ज्ञात करें `int (x^2 +1)/(x^4 +x^2+1) dx`

Explanation

`I = int (1+1/x^2)/(x^2+1+1/x^2)dx = int (1+1/x^2)/((x-1/x)^(2)+2x""1/x +1)dx `
`=int (dz)/(z^2 +(sqrt3)^2),` जहां `z= x -1/x`
`=1/sqrt3 tan^(-1)(z/sqrt3)+c=1/sqrt3 tan^(-1) [1/sqrt3 (x-1/x)]+c`