Optimal. Leaf size=44 \[ \frac{3 b \sqrt [3]{a+b x^3}}{4 a^2 x}-\frac{\sqrt [3]{a+b x^3}}{4 a x^4} \]
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Rubi [A] time = 0.0410695, antiderivative size = 44, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133 \[ \frac{3 b \sqrt [3]{a+b x^3}}{4 a^2 x}-\frac{\sqrt [3]{a+b x^3}}{4 a x^4} \]
Antiderivative was successfully verified.
[In] Int[1/(x^5*(a + b*x^3)^(2/3)),x]
[Out]
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Rubi in Sympy [A] time = 4.23445, size = 36, normalized size = 0.82 \[ - \frac{\sqrt [3]{a + b x^{3}}}{4 a x^{4}} + \frac{3 b \sqrt [3]{a + b x^{3}}}{4 a^{2} x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**5/(b*x**3+a)**(2/3),x)
[Out]
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Mathematica [A] time = 0.0218465, size = 29, normalized size = 0.66 \[ -\frac{\left (a-3 b x^3\right ) \sqrt [3]{a+b x^3}}{4 a^2 x^4} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^5*(a + b*x^3)^(2/3)),x]
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Maple [A] time = 0.007, size = 26, normalized size = 0.6 \[ -{\frac{-3\,b{x}^{3}+a}{4\,{x}^{4}{a}^{2}}\sqrt [3]{b{x}^{3}+a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^5/(b*x^3+a)^(2/3),x)
[Out]
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Maxima [A] time = 1.43592, size = 47, normalized size = 1.07 \[ \frac{\frac{4 \,{\left (b x^{3} + a\right )}^{\frac{1}{3}} b}{x} - \frac{{\left (b x^{3} + a\right )}^{\frac{4}{3}}}{x^{4}}}{4 \, a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^3 + a)^(2/3)*x^5),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.244261, size = 36, normalized size = 0.82 \[ \frac{{\left (3 \, b x^{3} - a\right )}{\left (b x^{3} + a\right )}^{\frac{1}{3}}}{4 \, a^{2} x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^3 + a)^(2/3)*x^5),x, algorithm="fricas")
[Out]
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Sympy [A] time = 3.37566, size = 68, normalized size = 1.55 \[ - \frac{\sqrt [3]{b} \sqrt [3]{\frac{a}{b x^{3}} + 1} \Gamma \left (- \frac{4}{3}\right )}{9 a x^{3} \Gamma \left (\frac{2}{3}\right )} + \frac{b^{\frac{4}{3}} \sqrt [3]{\frac{a}{b x^{3}} + 1} \Gamma \left (- \frac{4}{3}\right )}{3 a^{2} \Gamma \left (\frac{2}{3}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**5/(b*x**3+a)**(2/3),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{{\left (b x^{3} + a\right )}^{\frac{2}{3}} x^{5}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^3 + a)^(2/3)*x^5),x, algorithm="giac")
[Out]