Optimal. Leaf size=21 \[ \frac{x^3 \left (a+\frac{b}{x^2}\right )^{3/2}}{3 a} \]
[Out]
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Rubi [A] time = 0.0317097, antiderivative size = 21, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067 \[ \frac{x^3 \left (a+\frac{b}{x^2}\right )^{3/2}}{3 a} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[a + b/x^2]*x^2,x]
[Out]
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Rubi in Sympy [A] time = 2.69885, size = 15, normalized size = 0.71 \[ \frac{x^{3} \left (a + \frac{b}{x^{2}}\right )^{\frac{3}{2}}}{3 a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b/x**2)**(1/2)*x**2,x)
[Out]
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Mathematica [A] time = 0.0103431, size = 26, normalized size = 1.24 \[ \frac{x \sqrt{a+\frac{b}{x^2}} \left (a x^2+b\right )}{3 a} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[a + b/x^2]*x^2,x]
[Out]
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Maple [A] time = 0.006, size = 27, normalized size = 1.3 \[{\frac{ \left ( a{x}^{2}+b \right ) x}{3\,a}\sqrt{{\frac{a{x}^{2}+b}{{x}^{2}}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b/x^2)^(1/2)*x^2,x)
[Out]
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Maxima [A] time = 1.42735, size = 23, normalized size = 1.1 \[ \frac{{\left (a + \frac{b}{x^{2}}\right )}^{\frac{3}{2}} x^{3}}{3 \, a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(a + b/x^2)*x^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.237737, size = 36, normalized size = 1.71 \[ \frac{{\left (a x^{3} + b x\right )} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{3 \, a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(a + b/x^2)*x^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 2.62626, size = 41, normalized size = 1.95 \[ \frac{\sqrt{b} x^{2} \sqrt{\frac{a x^{2}}{b} + 1}}{3} + \frac{b^{\frac{3}{2}} \sqrt{\frac{a x^{2}}{b} + 1}}{3 a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b/x**2)**(1/2)*x**2,x)
[Out]
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GIAC/XCAS [A] time = 0.226259, size = 36, normalized size = 1.71 \[ \frac{{\left (a x^{2} + b\right )}^{\frac{3}{2}}{\rm sign}\left (x\right )}{3 \, a} - \frac{b^{\frac{3}{2}}{\rm sign}\left (x\right )}{3 \, a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(a + b/x^2)*x^2,x, algorithm="giac")
[Out]