_ ^ x ;dx ( x^2 - a^2 )( x^2 - b^2 ) = - Vidyadip

MCQ

$\int_{}^{} {\frac{{x\;dx}}{{({x^2} - {a^2})({x^2} - {b^2})}} = } $

A
$\frac{1}{{{a^2} - {b^2}}}\log \left( {\frac{{{x^2} - {a^2}}}{{{x^2} - {b^2}}}} \right) + c$
B
$\frac{1}{{{a^2} - {b^2}}}\log \left( {\frac{{{x^2} - {b^2}}}{{{x^2} - {a^2}}}} \right) + c$
✓
$\frac{1}{{2({a^2} - {b^2})}}\log \left( {\frac{{{x^2} - {a^2}}}{{{x^2} - {b^2}}}} \right) + c$
D
$\frac{1}{{2({a^2} - {b^2})}}\log \left( {\frac{{{x^2} - {b^2}}}{{{x^2} - {a^2}}}} \right) + c$

✓

Answer

Correct option: C.

$\frac{1}{{2({a^2} - {b^2})}}\log \left( {\frac{{{x^2} - {a^2}}}{{{x^2} - {b^2}}}} \right) + c$

c
(c)$\int_{}^{} {\frac{x}{{({x^2} - {a^2})({x^2} - {b^2})}}} \,dx$
$ = \frac{1}{{{a^2} - {b^2}}}\left[ {\int_{}^{} {\frac{x}{{{x^2} - {a^2}}}\,dx - \int_{}^{} {\frac{{x\,dx}}{{{x^2} - {b^2}}}} } } \right]$.

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