Optimal. Leaf size=53 \[ \frac{3 a^2 (a+b x)^{2/3}}{2 b^3}+\frac{3 (a+b x)^{8/3}}{8 b^3}-\frac{6 a (a+b x)^{5/3}}{5 b^3} \]
[Out]
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Rubi [A] time = 0.0386107, antiderivative size = 53, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ \frac{3 a^2 (a+b x)^{2/3}}{2 b^3}+\frac{3 (a+b x)^{8/3}}{8 b^3}-\frac{6 a (a+b x)^{5/3}}{5 b^3} \]
Antiderivative was successfully verified.
[In] Int[x^2/(a + b*x)^(1/3),x]
[Out]
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Rubi in Sympy [A] time = 7.85877, size = 49, normalized size = 0.92 \[ \frac{3 a^{2} \left (a + b x\right )^{\frac{2}{3}}}{2 b^{3}} - \frac{6 a \left (a + b x\right )^{\frac{5}{3}}}{5 b^{3}} + \frac{3 \left (a + b x\right )^{\frac{8}{3}}}{8 b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**2/(b*x+a)**(1/3),x)
[Out]
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Mathematica [A] time = 0.018934, size = 35, normalized size = 0.66 \[ \frac{3 (a+b x)^{2/3} \left (9 a^2-6 a b x+5 b^2 x^2\right )}{40 b^3} \]
Antiderivative was successfully verified.
[In] Integrate[x^2/(a + b*x)^(1/3),x]
[Out]
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Maple [A] time = 0.006, size = 32, normalized size = 0.6 \[{\frac{15\,{b}^{2}{x}^{2}-18\,abx+27\,{a}^{2}}{40\,{b}^{3}} \left ( bx+a \right ) ^{{\frac{2}{3}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^2/(b*x+a)^(1/3),x)
[Out]
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Maxima [A] time = 1.35349, size = 55, normalized size = 1.04 \[ \frac{3 \,{\left (b x + a\right )}^{\frac{8}{3}}}{8 \, b^{3}} - \frac{6 \,{\left (b x + a\right )}^{\frac{5}{3}} a}{5 \, b^{3}} + \frac{3 \,{\left (b x + a\right )}^{\frac{2}{3}} a^{2}}{2 \, b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/(b*x + a)^(1/3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.227355, size = 42, normalized size = 0.79 \[ \frac{3 \,{\left (5 \, b^{2} x^{2} - 6 \, a b x + 9 \, a^{2}\right )}{\left (b x + a\right )}^{\frac{2}{3}}}{40 \, b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/(b*x + a)^(1/3),x, algorithm="fricas")
[Out]
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Sympy [A] time = 5.33341, size = 600, normalized size = 11.32 \[ \frac{27 a^{\frac{32}{3}} \left (1 + \frac{b x}{a}\right )^{\frac{2}{3}}}{40 a^{8} b^{3} + 120 a^{7} b^{4} x + 120 a^{6} b^{5} x^{2} + 40 a^{5} b^{6} x^{3}} - \frac{27 a^{\frac{32}{3}}}{40 a^{8} b^{3} + 120 a^{7} b^{4} x + 120 a^{6} b^{5} x^{2} + 40 a^{5} b^{6} x^{3}} + \frac{63 a^{\frac{29}{3}} b x \left (1 + \frac{b x}{a}\right )^{\frac{2}{3}}}{40 a^{8} b^{3} + 120 a^{7} b^{4} x + 120 a^{6} b^{5} x^{2} + 40 a^{5} b^{6} x^{3}} - \frac{81 a^{\frac{29}{3}} b x}{40 a^{8} b^{3} + 120 a^{7} b^{4} x + 120 a^{6} b^{5} x^{2} + 40 a^{5} b^{6} x^{3}} + \frac{42 a^{\frac{26}{3}} b^{2} x^{2} \left (1 + \frac{b x}{a}\right )^{\frac{2}{3}}}{40 a^{8} b^{3} + 120 a^{7} b^{4} x + 120 a^{6} b^{5} x^{2} + 40 a^{5} b^{6} x^{3}} - \frac{81 a^{\frac{26}{3}} b^{2} x^{2}}{40 a^{8} b^{3} + 120 a^{7} b^{4} x + 120 a^{6} b^{5} x^{2} + 40 a^{5} b^{6} x^{3}} + \frac{18 a^{\frac{23}{3}} b^{3} x^{3} \left (1 + \frac{b x}{a}\right )^{\frac{2}{3}}}{40 a^{8} b^{3} + 120 a^{7} b^{4} x + 120 a^{6} b^{5} x^{2} + 40 a^{5} b^{6} x^{3}} - \frac{27 a^{\frac{23}{3}} b^{3} x^{3}}{40 a^{8} b^{3} + 120 a^{7} b^{4} x + 120 a^{6} b^{5} x^{2} + 40 a^{5} b^{6} x^{3}} + \frac{27 a^{\frac{20}{3}} b^{4} x^{4} \left (1 + \frac{b x}{a}\right )^{\frac{2}{3}}}{40 a^{8} b^{3} + 120 a^{7} b^{4} x + 120 a^{6} b^{5} x^{2} + 40 a^{5} b^{6} x^{3}} + \frac{15 a^{\frac{17}{3}} b^{5} x^{5} \left (1 + \frac{b x}{a}\right )^{\frac{2}{3}}}{40 a^{8} b^{3} + 120 a^{7} b^{4} x + 120 a^{6} b^{5} x^{2} + 40 a^{5} b^{6} x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**2/(b*x+a)**(1/3),x)
[Out]
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GIAC/XCAS [A] time = 0.207548, size = 62, normalized size = 1.17 \[ \frac{3 \,{\left (5 \,{\left (b x + a\right )}^{\frac{8}{3}} b^{14} - 16 \,{\left (b x + a\right )}^{\frac{5}{3}} a b^{14} + 20 \,{\left (b x + a\right )}^{\frac{2}{3}} a^{2} b^{14}\right )}}{40 \, b^{17}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/(b*x + a)^(1/3),x, algorithm="giac")
[Out]