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$\int_{}^{} {\frac{1}{{({x^2} + {a^2})({x^2} + {b^2})}}dx = } $

• ✓
  $\frac{1}{{({a^2} - {b^2})}}\left[ {\frac{1}{b}{{\tan }^{ - 1}}\left( {\frac{x}{b}} \right) - \frac{1}{a}{{\tan }^{ - 1}}\left( {\frac{x}{a}} \right)} \right] + c$
• B
  $\frac{1}{{({b^2} - {a^2})}}\left[ {\frac{1}{b}{{\tan }^{ - 1}}\left( {\frac{x}{b}} \right) - \frac{1}{a}{{\tan }^{ - 1}}\left( {\frac{x}{a}} \right)} \right] + c$
• C
  $\frac{1}{b}{\tan ^{ - 1}}\left( {\frac{x}{b}} \right) - \frac{1}{a}{\tan ^{ - 1}}\left( {\frac{x}{a}} \right) + c$
• D
  $\frac{1}{a}{\tan ^{ - 1}}\left( {\frac{x}{a}} \right) - \frac{1}{b}{\tan ^{ - 1}}\left( {\frac{x}{b}} \right) + c$