Integration of Rational Functions by Partial Fractions?

[black_yurizan]

Integration of Rational Functions by Partial Fractions?

Ok I'm working on some homework problems and I don't even know how to do the first one, here is my problems and the steps that I did thus far ( I don't know if I did them right)

5x-13/(x-3)(x-2)= A/x-3 + B/x-2$$\rightarrow$$ ...5x-13= A(x-3)(x-2)B(x-2)(x-3)$$\rightarrow$$... =(A+B)x²+(-5A-5B)x+(6A+6B)

That's how far I got, I don't know what to do next because in the textbook the next thing they do is equate the coefficients which I don't know how to do and other stuff ...please someone help if you know how to

 

[Char. Limit]

Well, I'm not entirely sure what you did there, but remember that A+B is the coefficient of x^2, and what's the coefficient of x^2 on the left side of the equation? Then do the same for the other two powers of x.

 

[black_yurizan]

what's the coefficient of x^2 on the left side of the equation?

Sorry, I forgot to put in the x I overlooked that