Optimal. Leaf size=19 \[ -\frac{b^2 \sqrt{b x^2}}{2 x^3} \]
[Out]
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Rubi [A] time = 0.0083058, 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 \[ -\frac{b^2 \sqrt{b x^2}}{2 x^3} \]
Antiderivative was successfully verified.
[In] Int[(b*x^2)^(5/2)/x^8,x]
[Out]
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Rubi in Sympy [A] time = 2.28584, size = 17, normalized size = 0.89 \[ - \frac{b^{2} \sqrt{b x^{2}}}{2 x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**2)**(5/2)/x**8,x)
[Out]
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Mathematica [A] time = 0.00287313, size = 16, normalized size = 0.84 \[ -\frac{\left (b x^2\right )^{5/2}}{2 x^7} \]
Antiderivative was successfully verified.
[In] Integrate[(b*x^2)^(5/2)/x^8,x]
[Out]
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Maple [A] time = 0.003, size = 13, normalized size = 0.7 \[ -{\frac{1}{2\,{x}^{7}} \left ( b{x}^{2} \right ) ^{{\frac{5}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^2)^(5/2)/x^8,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)^(5/2)/x^8,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.262848, size = 20, normalized size = 1.05 \[ -\frac{\sqrt{b x^{2}} b^{2}}{2 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2)^(5/2)/x^8,x, algorithm="fricas")
[Out]
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Sympy [A] time = 8.65853, size = 17, normalized size = 0.89 \[ - \frac{b^{\frac{5}{2}} \left (x^{2}\right )^{\frac{5}{2}}}{2 x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**2)**(5/2)/x**8,x)
[Out]
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GIAC/XCAS [A] time = 0.232869, size = 14, normalized size = 0.74 \[ -\frac{b^{\frac{5}{2}}{\rm sign}\left (x\right )}{2 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2)^(5/2)/x^8,x, algorithm="giac")
[Out]