| + C \cr} $$
