Optimal. Leaf size=56 \[ \frac{a^2 \sqrt [3]{a+b x^3}}{b^3}+\frac{\left (a+b x^3\right )^{7/3}}{7 b^3}-\frac{a \left (a+b x^3\right )^{4/3}}{2 b^3} \]
[Out]
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Rubi [A] time = 0.083769, antiderivative size = 56, 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 \[ \frac{a^2 \sqrt [3]{a+b x^3}}{b^3}+\frac{\left (a+b x^3\right )^{7/3}}{7 b^3}-\frac{a \left (a+b x^3\right )^{4/3}}{2 b^3} \]
Antiderivative was successfully verified.
[In] Int[x^8/(a + b*x^3)^(2/3),x]
[Out]
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Rubi in Sympy [A] time = 10.5464, size = 48, normalized size = 0.86 \[ \frac{a^{2} \sqrt [3]{a + b x^{3}}}{b^{3}} - \frac{a \left (a + b x^{3}\right )^{\frac{4}{3}}}{2 b^{3}} + \frac{\left (a + b x^{3}\right )^{\frac{7}{3}}}{7 b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**8/(b*x**3+a)**(2/3),x)
[Out]
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Mathematica [A] time = 0.0267451, size = 39, normalized size = 0.7 \[ \frac{\sqrt [3]{a+b x^3} \left (9 a^2-3 a b x^3+2 b^2 x^6\right )}{14 b^3} \]
Antiderivative was successfully verified.
[In] Integrate[x^8/(a + b*x^3)^(2/3),x]
[Out]
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Maple [A] time = 0.006, size = 36, normalized size = 0.6 \[{\frac{2\,{b}^{2}{x}^{6}-3\,ab{x}^{3}+9\,{a}^{2}}{14\,{b}^{3}}\sqrt [3]{b{x}^{3}+a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^8/(b*x^3+a)^(2/3),x)
[Out]
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Maxima [A] time = 1.4392, size = 62, normalized size = 1.11 \[ \frac{{\left (b x^{3} + a\right )}^{\frac{7}{3}}}{7 \, b^{3}} - \frac{{\left (b x^{3} + a\right )}^{\frac{4}{3}} a}{2 \, b^{3}} + \frac{{\left (b x^{3} + a\right )}^{\frac{1}{3}} a^{2}}{b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^8/(b*x^3 + a)^(2/3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.22636, size = 47, normalized size = 0.84 \[ \frac{{\left (2 \, b^{2} x^{6} - 3 \, a b x^{3} + 9 \, a^{2}\right )}{\left (b x^{3} + a\right )}^{\frac{1}{3}}}{14 \, b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^8/(b*x^3 + a)^(2/3),x, algorithm="fricas")
[Out]
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Sympy [A] time = 5.05947, size = 68, normalized size = 1.21 \[ \begin{cases} \frac{9 a^{2} \sqrt [3]{a + b x^{3}}}{14 b^{3}} - \frac{3 a x^{3} \sqrt [3]{a + b x^{3}}}{14 b^{2}} + \frac{x^{6} \sqrt [3]{a + b x^{3}}}{7 b} & \text{for}\: b \neq 0 \\\frac{x^{9}}{9 a^{\frac{2}{3}}} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**8/(b*x**3+a)**(2/3),x)
[Out]
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GIAC/XCAS [A] time = 0.295931, size = 58, normalized size = 1.04 \[ \frac{2 \,{\left (b x^{3} + a\right )}^{\frac{7}{3}} - 7 \,{\left (b x^{3} + a\right )}^{\frac{4}{3}} a + 14 \,{\left (b x^{3} + a\right )}^{\frac{1}{3}} a^{2}}{14 \, b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^8/(b*x^3 + a)^(2/3),x, algorithm="giac")
[Out]