Optimal. Leaf size=15 \[ \frac{1}{2} b x \sqrt{b x^2} \]
[Out]
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Rubi [A] time = 0.00760952, antiderivative size = 15, 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 \[ \frac{1}{2} b x \sqrt{b x^2} \]
Antiderivative was successfully verified.
[In] Int[(b*x^2)^(3/2)/x^2,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{b \sqrt{b x^{2}} \int x\, dx}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**2)**(3/2)/x**2,x)
[Out]
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Mathematica [A] time = 0.00164343, size = 15, normalized size = 1. \[ \frac{1}{2} b x \sqrt{b x^2} \]
Antiderivative was successfully verified.
[In] Integrate[(b*x^2)^(3/2)/x^2,x]
[Out]
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Maple [A] time = 0.002, size = 13, normalized size = 0.9 \[{\frac{1}{2\,x} \left ( b{x}^{2} \right ) ^{{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^2)^(3/2)/x^2,x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: RuntimeError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2)^(3/2)/x^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.244749, size = 15, normalized size = 1. \[ \frac{1}{2} \, \sqrt{b x^{2}} b x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2)^(3/2)/x^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.17319, size = 14, normalized size = 0.93 \[ \frac{b^{\frac{3}{2}} \left (x^{2}\right )^{\frac{3}{2}}}{2 x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**2)**(3/2)/x**2,x)
[Out]
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GIAC/XCAS [A] time = 0.212813, size = 14, normalized size = 0.93 \[ \frac{1}{2} \, b^{\frac{3}{2}} x^{2}{\rm sign}\left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2)^(3/2)/x^2,x, algorithm="giac")
[Out]