Optimal. Leaf size=25 \[ \frac{x \left (a^2+x^2\right )}{a^2 \sqrt{\left (a^2+x^2\right )^3}} \]
[Out]
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Rubi [A] time = 0.0305376, antiderivative size = 25, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ \frac{x \left (a^2+x^2\right )}{a^2 \sqrt{\left (a^2+x^2\right )^3}} \]
Antiderivative was successfully verified.
[In] Int[1/Sqrt[(a^2 + x^2)^3],x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\sqrt{\left (a^{2} + x^{2}\right )^{3}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/((a**2+x**2)**3)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0380825, size = 25, normalized size = 1. \[ \frac{x \left (a^2+x^2\right )}{a^2 \sqrt{\left (a^2+x^2\right )^3}} \]
Antiderivative was successfully verified.
[In] Integrate[1/Sqrt[(a^2 + x^2)^3],x]
[Out]
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Maple [A] time = 0.006, size = 24, normalized size = 1. \[{\frac{x \left ({a}^{2}+{x}^{2} \right ) }{{a}^{2}}{\frac{1}{\sqrt{ \left ({a}^{2}+{x}^{2} \right ) ^{3}}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/((a^2+x^2)^3)^(1/2),x)
[Out]
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Maxima [A] time = 0.707499, size = 19, normalized size = 0.76 \[ \frac{x}{\sqrt{a^{2} + x^{2}} a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/sqrt((a^2 + x^2)^3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.277155, size = 86, normalized size = 3.44 \[ \frac{a^{4} + 2 \, a^{2} x^{2} + x^{4} + \sqrt{a^{6} + 3 \, a^{4} x^{2} + 3 \, a^{2} x^{4} + x^{6}} x}{a^{6} + 2 \, a^{4} x^{2} + a^{2} x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/sqrt((a^2 + x^2)^3),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\sqrt{\left (a^{2} + x^{2}\right )^{3}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a**2+x**2)**3)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.264094, size = 19, normalized size = 0.76 \[ \frac{x}{\sqrt{a^{2} + x^{2}} a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/sqrt((a^2 + x^2)^3),x, algorithm="giac")
[Out]