Paragraph If f(x)= x x^2+x+1 , then On the basis of above information, answer the following : Question If f (x^2 ) d x+ f ( 1 x ^2 ) d ( 1 x )= | x ^2- x +1 x ^2+ x +1 |+ c , then is -

Step-by-step solution

aligned & x^2 d x (x^4+x^2+1 ) + x^2 ( 1 x^4 + 1 x^2 +1 )- ( 1 x^2 ) d x & = (x^2-1 ) d x (x^4+x^2+1 ) = (1- 1 x^2 ) d x (x^2+ 1 x^2 +1 ) & = (1- 1 x^2 ) d x (x^2+ 1 x^2 )^2-1 Let x+ 1 x =t & = d t (t^2-1 ) = 1 2 ( t-1 t+1 )= 1 2 ( x+ 1 x -1 x+ 1 x +1 ) & = 1 2 ( x^2-x+1 x^2+x+1 )+c aligned