The form of the partial fraction decomposition of a rational function is given below...find A, B, and C?

((–1x^2–2x–14)/(x+5)(x^2+4)) = ((A)/(x+5)) + ((Bx+C)/(x^2+4))





Now evaluate the indefinite integral.


*int* ((–1x^2–2x–14)/((x+5)(x^2+4))dx





If you can give me the answer to the integral as well as A,B,and C please?!

The form of the partial fraction decomposition of a rational function is given below...find A, B, and C?
A(x^2 + 4) + (Bx + C)(x + 5) = - x^2 - 2x -14





Putting x = - 5:


29A = - 25 + 10 - 14


A = - 1





Equating absolute terms:


- 4 + 5C = - 14


C = - 2





Equating coefficients of x:


- 2 + 5B = - 2


B = 0





int[ (–1x^2–2x–14)/((x+5)(x^2+4))dx


= int[ - 1 / (x + 5) - 2 / (x^2 + 4) ] dx


= - ln | x + 5 | - arctan(x / 2) + c.