Optimal. Leaf size=17 \[ \frac{2}{11} b x^4 \sqrt{b x^3} \]
[Out]
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Rubi [A] time = 0.00774167, antiderivative size = 17, 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 \[ \frac{2}{11} b x^4 \sqrt{b x^3} \]
Antiderivative was successfully verified.
[In] Int[(b*x^3)^(3/2),x]
[Out]
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Rubi in Sympy [A] time = 1.30868, size = 15, normalized size = 0.88 \[ \frac{2 b x^{4} \sqrt{b x^{3}}}{11} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**3)**(3/2),x)
[Out]
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Mathematica [A] time = 0.00273681, size = 14, normalized size = 0.82 \[ \frac{2}{11} x \left (b x^3\right )^{3/2} \]
Antiderivative was successfully verified.
[In] Integrate[(b*x^3)^(3/2),x]
[Out]
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Maple [A] time = 0.003, size = 11, normalized size = 0.7 \[{\frac{2\,x}{11} \left ( b{x}^{3} \right ) ^{{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^3)^(3/2),x)
[Out]
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Maxima [A] time = 1.4247, size = 14, normalized size = 0.82 \[ \frac{2}{11} \, \left (b x^{3}\right )^{\frac{3}{2}} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3)^(3/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.225569, size = 18, normalized size = 1.06 \[ \frac{2}{11} \, \sqrt{b x^{3}} b x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3)^(3/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.12844, size = 15, normalized size = 0.88 \[ \frac{2 b^{\frac{3}{2}} x \left (x^{3}\right )^{\frac{3}{2}}}{11} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**3)**(3/2),x)
[Out]
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GIAC/XCAS [A] time = 0.216178, size = 18, normalized size = 1.06 \[ \frac{2}{11} \, \sqrt{b x} b x^{5}{\rm sign}\left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3)^(3/2),x, algorithm="giac")
[Out]