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

\[\frac{1}{({{b}^{2}}-{{a}^{2}})}\left[ \frac{1}{b}{{\tan }^{-1}}\left( \frac{x}{b} \right)-\frac{1}{a}{{\tan }^{-1}}\left( \frac{x}{a} \right) \right]+c\]

\[\frac{1}{({{a}^{2}}-{{b}^{2}})}\left[ \frac{1}{b}{{\tan }^{-1}}\left( \frac{x}{b} \right)-\frac{1}{a}{{\tan }^{-1}}\left( \frac{x}{a} \right) \right]+c\]

\[\frac{1}{b}{{\tan }^{-1}}\left( \frac{x}{b} \right)-\frac{1}{a}{{\tan }^{-1}}\left( \frac{x}{a} \right)+c\]

\[\frac{1}{a}{{\tan }^{-1}}\left( \frac{x}{a} \right)-\frac{1}{b}{{\tan }^{-1}}\left( \frac{x}{b} \right)+c\]

\[\int_{{}}^{{}}{\frac{1}{({{x}^{2}}+{{a}^{2}})({{x}^{2}}+{{b}^{2}})}d

1.	\[\int_{{}}^{{}}{\frac{1}{({{x}^{2}}+{{a}^{2}})({{x}^{2}}+{{b}^{2}})}dx=}\]
A.	\[\frac{1}{({{a}^{2}}-{{b}^{2}})}\left[ \frac{1}{b}{{\tan }^{-1}}\left( \frac{x}{b} \right)-\frac{1}{a}{{\tan }^{-1}}\left( \frac{x}{a} \right) \right]+c\]
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.	\[\frac{1}{a}{{\tan }^{-1}}\left( \frac{x}{a} \right)-\frac{1}{b}{{\tan }^{-1}}\left( \frac{x}{b} \right)+c\]
Answer» B. \[\frac{1}{({{b}^{2}}-{{a}^{2}})}\left[ \frac{1}{b}{{\tan }^{-1}}\left( \frac{x}{b} \right)-\frac{1}{a}{{\tan }^{-1}}\left( \frac{x}{a} \right) \right]+c\]

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