Optimal. Leaf size=16 \[ -\frac{\sqrt{b x^2}}{2 x^3} \]
[Out]
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Rubi [A] time = 0.00678716, antiderivative size = 16, 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 \[ -\frac{\sqrt{b x^2}}{2 x^3} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[b*x^2]/x^4,x]
[Out]
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Rubi in Sympy [A] time = 1.92961, size = 14, normalized size = 0.88 \[ - \frac{\sqrt{b x^{2}}}{2 x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**2)**(1/2)/x**4,x)
[Out]
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Mathematica [A] time = 0.00207829, size = 16, normalized size = 1. \[ -\frac{\sqrt{b x^2}}{2 x^3} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[b*x^2]/x^4,x]
[Out]
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Maple [A] time = 0.003, size = 13, normalized size = 0.8 \[ -{\frac{1}{2\,{x}^{3}}\sqrt{b{x}^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^2)^(1/2)/x^4,x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: RuntimeError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(b*x^2)/x^4,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.253553, size = 16, normalized size = 1. \[ -\frac{\sqrt{b x^{2}}}{2 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(b*x^2)/x^4,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.90889, size = 17, normalized size = 1.06 \[ - \frac{\sqrt{b} \sqrt{x^{2}}}{2 x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**2)**(1/2)/x**4,x)
[Out]
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GIAC/XCAS [A] time = 0.214985, size = 14, normalized size = 0.88 \[ -\frac{\sqrt{b}{\rm sign}\left (x\right )}{2 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(b*x^2)/x^4,x, algorithm="giac")
[Out]