Optimal. Leaf size=38 \[ -\frac{\left (a+b x^3\right )^{4/3} \, _2F_1\left (\frac{2}{3},1;\frac{1}{3};-\frac{b x^3}{a}\right )}{2 a x^2} \]
[Out]
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Rubi [A] time = 0.0520507, antiderivative size = 51, normalized size of antiderivative = 1.34, number of steps used = 2, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133 \[ -\frac{\sqrt [3]{a+b x^3} \, _2F_1\left (-\frac{2}{3},-\frac{1}{3};\frac{1}{3};-\frac{b x^3}{a}\right )}{2 x^2 \sqrt [3]{\frac{b x^3}{a}+1}} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^3)^(1/3)/x^3,x]
[Out]
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Rubi in Sympy [A] time = 5.99749, size = 46, normalized size = 1.21 \[ - \frac{\sqrt [3]{a + b x^{3}}{{}_{2}F_{1}\left (\begin{matrix} - \frac{1}{3}, - \frac{2}{3} \\ \frac{1}{3} \end{matrix}\middle |{- \frac{b x^{3}}{a}} \right )}}{2 x^{2} \sqrt [3]{1 + \frac{b x^{3}}{a}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**3+a)**(1/3)/x**3,x)
[Out]
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Mathematica [A] time = 0.0489808, size = 66, normalized size = 1.74 \[ \frac{b x^3 \left (\frac{b x^3}{a}+1\right )^{2/3} \, _2F_1\left (\frac{1}{3},\frac{2}{3};\frac{4}{3};-\frac{b x^3}{a}\right )-a-b x^3}{2 x^2 \left (a+b x^3\right )^{2/3}} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^3)^(1/3)/x^3,x]
[Out]
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Maple [F] time = 0.039, size = 0, normalized size = 0. \[ \int{\frac{1}{{x}^{3}}\sqrt [3]{b{x}^{3}+a}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^3+a)^(1/3)/x^3,x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{{\left (b x^{3} + a\right )}^{\frac{1}{3}}}{x^{3}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^(1/3)/x^3,x, algorithm="maxima")
[Out]
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Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (\frac{{\left (b x^{3} + a\right )}^{\frac{1}{3}}}{x^{3}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^(1/3)/x^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 2.5501, size = 42, normalized size = 1.11 \[ \frac{\sqrt [3]{a} \Gamma \left (- \frac{2}{3}\right ){{}_{2}F_{1}\left (\begin{matrix} - \frac{2}{3}, - \frac{1}{3} \\ \frac{1}{3} \end{matrix}\middle |{\frac{b x^{3} e^{i \pi }}{a}} \right )}}{3 x^{2} \Gamma \left (\frac{1}{3}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**3+a)**(1/3)/x**3,x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{{\left (b x^{3} + a\right )}^{\frac{1}{3}}}{x^{3}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^(1/3)/x^3,x, algorithm="giac")
[Out]