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$\int \frac{d x}{{(a^{2} - b^{2} x^{2})}^{3 / 2}}$ equals

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xa2−b2x2+C

xa2a2−b2x2+C

axa2−b2x2+C

1a2a2−b2x2+C

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detailed solution

Correct option is B

Put x=absin⁡θ⇒dx=abcos⁡θdθ∫dxa2−b2x23/2=ab∫cos⁡θdθa3cos3⁡θ=1a2btan⁡θ+C =1a2bsin⁡θ1−sin2⁡θ+C =1a2bbxa1−b2a2x2+C=1a2xa2−b2x2+C

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∫dxa2−b2x23/2 equals

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$\int \frac{d x}{{(a^{2} - b^{2} x^{2})}^{3 / 2}}$ equals