Optimal. Leaf size=19 \[ \frac{1}{7} b^2 x^6 \sqrt{b x^2} \]
[Out]
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Rubi [A] time = 0.00849907, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.182 \[ \frac{1}{7} b^2 x^6 \sqrt{b x^2} \]
Antiderivative was successfully verified.
[In] Int[x*(b*x^2)^(5/2),x]
[Out]
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Rubi in Sympy [A] time = 2.14828, size = 10, normalized size = 0.53 \[ \frac{\left (b x^{2}\right )^{\frac{7}{2}}}{7 b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x*(b*x**2)**(5/2),x)
[Out]
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Mathematica [A] time = 0.00304912, size = 16, normalized size = 0.84 \[ \frac{1}{7} x^2 \left (b x^2\right )^{5/2} \]
Antiderivative was successfully verified.
[In] Integrate[x*(b*x^2)^(5/2),x]
[Out]
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Maple [A] time = 0.005, size = 13, normalized size = 0.7 \[{\frac{{x}^{2}}{7} \left ( b{x}^{2} \right ) ^{{\frac{5}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x*(b*x^2)^(5/2),x)
[Out]
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Maxima [A] time = 1.43312, size = 16, normalized size = 0.84 \[ \frac{\left (b x^{2}\right )^{\frac{7}{2}}}{7 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2)^(5/2)*x,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.219742, size = 20, normalized size = 1.05 \[ \frac{1}{7} \, \sqrt{b x^{2}} b^{2} x^{6} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2)^(5/2)*x,x, algorithm="fricas")
[Out]
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Sympy [A] time = 4.93474, size = 15, normalized size = 0.79 \[ \frac{b^{\frac{5}{2}} x^{2} \left (x^{2}\right )^{\frac{5}{2}}}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*(b*x**2)**(5/2),x)
[Out]
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GIAC/XCAS [A] time = 0.227917, size = 14, normalized size = 0.74 \[ \frac{1}{7} \, b^{\frac{5}{2}} x^{7}{\rm sign}\left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2)^(5/2)*x,x, algorithm="giac")
[Out]