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7.1 inderfinite integral — ગણિત ધોરણ 12 સાયન્સ — Question

Gujarat Boardગુજરાતી માધ્યમધોરણ 12 સાયન્સગણિત7.1 inderfinite integral1 Mark
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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