Optimal. Leaf size=21 \[ -\frac{\left (a+b x^3\right )^{5/3}}{5 a x^5} \]
[Out]
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Rubi [A] time = 0.0203909, antiderivative size = 21, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067 \[ -\frac{\left (a+b x^3\right )^{5/3}}{5 a x^5} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^3)^(2/3)/x^6,x]
[Out]
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Rubi in Sympy [A] time = 2.72961, size = 17, normalized size = 0.81 \[ - \frac{\left (a + b x^{3}\right )^{\frac{5}{3}}}{5 a x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**3+a)**(2/3)/x**6,x)
[Out]
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Mathematica [A] time = 0.0169421, size = 21, normalized size = 1. \[ -\frac{\left (a+b x^3\right )^{5/3}}{5 a x^5} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^3)^(2/3)/x^6,x]
[Out]
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Maple [A] time = 0.007, size = 18, normalized size = 0.9 \[ -{\frac{1}{5\,a{x}^{5}} \left ( b{x}^{3}+a \right ) ^{{\frac{5}{3}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^3+a)^(2/3)/x^6,x)
[Out]
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Maxima [A] time = 1.41636, size = 23, normalized size = 1.1 \[ -\frac{{\left (b x^{3} + a\right )}^{\frac{5}{3}}}{5 \, a x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^(2/3)/x^6,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.248244, size = 23, normalized size = 1.1 \[ -\frac{{\left (b x^{3} + a\right )}^{\frac{5}{3}}}{5 \, a x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^(2/3)/x^6,x, algorithm="fricas")
[Out]
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Sympy [A] time = 3.24127, size = 68, normalized size = 3.24 \[ \frac{b^{\frac{2}{3}} \left (\frac{a}{b x^{3}} + 1\right )^{\frac{2}{3}} \Gamma \left (- \frac{5}{3}\right )}{3 x^{3} \Gamma \left (- \frac{2}{3}\right )} + \frac{b^{\frac{5}{3}} \left (\frac{a}{b x^{3}} + 1\right )^{\frac{2}{3}} \Gamma \left (- \frac{5}{3}\right )}{3 a \Gamma \left (- \frac{2}{3}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**3+a)**(2/3)/x**6,x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{{\left (b x^{3} + a\right )}^{\frac{2}{3}}}{x^{6}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^(2/3)/x^6,x, algorithm="giac")
[Out]