Optimal. Leaf size=92 \[ \frac{81 b^3 \left (a+b x^3\right )^{2/3}}{440 a^4 x^2}-\frac{27 b^2 \left (a+b x^3\right )^{2/3}}{220 a^3 x^5}+\frac{9 b \left (a+b x^3\right )^{2/3}}{88 a^2 x^8}-\frac{\left (a+b x^3\right )^{2/3}}{11 a x^{11}} \]
[Out]
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Rubi [A] time = 0.0927548, antiderivative size = 92, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133 \[ \frac{81 b^3 \left (a+b x^3\right )^{2/3}}{440 a^4 x^2}-\frac{27 b^2 \left (a+b x^3\right )^{2/3}}{220 a^3 x^5}+\frac{9 b \left (a+b x^3\right )^{2/3}}{88 a^2 x^8}-\frac{\left (a+b x^3\right )^{2/3}}{11 a x^{11}} \]
Antiderivative was successfully verified.
[In] Int[1/(x^12*(a + b*x^3)^(1/3)),x]
[Out]
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Rubi in Sympy [A] time = 9.74709, size = 85, normalized size = 0.92 \[ - \frac{\left (a + b x^{3}\right )^{\frac{2}{3}}}{11 a x^{11}} + \frac{9 b \left (a + b x^{3}\right )^{\frac{2}{3}}}{88 a^{2} x^{8}} - \frac{27 b^{2} \left (a + b x^{3}\right )^{\frac{2}{3}}}{220 a^{3} x^{5}} + \frac{81 b^{3} \left (a + b x^{3}\right )^{\frac{2}{3}}}{440 a^{4} x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**12/(b*x**3+a)**(1/3),x)
[Out]
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Mathematica [A] time = 0.0391778, size = 53, normalized size = 0.58 \[ \frac{\left (a+b x^3\right )^{2/3} \left (-40 a^3+45 a^2 b x^3-54 a b^2 x^6+81 b^3 x^9\right )}{440 a^4 x^{11}} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^12*(a + b*x^3)^(1/3)),x]
[Out]
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Maple [A] time = 0.01, size = 50, normalized size = 0.5 \[ -{\frac{-81\,{b}^{3}{x}^{9}+54\,a{b}^{2}{x}^{6}-45\,{a}^{2}b{x}^{3}+40\,{a}^{3}}{440\,{x}^{11}{a}^{4}} \left ( b{x}^{3}+a \right ) ^{{\frac{2}{3}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^12/(b*x^3+a)^(1/3),x)
[Out]
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Maxima [A] time = 1.44616, size = 93, normalized size = 1.01 \[ \frac{\frac{220 \,{\left (b x^{3} + a\right )}^{\frac{2}{3}} b^{3}}{x^{2}} - \frac{264 \,{\left (b x^{3} + a\right )}^{\frac{5}{3}} b^{2}}{x^{5}} + \frac{165 \,{\left (b x^{3} + a\right )}^{\frac{8}{3}} b}{x^{8}} - \frac{40 \,{\left (b x^{3} + a\right )}^{\frac{11}{3}}}{x^{11}}}{440 \, a^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^3 + a)^(1/3)*x^12),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.236288, size = 66, normalized size = 0.72 \[ \frac{{\left (81 \, b^{3} x^{9} - 54 \, a b^{2} x^{6} + 45 \, a^{2} b x^{3} - 40 \, a^{3}\right )}{\left (b x^{3} + a\right )}^{\frac{2}{3}}}{440 \, a^{4} x^{11}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^3 + a)^(1/3)*x^12),x, algorithm="fricas")
[Out]
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Sympy [A] time = 10.6426, size = 692, normalized size = 7.52 \[ \text{result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**12/(b*x**3+a)**(1/3),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{{\left (b x^{3} + a\right )}^{\frac{1}{3}} x^{12}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^3 + a)^(1/3)*x^12),x, algorithm="giac")
[Out]