integrate x^2/(x^2+1)*(x^2+4) dx

I = x²/(x²+1)(x²+4) dx

let x² = t then

x²/(x²+1)(x²+4) = t/(t+1)(t+4)

now using partial fraction

t/(t+1)(t+4) = A/(t+1) + B/(t+4) 

A,B = -1/3 , 4/3

t/(t+1)(t+4) = -1/3(t+1) + 4/3(t+4)

again replacing t by x²

I  = [-1/3(x²+1) + 4/3(x²+4) ]dx                                             [ 1/x²+a² dx = tan^-1(x/a)/a ]

I = [ -tan^-1x]/3 + 2tan^-1(x/2)/3 ] + C

approve my ans if u like