ज्ञात करें `int x^2/(x^2 + 6x +12)dx`

Explanation

माना कि `I = int x^2/(x^2 +6x +12) dx = int (x^2+6x+12-(6x+12))/(x^2 +6x+12)dx`
तो, `I=int[1-(6x+12)/(x^2 +6x+12)]dx = int [1-(3(2x+6)-6)/(x^2+6x+12)] dx`
`=int 1 dx -3 int (2x+6)/(x^2+6x+12) dx +6 (dx)/(x^2+6x+12)`
` = x-3"log"|x^2 + 6x+12 | + 6 int (dx)/((x+3)^2 +(sqrt3)^2)`
`=x-3 log| x^2 +6x+12|+6/sqrt3 tan^(-1)((x+3)/sqrt3)+c`