Write out the form of the partial fraction decomposition of the function appearing in the integral:

Question

integral (6x-58)/(x^2+2x-63)

Determine the numerical values of the coefficients, A and B, where A <= B

A=?
B=?

Thank you guys so much!

=)

Answer 1

I will split it up for you ...

(6x-58)/( (x+9)(x-7) )
let
A/(x+9) + B/(x-7) = (6x-58)/( (x+9)(x-7) )

A(x-7) + B(x+9) = 6x - 58
let x = 7
0 + 16B = -16
B = -1

let x = -9
-16A + 0 = -112
A = -7

so ....
(6x-58)/( (x+9)(x-7) ) = -7/(x+9) - 1/(x-7)

now it integrates easily using ln
take it from here

Answer 2

Thanks! Got it!