ज्ञात करें `int(x^2+3x-1)/((x+1)^2)dx`

Explanation

`z=x+1,` रखे तो `dz=dx` तथा `x=z-1`
अब, `I=int((z-1)^2+3(z-1)-1)/z^2dz=int(z^2+z-3)/z^2dz`
`=int(1+1/z-3z^-2)dz=z+log|z|3/z+c`
`=x+1+log|x+1|+3/(x+1)+c=x+log|x+1|+3/(x+1)+k`