Optimal. Leaf size=16 \[ -\frac{1}{3 x^2 \sqrt{b x^2}} \]
[Out]
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Rubi [A] time = 0.00631486, 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 \[ -\frac{1}{3 x^2 \sqrt{b x^2}} \]
Antiderivative was successfully verified.
[In] Int[1/(x^3*Sqrt[b*x^2]),x]
[Out]
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Rubi in Sympy [A] time = 2.48876, size = 12, normalized size = 0.75 \[ - \frac{b}{3 \left (b x^{2}\right )^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**3/(b*x**2)**(1/2),x)
[Out]
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Mathematica [A] time = 0.00404139, size = 16, normalized size = 1. \[ -\frac{1}{3 x^2 \sqrt{b x^2}} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^3*Sqrt[b*x^2]),x]
[Out]
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Maple [A] time = 0.002, size = 13, normalized size = 0.8 \[ -{\frac{1}{3\,{x}^{2}}{\frac{1}{\sqrt{b{x}^{2}}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^3/(b*x^2)^(1/2),x)
[Out]
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Maxima [A] time = 1.43133, size = 11, normalized size = 0.69 \[ -\frac{1}{3 \, \sqrt{b} x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(b*x^2)*x^3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.240641, size = 20, normalized size = 1.25 \[ -\frac{\sqrt{b x^{2}}}{3 \, b x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(b*x^2)*x^3),x, algorithm="fricas")
[Out]
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Sympy [A] time = 2.31415, size = 19, normalized size = 1.19 \[ - \frac{1}{3 \sqrt{b} x^{2} \sqrt{x^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**3/(b*x**2)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.209753, size = 16, normalized size = 1. \[ -\frac{1}{3 \, \sqrt{b x^{2}} x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(b*x^2)*x^3),x, algorithm="giac")
[Out]