`(x)/((x+1)(x+2))`

Explanation

`int(x)/((x+1)(x+2))dx=I" "` (माना )
माना `(x)/((x+1)(x+2))=(A)/((x+1))+(B)/((x+2))`
`rArr" "(x)/((x+1)(x+2))=(A(x+2)+B(x+1))/((x+1)(x+2))`
`rArr" "x=A(x+2)+B(x+1)`
`{:(x=-1,"तो ",-1=A(-1+2)+0,rArr.,A=-1),(x=-2,"तो ",-2=0+B(-1),rArr.,B=2):}`
`therefore" "I=int(x)/((x+1)(x+2))dx`
`=int((-1))/(x+1)dx+int(2)/(x+2)dx`
`" "=-log(x+1)+2log(x+2)+C`
`" "=-log(x+1)+log(x+2)^(2)+C`
`" "=log|((x+2)^(2))/(x+1)|+C`