Optimal. Leaf size=19 \[ -\frac{1}{6 b^2 x^5 \sqrt{b x^2}} \]
[Out]
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Rubi [A] time = 0.00847571, 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 \[ -\frac{1}{6 b^2 x^5 \sqrt{b x^2}} \]
Antiderivative was successfully verified.
[In] Int[1/(x^2*(b*x^2)^(5/2)),x]
[Out]
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Rubi in Sympy [A] time = 2.29816, size = 17, normalized size = 0.89 \[ - \frac{\sqrt{b x^{2}}}{6 b^{3} x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**2/(b*x**2)**(5/2),x)
[Out]
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Mathematica [A] time = 0.00357741, size = 15, normalized size = 0.79 \[ -\frac{b x}{6 \left (b x^2\right )^{7/2}} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^2*(b*x^2)^(5/2)),x]
[Out]
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Maple [A] time = 0.003, size = 13, normalized size = 0.7 \[ -{\frac{1}{6\,x} \left ( b{x}^{2} \right ) ^{-{\frac{5}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^2/(b*x^2)^(5/2),x)
[Out]
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Maxima [A] time = 1.4426, size = 11, normalized size = 0.58 \[ -\frac{1}{6 \, b^{\frac{5}{2}} x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^2)^(5/2)*x^2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.216142, size = 20, normalized size = 1.05 \[ -\frac{\sqrt{b x^{2}}}{6 \, b^{3} x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^2)^(5/2)*x^2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 4.635, size = 17, normalized size = 0.89 \[ - \frac{1}{6 b^{\frac{5}{2}} x \left (x^{2}\right )^{\frac{5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**2/(b*x**2)**(5/2),x)
[Out]
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GIAC/XCAS [A] time = 0.535131, 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)^(5/2)*x^2),x, algorithm="giac")
[Out]