समाकलन कीजिए
`(3x-1)/((x-1)(x-2)(x-3))`

Explanation

माना `(3x-1)/((x-1)(x-2)(x-3))`
`=(A)/((x-1))+(B)/((x-2))+(C)/((x-3))`
`rArr" "(3x-1)/((x-1)(x-2)(x-3))=(A(x-2)(x-3)+B(x-1)(x-3)+C(x-1)(x-2))/((x-1)(x-2)(x-3))`
`rArr" "(3x-1)=A(x-2)(x-3)+B(x-1)(x-3)+C(x-1)(x-2)`
`{:(x=1,"तो ",3-1=A(-1)(-2)+0+0,rArr.,A=1),(x=2,"तो ",6-1=0+B(1)(-1)+0,rArr.,B=-5),(x=3,"तो ",9-1=0+0+C(2)(1),rArr.,C=4):}`
अब `int(3x-1)/((x-1)(x-2)(x-3))dx`
`=int[(A)/((x-1))+(B)/((x-2))+(C)/((x-3))]dx`
`=int(1)/((x-1))dx+int((-5))/((x-2))dx+int(4)/((x-3))dx`
`=log|x-1|-5log|x-2|+4log|x-3|+C_(1)`