Optimal. Leaf size=68 \[ -\frac{9 b^2 \sqrt [3]{a+b x^3}}{14 a^3 x}+\frac{3 b \sqrt [3]{a+b x^3}}{14 a^2 x^4}-\frac{\sqrt [3]{a+b x^3}}{7 a x^7} \]
[Out]
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Rubi [A] time = 0.0646689, antiderivative size = 68, 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 \[ -\frac{9 b^2 \sqrt [3]{a+b x^3}}{14 a^3 x}+\frac{3 b \sqrt [3]{a+b x^3}}{14 a^2 x^4}-\frac{\sqrt [3]{a+b x^3}}{7 a x^7} \]
Antiderivative was successfully verified.
[In] Int[1/(x^8*(a + b*x^3)^(2/3)),x]
[Out]
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Rubi in Sympy [A] time = 6.63645, size = 60, normalized size = 0.88 \[ - \frac{\sqrt [3]{a + b x^{3}}}{7 a x^{7}} + \frac{3 b \sqrt [3]{a + b x^{3}}}{14 a^{2} x^{4}} - \frac{9 b^{2} \sqrt [3]{a + b x^{3}}}{14 a^{3} x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**8/(b*x**3+a)**(2/3),x)
[Out]
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Mathematica [A] time = 0.0302845, size = 42, normalized size = 0.62 \[ -\frac{\sqrt [3]{a+b x^3} \left (2 a^2-3 a b x^3+9 b^2 x^6\right )}{14 a^3 x^7} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^8*(a + b*x^3)^(2/3)),x]
[Out]
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Maple [A] time = 0.007, size = 39, normalized size = 0.6 \[ -{\frac{9\,{b}^{2}{x}^{6}-3\,ab{x}^{3}+2\,{a}^{2}}{14\,{a}^{3}{x}^{7}}\sqrt [3]{b{x}^{3}+a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^8/(b*x^3+a)^(2/3),x)
[Out]
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Maxima [A] time = 1.43645, size = 70, normalized size = 1.03 \[ -\frac{\frac{14 \,{\left (b x^{3} + a\right )}^{\frac{1}{3}} b^{2}}{x} - \frac{7 \,{\left (b x^{3} + a\right )}^{\frac{4}{3}} b}{x^{4}} + \frac{2 \,{\left (b x^{3} + a\right )}^{\frac{7}{3}}}{x^{7}}}{14 \, a^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^3 + a)^(2/3)*x^8),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.24131, size = 51, normalized size = 0.75 \[ -\frac{{\left (9 \, b^{2} x^{6} - 3 \, a b x^{3} + 2 \, a^{2}\right )}{\left (b x^{3} + a\right )}^{\frac{1}{3}}}{14 \, a^{3} x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^3 + a)^(2/3)*x^8),x, algorithm="fricas")
[Out]
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Sympy [A] time = 6.42866, size = 406, normalized size = 5.97 \[ \frac{4 a^{4} b^{\frac{13}{3}} \sqrt [3]{\frac{a}{b x^{3}} + 1} \Gamma \left (- \frac{7}{3}\right )}{27 a^{5} b^{4} x^{6} \Gamma \left (\frac{2}{3}\right ) + 54 a^{4} b^{5} x^{9} \Gamma \left (\frac{2}{3}\right ) + 27 a^{3} b^{6} x^{12} \Gamma \left (\frac{2}{3}\right )} + \frac{2 a^{3} b^{\frac{16}{3}} x^{3} \sqrt [3]{\frac{a}{b x^{3}} + 1} \Gamma \left (- \frac{7}{3}\right )}{27 a^{5} b^{4} x^{6} \Gamma \left (\frac{2}{3}\right ) + 54 a^{4} b^{5} x^{9} \Gamma \left (\frac{2}{3}\right ) + 27 a^{3} b^{6} x^{12} \Gamma \left (\frac{2}{3}\right )} + \frac{10 a^{2} b^{\frac{19}{3}} x^{6} \sqrt [3]{\frac{a}{b x^{3}} + 1} \Gamma \left (- \frac{7}{3}\right )}{27 a^{5} b^{4} x^{6} \Gamma \left (\frac{2}{3}\right ) + 54 a^{4} b^{5} x^{9} \Gamma \left (\frac{2}{3}\right ) + 27 a^{3} b^{6} x^{12} \Gamma \left (\frac{2}{3}\right )} + \frac{30 a b^{\frac{22}{3}} x^{9} \sqrt [3]{\frac{a}{b x^{3}} + 1} \Gamma \left (- \frac{7}{3}\right )}{27 a^{5} b^{4} x^{6} \Gamma \left (\frac{2}{3}\right ) + 54 a^{4} b^{5} x^{9} \Gamma \left (\frac{2}{3}\right ) + 27 a^{3} b^{6} x^{12} \Gamma \left (\frac{2}{3}\right )} + \frac{18 b^{\frac{25}{3}} x^{12} \sqrt [3]{\frac{a}{b x^{3}} + 1} \Gamma \left (- \frac{7}{3}\right )}{27 a^{5} b^{4} x^{6} \Gamma \left (\frac{2}{3}\right ) + 54 a^{4} b^{5} x^{9} \Gamma \left (\frac{2}{3}\right ) + 27 a^{3} b^{6} x^{12} \Gamma \left (\frac{2}{3}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**8/(b*x**3+a)**(2/3),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{{\left (b x^{3} + a\right )}^{\frac{2}{3}} x^{8}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^3 + a)^(2/3)*x^8),x, algorithm="giac")
[Out]