Evaluate the integral integral 2x 7x 1x 3 dxSolutionI in

Evaluate the integral integral 2x - 7/(x + 1)(x - 3) dx

I = int{(2x-7)/(x+1)(x-3)}dx

I will be using integration by partial fration

let (2x-7)/(x+1)(x-3) = A/(x+1) + B/(x-3)

= {x(A+B) +(B-3A)}/(x+1)(x-3)

compairing coefficients , we get

A+B = 2 and B - 3A = -7

=>A= 9/4 ;B = -1/4

so I = int[{(9/4)*1/(x+1)} +{(-1/4)*1/(x-3)}]dx

= (9/4)ln(x+1) - (1/4)ln(x-3) + ln(c)

= ln(x+1)^(9/4) - ln(x-3)^1/4 +ln(c) (c is integration constant)

= ln{c*(x+1)^(9/4) /(x-3)^1/4} answer