Optimal. Leaf size=38 \[ \frac{\left (a+b x^3\right )^{5/3}}{5 b^2}-\frac{a \left (a+b x^3\right )^{2/3}}{2 b^2} \]
[Out]
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Rubi [A] time = 0.059681, antiderivative size = 38, 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 \[ \frac{\left (a+b x^3\right )^{5/3}}{5 b^2}-\frac{a \left (a+b x^3\right )^{2/3}}{2 b^2} \]
Antiderivative was successfully verified.
[In] Int[x^5/(a + b*x^3)^(1/3),x]
[Out]
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Rubi in Sympy [A] time = 7.08692, size = 31, normalized size = 0.82 \[ - \frac{a \left (a + b x^{3}\right )^{\frac{2}{3}}}{2 b^{2}} + \frac{\left (a + b x^{3}\right )^{\frac{5}{3}}}{5 b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**5/(b*x**3+a)**(1/3),x)
[Out]
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Mathematica [A] time = 0.0223652, size = 28, normalized size = 0.74 \[ \frac{\left (a+b x^3\right )^{2/3} \left (2 b x^3-3 a\right )}{10 b^2} \]
Antiderivative was successfully verified.
[In] Integrate[x^5/(a + b*x^3)^(1/3),x]
[Out]
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Maple [A] time = 0.006, size = 25, normalized size = 0.7 \[ -{\frac{-2\,b{x}^{3}+3\,a}{10\,{b}^{2}} \left ( b{x}^{3}+a \right ) ^{{\frac{2}{3}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^5/(b*x^3+a)^(1/3),x)
[Out]
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Maxima [A] time = 1.43532, size = 41, normalized size = 1.08 \[ \frac{{\left (b x^{3} + a\right )}^{\frac{5}{3}}}{5 \, b^{2}} - \frac{{\left (b x^{3} + a\right )}^{\frac{2}{3}} a}{2 \, b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^5/(b*x^3 + a)^(1/3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.269152, size = 32, normalized size = 0.84 \[ \frac{{\left (2 \, b x^{3} - 3 \, a\right )}{\left (b x^{3} + a\right )}^{\frac{2}{3}}}{10 \, b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^5/(b*x^3 + a)^(1/3),x, algorithm="fricas")
[Out]
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Sympy [A] time = 2.39381, size = 44, normalized size = 1.16 \[ \begin{cases} - \frac{3 a \left (a + b x^{3}\right )^{\frac{2}{3}}}{10 b^{2}} + \frac{x^{3} \left (a + b x^{3}\right )^{\frac{2}{3}}}{5 b} & \text{for}\: b \neq 0 \\\frac{x^{6}}{6 \sqrt [3]{a}} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**5/(b*x**3+a)**(1/3),x)
[Out]
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GIAC/XCAS [A] time = 0.325993, size = 39, normalized size = 1.03 \[ \frac{2 \,{\left (b x^{3} + a\right )}^{\frac{5}{3}} - 5 \,{\left (b x^{3} + a\right )}^{\frac{2}{3}} a}{10 \, b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^5/(b*x^3 + a)^(1/3),x, algorithm="giac")
[Out]