Optimal. Leaf size=19 \[ -\frac{1}{3 b^2 x^2 \sqrt{b x^2}} \]
[Out]
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Rubi [A] time = 0.00903984, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.182 \[ -\frac{1}{3 b^2 x^2 \sqrt{b x^2}} \]
Antiderivative was successfully verified.
[In] Int[x/(b*x^2)^(5/2),x]
[Out]
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Rubi in Sympy [A] time = 2.17288, size = 14, normalized size = 0.74 \[ - \frac{1}{3 b \left (b x^{2}\right )^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x/(b*x**2)**(5/2),x)
[Out]
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Mathematica [A] time = 0.00137081, size = 16, normalized size = 0.84 \[ -\frac{x^2}{3 \left (b x^2\right )^{5/2}} \]
Antiderivative was successfully verified.
[In] Integrate[x/(b*x^2)^(5/2),x]
[Out]
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Maple [A] time = 0.004, size = 13, normalized size = 0.7 \[ -{\frac{{x}^{2}}{3} \left ( b{x}^{2} \right ) ^{-{\frac{5}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x/(b*x^2)^(5/2),x)
[Out]
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Maxima [A] time = 1.41008, size = 16, normalized size = 0.84 \[ -\frac{1}{3 \, \left (b x^{2}\right )^{\frac{3}{2}} b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(b*x^2)^(5/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.238555, size = 20, normalized size = 1.05 \[ -\frac{\sqrt{b x^{2}}}{3 \, b^{3} x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(b*x^2)^(5/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 3.09319, size = 17, normalized size = 0.89 \[ - \frac{x^{2}}{3 b^{\frac{5}{2}} \left (x^{2}\right )^{\frac{5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(b*x**2)**(5/2),x)
[Out]
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GIAC/XCAS [A] time = 0.221392, size = 20, normalized size = 1.05 \[ -\frac{1}{3 \, \sqrt{b x^{2}} b^{2} x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(b*x^2)^(5/2),x, algorithm="giac")
[Out]