please help me to solve:

1) integral 2X *X / (X *X +1)(X *X +1) dx

2) integral dx/( X *X*X*X+X *X +2)

1)        2x²/(x²+1)² dx

     =  [2(x²+1) - 2]dx/(x²+1)²

     =[2/(x²+1) - 2/(x²+1)²]dx

I = 2tan^-1x - 2dx/(x²+1)²

I - 2tan^-1x = -2dx /(x²+1)²       .........................1

taking RHS

put x = tan@ so

     dx = sec²@d@

now

        RHS = -2d@/sec²@  =  -2cos²@ = -(1+cos2@)d@

               =-(@ + sin2@ /2) + c

               =- [ tan^-1x + sin(2tan^-1x)/2] + c

put RHS in eq 1 then

 I = tan^-1x - sin(2tan^-1x) / 2  + c    or

 I = tan^-1x -  x/1+x²  +  c

Approved