Optimal. Leaf size=44 \[ \frac{3 b \left (a+b x^3\right )^{5/3}}{40 a^2 x^5}-\frac{\left (a+b x^3\right )^{5/3}}{8 a x^8} \]
[Out]
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Rubi [A] time = 0.0420266, antiderivative size = 44, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133 \[ \frac{3 b \left (a+b x^3\right )^{5/3}}{40 a^2 x^5}-\frac{\left (a+b x^3\right )^{5/3}}{8 a x^8} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^3)^(2/3)/x^9,x]
[Out]
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Rubi in Sympy [A] time = 4.25496, size = 37, normalized size = 0.84 \[ - \frac{\left (a + b x^{3}\right )^{\frac{5}{3}}}{8 a x^{8}} + \frac{3 b \left (a + b x^{3}\right )^{\frac{5}{3}}}{40 a^{2} x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**3+a)**(2/3)/x**9,x)
[Out]
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Mathematica [A] time = 0.0252886, size = 44, normalized size = 1. \[ \left (\frac{3 b^2}{40 a^2 x^2}-\frac{b}{20 a x^5}-\frac{1}{8 x^8}\right ) \left (a+b x^3\right )^{2/3} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^3)^(2/3)/x^9,x]
[Out]
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Maple [A] time = 0.007, size = 28, normalized size = 0.6 \[ -{\frac{-3\,b{x}^{3}+5\,a}{40\,{x}^{8}{a}^{2}} \left ( b{x}^{3}+a \right ) ^{{\frac{5}{3}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^3+a)^(2/3)/x^9,x)
[Out]
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Maxima [A] time = 1.44913, size = 47, normalized size = 1.07 \[ \frac{\frac{8 \,{\left (b x^{3} + a\right )}^{\frac{5}{3}} b}{x^{5}} - \frac{5 \,{\left (b x^{3} + a\right )}^{\frac{8}{3}}}{x^{8}}}{40 \, a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^(2/3)/x^9,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.254371, size = 51, normalized size = 1.16 \[ \frac{{\left (3 \, b^{2} x^{6} - 2 \, a b x^{3} - 5 \, a^{2}\right )}{\left (b x^{3} + a\right )}^{\frac{2}{3}}}{40 \, a^{2} x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^(2/3)/x^9,x, algorithm="fricas")
[Out]
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Sympy [A] time = 6.09448, size = 110, normalized size = 2.5 \[ - \frac{5 b^{\frac{2}{3}} \left (\frac{a}{b x^{3}} + 1\right )^{\frac{2}{3}} \Gamma \left (- \frac{8}{3}\right )}{9 x^{6} \Gamma \left (- \frac{2}{3}\right )} - \frac{2 b^{\frac{5}{3}} \left (\frac{a}{b x^{3}} + 1\right )^{\frac{2}{3}} \Gamma \left (- \frac{8}{3}\right )}{9 a x^{3} \Gamma \left (- \frac{2}{3}\right )} + \frac{b^{\frac{8}{3}} \left (\frac{a}{b x^{3}} + 1\right )^{\frac{2}{3}} \Gamma \left (- \frac{8}{3}\right )}{3 a^{2} \Gamma \left (- \frac{2}{3}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**3+a)**(2/3)/x**9,x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{{\left (b x^{3} + a\right )}^{\frac{2}{3}}}{x^{9}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^(2/3)/x^9,x, algorithm="giac")
[Out]