What is x^4-1 x^2 x^4+x^2+1 d x equal to?

Step-by-step solution

Take option (1) I₁= x^4+x^3+1 x +C aligned d I₁ d x & = d d x [ (x^3+x^2+x⁻¹ )^ 1 / 2 +C ] d I₂ d x & = 1 2 (x^3+x^2+x⁻¹ )^ -1 / 2 (3 x^2+2 x-x⁻² ) & = 1 2 [ 3 x^2+2 x- 1 x^2 x^3+x^2+ 1 x ] d I₂ d x & = 1 2 [ 3 x^4+2 x^3-1 x^2 x x^4+x^3+1 ] aligned Take option (b) : aligned I₂ & = x^4+2- 1 x^2 +C d I₂ d x & = 1 2 [x^4+2-x⁻² ]^ -1 / 2 [4 x^3+0+2 x⁻³ ] & = 1 2 [ 4 x^3+ 2 x^3 x^4+2- 1 x^2 ]= 2 x^6+1 x^3 x x^6+2 x^2-1 d I₂ d x & = 2 x^6+1 x^2 x^6+2 x-1 aligned Take option (3) : aligned & I₃= x^2+x⁻²+1 +C & d I₃ d x = 1