∫$$dx(a2+x2)32$$ $$=$$

Correct option is 2xa2(a2+x2)32+c

Questions

$\int \frac{d x}{{(a^{2} + x^{2})}^{\frac{3}{2}}} =$

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x(a2+x2)32+c

xa2(a2+x2)32+c

1a2(a2+x2)32+c

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detailed solution

Correct option is B

Put x=a tanθ ⇒dx=asec2θ dθ∴I=∫asec2θa2+a2tan2θ32dθ =∫asec2θa3sec2θ32dθ =1a2∫dθsecθ =1a2∫cosθ dθ =1a2sinθ+c =xa2a2+x232+c

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∫dx(a2+x2)32 =

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$\int \frac{d x}{{(a^{2} + x^{2})}^{\frac{3}{2}}} =$