A) \[\frac{1}{{{a}^{2}}-{{b}^{2}}}\log \left( \frac{{{x}^{2}}-{{a}^{2}}}{{{x}^{2}}-{{b}^{2}}} \right)+c\]
B) \[\frac{1}{{{a}^{2}}-{{b}^{2}}}\log \left( \frac{{{x}^{2}}-{{b}^{2}}}{{{x}^{2}}-{{a}^{2}}} \right)+c\]
C) \[\frac{1}{2({{a}^{2}}-{{b}^{2}})}\log \left( \frac{{{x}^{2}}-{{a}^{2}}}{{{x}^{2}}-{{b}^{2}}} \right)+c\]
D) \[\frac{1}{2({{a}^{2}}-{{b}^{2}})}\log \left( \frac{{{x}^{2}}-{{b}^{2}}}{{{x}^{2}}-{{a}^{2}}} \right)+c\]
Correct Answer: C
Solution :
\[\int_{{}}^{{}}{\frac{x}{({{x}^{2}}-{{a}^{2}})({{x}^{2}}-{{b}^{2}})}}\,dx\] \[=\frac{1}{{{a}^{2}}-{{b}^{2}}}\left[ \int_{{}}^{{}}{\frac{x}{{{x}^{2}}-{{a}^{2}}}\,dx-\int_{{}}^{{}}{\frac{x\,dx}{{{x}^{2}}-{{b}^{2}}}}} \right]\].You need to login to perform this action.
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