Optimal. Leaf size=19 \[ -\frac{1}{4 b x^3 \sqrt{b x^2}} \]
[Out]
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Rubi [A] time = 0.00937006, antiderivative size = 19, 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 \[ -\frac{1}{4 b x^3 \sqrt{b x^2}} \]
Antiderivative was successfully verified.
[In] Int[1/(x^2*(b*x^2)^(3/2)),x]
[Out]
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Rubi in Sympy [A] time = 2.37632, size = 17, normalized size = 0.89 \[ - \frac{\sqrt{b x^{2}}}{4 b^{2} x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**2/(b*x**2)**(3/2),x)
[Out]
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Mathematica [A] time = 0.00325231, size = 15, normalized size = 0.79 \[ -\frac{b x}{4 \left (b x^2\right )^{5/2}} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^2*(b*x^2)^(3/2)),x]
[Out]
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Maple [A] time = 0.003, size = 13, normalized size = 0.7 \[ -{\frac{1}{4\,x} \left ( b{x}^{2} \right ) ^{-{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^2/(b*x^2)^(3/2),x)
[Out]
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Maxima [A] time = 1.41225, size = 11, normalized size = 0.58 \[ -\frac{1}{4 \, b^{\frac{3}{2}} x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^2)^(3/2)*x^2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.21902, size = 20, normalized size = 1.05 \[ -\frac{\sqrt{b x^{2}}}{4 \, b^{2} x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^2)^(3/2)*x^2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 2.56247, size = 17, normalized size = 0.89 \[ - \frac{1}{4 b^{\frac{3}{2}} x \left (x^{2}\right )^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**2/(b*x**2)**(3/2),x)
[Out]
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GIAC/XCAS [A] time = 0.562998, size = 4, normalized size = 0.21 \[ \mathit{sage}_{0} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^2)^(3/2)*x^2),x, algorithm="giac")
[Out]