Answer:
Option C
Explanation:
Let l= $\int\frac{x^{2}+1}{x^{4}-x^{2}+1}dx$
= $\int\frac{1+\frac{1}{x^{2}}}{x^{2}-1+\frac{1}{x^{2}}}dx=\int\frac{1+\frac{1}{x^{2}}}{(x-\frac{1}{x})^{2}+1}$
put $x-\frac{1}{x}=t$
$(1+\frac{1}{x^{2}})dx=dt$
$\therefore$
$l=\int \frac{dt}{t^{2}+1})= \tan^{-1}(t)+c$
$= \tan^{-1}(x-\frac{1}{x})+c= \tan^{-1}(\frac{x^{2}-1}{x})+c$