Optimal. Leaf size=14 \[ \frac{2}{5} x \sqrt{b x^3} \]
[Out]
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Rubi [A] time = 0.00659037, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.222 \[ \frac{2}{5} x \sqrt{b x^3} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[b*x^3],x]
[Out]
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Rubi in Sympy [A] time = 1.16916, size = 12, normalized size = 0.86 \[ \frac{2 x \sqrt{b x^{3}}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**3)**(1/2),x)
[Out]
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Mathematica [A] time = 0.00226548, size = 14, normalized size = 1. \[ \frac{2}{5} x \sqrt{b x^3} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[b*x^3],x]
[Out]
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Maple [A] time = 0.003, size = 11, normalized size = 0.8 \[{\frac{2\,x}{5}\sqrt{b{x}^{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^3)^(1/2),x)
[Out]
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Maxima [A] time = 1.43633, size = 14, normalized size = 1. \[ \frac{2}{5} \, \sqrt{b x^{3}} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(b*x^3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.256495, size = 14, normalized size = 1. \[ \frac{2}{5} \, \sqrt{b x^{3}} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(b*x^3),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.378517, size = 15, normalized size = 1.07 \[ \frac{2 \sqrt{b} x \sqrt{x^{3}}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**3)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.227197, size = 16, normalized size = 1.14 \[ \frac{2}{5} \, \sqrt{b x} x^{2}{\rm sign}\left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(b*x^3),x, algorithm="giac")
[Out]