=3/2. $\int\limits_{2}^{3}$$\frac{2x+6}{x^{2}-4x-5}$.dx= 3/2. $\int\limits_{2}^{3}$$\frac{(2x-4)+10}{x^{2}-4x-5}$.dx= 3/2. $\int\limits_{2}^{3}$$\frac{(x^{2}-4x-5)^{'}}{x^{2}-4x-5}$.dx + 15. $\int\limits_{2}^{3}$$\frac{1}{x^{2}-4x-5}$.dx = 3/2. $\ln \left| {x^{2}-4x-5} \right|$ + 15. $\int\limits_{2}^{3}$$\frac{1}{(x-5)(x+1)}$.dx =3/2. $\ln \left| {x^{2}-4x-5} \right|$ + 15. $\int\limits_{2}^{3}$$(\frac{1}{(x-5)}-\frac{1}{x+1})$.dx =3/2. $\ln \left| {x^{2}-4x-5} \right|$ + 15. ($\ln \left| {x-5} \right|$- $\ln \left| {x+1} \right|$) = 3/2 $\ln 8/9$+ 15$\ln 1/2$
=3/2. $\int\limits_{2}^{3}$$\frac{2x+6}{x^{2}-4x-5}$.dx= 3/2. $\int\limits_{2}^{3}$$\frac{(2x-4)+10}{x^{2}-4x-5}$.dx= 3/2. $\int\limits_{2}^{3}$$\frac{(x^{2}-4x-5)^{'}}{x^{2}-4x-5}$.dx + 15. $\int\limits_{2}^{3}$$\frac{1}{x^{2}-4x-5}$.dx = 3/2. $\ln \left| {x^{2}-4x-5} \right|$ ...+ 15. $\int\limits_{2}^{3}$$\frac{1}{(x-5)(x+1)}$.dx =3/2. $\ln \left| {x^{2}-4x-5} \right|$ ...+ 15. $\int\limits_{2}^{3}$$(\frac{1}{(x-5)}-\frac{1}{x+1})$.dx =3/2. $\ln \left| {x^{2}-4x-5} \right|$ ...+ 15. ($\ln \left| {x-5} \right|$- $\ln \left| {x+1} \right|$)... = 3/2 $\ln 8/9$+ 15$\ln 1/2$
=3/2. $\int\limits_{2}^{3}$$\frac{2x+6}{x^{2}-4x-5}$.dx= 3/2. $\int\limits_{2}^{3}$$\frac{(2x-4)+10}{x^{2}-4x-5}$.dx= 3/2. $\int\limits_{2}^{3}$$\frac{(x^{2}-4x-5)^{'}}{x^{2}-4x-5}$.dx + 15. $\int\limits_{2}^{3}$$\frac{1}{x^{2}-4x-5}$.dx = 3/2. $\ln \left| {x^{2}-4x-5} \right|$ + 15. $\int\limits_{2}^{3}$$\frac{1}{(x-5)(x+1)}$.dx =3/2. $\ln \left| {x^{2}-4x-5} \right|$ + 15. $\int\limits_{2}^{3}$$(\frac{1}{(x-5)}-\frac{1}{x+1})$.dx =3/2. $\ln \left| {x^{2}-4x-5} \right|$ + 15. ($\ln \left| {x-5} \right|$- $\ln \left| {x+1} \right|$) = 3/2 $\ln 8/9$+ 15$\ln 1/2$