ज्ञात करें `int (x^2-1)/(1+x^4)dx`

Explanation

`I=int (x^2-1)/(1+x^4)dx = int (1-1/x^2)/(2/x^2 +x^2)dx = int (1-1/x^2)/((x+1/x)^2 -2)dx`
`z = x+1/x,` रखे तो, `dz = (1-1/x^2)dx`
अब, `I = int (dz)/(z^2-2)=int (dz)/(z^2 -(sqrt2)^2) = 1/(2sqrt2)log |(z-sqrt2)/(z+sqrt2)|+c`
`=1/(2sqrt2)log |(x^2 -sqrtx +1)/(x^2 +sqrtx+1)|+c`