If ∫x2−1dxx4+3x2+1tan−1x2+1x=logtan−1f(x)+C, then

I=∫x2−1dxx4+3x2+1tan−1x2+1x            divide Nr and Dr by x2                      ⇒I=∫1−1x2dxx2+3+1x2tan−1x+1x                                                                         =∫dtt2+1tan−1t                                · where t=x+1x⇒dt=1−1x2dx  =logtan−1t+C                =logtan−1x2+1x+C                                                    ⇒f(x)=x2+1x