Optimal. Leaf size=80 \[ -\frac{a^3 \left (a+b x^3\right )^{5/3}}{5 b^4}+\frac{3 a^2 \left (a+b x^3\right )^{8/3}}{8 b^4}+\frac{\left (a+b x^3\right )^{14/3}}{14 b^4}-\frac{3 a \left (a+b x^3\right )^{11/3}}{11 b^4} \]
[Out]
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Rubi [A] time = 0.105074, antiderivative size = 80, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133 \[ -\frac{a^3 \left (a+b x^3\right )^{5/3}}{5 b^4}+\frac{3 a^2 \left (a+b x^3\right )^{8/3}}{8 b^4}+\frac{\left (a+b x^3\right )^{14/3}}{14 b^4}-\frac{3 a \left (a+b x^3\right )^{11/3}}{11 b^4} \]
Antiderivative was successfully verified.
[In] Int[x^11*(a + b*x^3)^(2/3),x]
[Out]
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Rubi in Sympy [A] time = 14.5799, size = 71, normalized size = 0.89 \[ - \frac{a^{3} \left (a + b x^{3}\right )^{\frac{5}{3}}}{5 b^{4}} + \frac{3 a^{2} \left (a + b x^{3}\right )^{\frac{8}{3}}}{8 b^{4}} - \frac{3 a \left (a + b x^{3}\right )^{\frac{11}{3}}}{11 b^{4}} + \frac{\left (a + b x^{3}\right )^{\frac{14}{3}}}{14 b^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**11*(b*x**3+a)**(2/3),x)
[Out]
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Mathematica [A] time = 0.0304697, size = 61, normalized size = 0.76 \[ \frac{\left (a+b x^3\right )^{2/3} \left (-81 a^4+54 a^3 b x^3-45 a^2 b^2 x^6+40 a b^3 x^9+220 b^4 x^{12}\right )}{3080 b^4} \]
Antiderivative was successfully verified.
[In] Integrate[x^11*(a + b*x^3)^(2/3),x]
[Out]
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Maple [A] time = 0.008, size = 47, normalized size = 0.6 \[ -{\frac{-220\,{b}^{3}{x}^{9}+180\,a{b}^{2}{x}^{6}-135\,{a}^{2}b{x}^{3}+81\,{a}^{3}}{3080\,{b}^{4}} \left ( b{x}^{3}+a \right ) ^{{\frac{5}{3}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^11*(b*x^3+a)^(2/3),x)
[Out]
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Maxima [A] time = 1.44635, size = 86, normalized size = 1.08 \[ \frac{{\left (b x^{3} + a\right )}^{\frac{14}{3}}}{14 \, b^{4}} - \frac{3 \,{\left (b x^{3} + a\right )}^{\frac{11}{3}} a}{11 \, b^{4}} + \frac{3 \,{\left (b x^{3} + a\right )}^{\frac{8}{3}} a^{2}}{8 \, b^{4}} - \frac{{\left (b x^{3} + a\right )}^{\frac{5}{3}} a^{3}}{5 \, b^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^(2/3)*x^11,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.263038, size = 77, normalized size = 0.96 \[ \frac{{\left (220 \, b^{4} x^{12} + 40 \, a b^{3} x^{9} - 45 \, a^{2} b^{2} x^{6} + 54 \, a^{3} b x^{3} - 81 \, a^{4}\right )}{\left (b x^{3} + a\right )}^{\frac{2}{3}}}{3080 \, b^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^(2/3)*x^11,x, algorithm="fricas")
[Out]
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Sympy [A] time = 20.9894, size = 110, normalized size = 1.38 \[ \begin{cases} - \frac{81 a^{4} \left (a + b x^{3}\right )^{\frac{2}{3}}}{3080 b^{4}} + \frac{27 a^{3} x^{3} \left (a + b x^{3}\right )^{\frac{2}{3}}}{1540 b^{3}} - \frac{9 a^{2} x^{6} \left (a + b x^{3}\right )^{\frac{2}{3}}}{616 b^{2}} + \frac{a x^{9} \left (a + b x^{3}\right )^{\frac{2}{3}}}{77 b} + \frac{x^{12} \left (a + b x^{3}\right )^{\frac{2}{3}}}{14} & \text{for}\: b \neq 0 \\\frac{a^{\frac{2}{3}} x^{12}}{12} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**11*(b*x**3+a)**(2/3),x)
[Out]
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GIAC/XCAS [A] time = 0.229222, size = 77, normalized size = 0.96 \[ \frac{220 \,{\left (b x^{3} + a\right )}^{\frac{14}{3}} - 840 \,{\left (b x^{3} + a\right )}^{\frac{11}{3}} a + 1155 \,{\left (b x^{3} + a\right )}^{\frac{8}{3}} a^{2} - 616 \,{\left (b x^{3} + a\right )}^{\frac{5}{3}} a^{3}}{3080 \, b^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^(2/3)*x^11,x, algorithm="giac")
[Out]