If f (x)= x^2 ~d x (1+x^2 ) (1+ 1+x^2 ) and f (0)=0 , then f(1) is

Step-by-step solution

aligned Put & x= d x= ^2 d f (x) & = ^2 ^2 d ^2 (1+ ) & = ^2 d 1+ & = ^2 d (1+ ) & = 1- ^2 d (1+ ) & = (1- ) d & = d - d & = | + |- + c f (x) & = |x+ 1+x^2 |- ⁻¹ x+ c f (0) & = |0+ 1+0 |- ⁻¹(0)+ c 0 & = 1-0+ c c =0 f (x) & = |x+ 1+x^2 |- ⁻¹ x f (1) & = |1+ 1+1^2 |- ⁻¹(1) & (1+ 2 )- 4 aligned