5.4 Indefinite Integrals and the Net Change Theorem/41

Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\begin{aligned}\int _{0}^{\frac {1}{\sqrt {3}}}{\frac {t^{2}-1}{t^{4}-1}}dt&=\int _{0}^{\frac {1}{\sqrt {3}}}{\frac {(t^{2}-1)}{(t^{2}-1)(t^{2}+1)}}dt=\int _{0}^{\frac {1}{\sqrt {3}}}{\frac {1}{(t^{2}+1)}}dt\\[2ex]&=\tan ^{-1}{(t)}{\bigg |}_{0}^{\frac {1}{\sqrt {3}}}=\tan ^{-1}({\frac {1}{\sqrt {3}}})^{-1}-[tan(0)^{-1}]\\[2ex]&={\frac {\pi }{6}}-0={\frac {\pi }{6}}\end{aligned}}}