Question

Find: `int 1/ (5 + 4x - x^2) dx`

Answer 1

Let I = `int dx/(5 + 4x - x^2)`

= `int dx/(5 + 4 - 4 + 4x - x^2)`

= `int dx/((3)^2 - (x - 2)^2)`

= `1/(2 xx 3) log |(3 + (x - 2))/(3 - (x - 2))| + c     ...["using" int 1/(a^2 - x^2) dx = 1/(2a) log |(a + x)/(a - x)| + C]`

= `1/6 log |(x + 1)/(5 - x)| + C`