`(3x-1)/((x+2)^(2))`

Explanation

माना `(3x-1)/((x+2)^(2))=(A)/((x+2))+(B)/((x+2)^(2))`
`rArr" "(3x-1)/((x+2)^(2))=(A(x+2)+B)/((x+2)^(2))`
`rArr" "3x-1=A(x+2)+B`
`x=-2" तो "-6-1=0+B" "rArr" "B=-7`
x के गुणकों को समान रखने पर,
3 = A
`therefore" "(3x-1)/((x+2)^(2))=(3)/((x+2))-(7)/((x+2)^(2))`
`rArr" "int(3x-1)/((x+2)^(2))dx`
`" "3int(1)/((x+2))dx-7int(1)/((x+2)^(2))dx`
`" "=3log|x-2|-7((-1)/(x+2))+C`
`=3log|x+2|+(7)/(x+2)+C`