Optimal. Leaf size=68 \[ -\frac{9 b^2 \left (a+b x^3\right )^{4/3}}{140 a^3 x^4}+\frac{3 b \left (a+b x^3\right )^{4/3}}{35 a^2 x^7}-\frac{\left (a+b x^3\right )^{4/3}}{10 a x^{10}} \]
[Out]
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Rubi [A] time = 0.0643479, 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 \[ -\frac{9 b^2 \left (a+b x^3\right )^{4/3}}{140 a^3 x^4}+\frac{3 b \left (a+b x^3\right )^{4/3}}{35 a^2 x^7}-\frac{\left (a+b x^3\right )^{4/3}}{10 a x^{10}} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^3)^(1/3)/x^11,x]
[Out]
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Rubi in Sympy [A] time = 6.76377, size = 61, normalized size = 0.9 \[ - \frac{\left (a + b x^{3}\right )^{\frac{4}{3}}}{10 a x^{10}} + \frac{3 b \left (a + b x^{3}\right )^{\frac{4}{3}}}{35 a^{2} x^{7}} - \frac{9 b^{2} \left (a + b x^{3}\right )^{\frac{4}{3}}}{140 a^{3} x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**3+a)**(1/3)/x**11,x)
[Out]
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Mathematica [A] time = 0.0269378, size = 53, normalized size = 0.78 \[ -\frac{\sqrt [3]{a+b x^3} \left (14 a^3+2 a^2 b x^3-3 a b^2 x^6+9 b^3 x^9\right )}{140 a^3 x^{10}} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^3)^(1/3)/x^11,x]
[Out]
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Maple [A] time = 0.008, size = 39, normalized size = 0.6 \[ -{\frac{9\,{b}^{2}{x}^{6}-12\,ab{x}^{3}+14\,{a}^{2}}{140\,{x}^{10}{a}^{3}} \left ( b{x}^{3}+a \right ) ^{{\frac{4}{3}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^3+a)^(1/3)/x^11,x)
[Out]
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Maxima [A] time = 1.44004, size = 70, normalized size = 1.03 \[ -\frac{\frac{35 \,{\left (b x^{3} + a\right )}^{\frac{4}{3}} b^{2}}{x^{4}} - \frac{40 \,{\left (b x^{3} + a\right )}^{\frac{7}{3}} b}{x^{7}} + \frac{14 \,{\left (b x^{3} + a\right )}^{\frac{10}{3}}}{x^{10}}}{140 \, a^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^(1/3)/x^11,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.291911, size = 66, normalized size = 0.97 \[ -\frac{{\left (9 \, b^{3} x^{9} - 3 \, a b^{2} x^{6} + 2 \, a^{2} b x^{3} + 14 \, a^{3}\right )}{\left (b x^{3} + a\right )}^{\frac{1}{3}}}{140 \, a^{3} x^{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^(1/3)/x^11,x, algorithm="fricas")
[Out]
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Sympy [A] time = 7.98144, size = 520, normalized size = 7.65 \[ \frac{28 a^{5} b^{\frac{13}{3}} \sqrt [3]{\frac{a}{b x^{3}} + 1} \Gamma \left (- \frac{10}{3}\right )}{27 a^{5} b^{4} x^{9} \Gamma \left (- \frac{1}{3}\right ) + 54 a^{4} b^{5} x^{12} \Gamma \left (- \frac{1}{3}\right ) + 27 a^{3} b^{6} x^{15} \Gamma \left (- \frac{1}{3}\right )} + \frac{60 a^{4} b^{\frac{16}{3}} x^{3} \sqrt [3]{\frac{a}{b x^{3}} + 1} \Gamma \left (- \frac{10}{3}\right )}{27 a^{5} b^{4} x^{9} \Gamma \left (- \frac{1}{3}\right ) + 54 a^{4} b^{5} x^{12} \Gamma \left (- \frac{1}{3}\right ) + 27 a^{3} b^{6} x^{15} \Gamma \left (- \frac{1}{3}\right )} + \frac{30 a^{3} b^{\frac{19}{3}} x^{6} \sqrt [3]{\frac{a}{b x^{3}} + 1} \Gamma \left (- \frac{10}{3}\right )}{27 a^{5} b^{4} x^{9} \Gamma \left (- \frac{1}{3}\right ) + 54 a^{4} b^{5} x^{12} \Gamma \left (- \frac{1}{3}\right ) + 27 a^{3} b^{6} x^{15} \Gamma \left (- \frac{1}{3}\right )} + \frac{10 a^{2} b^{\frac{22}{3}} x^{9} \sqrt [3]{\frac{a}{b x^{3}} + 1} \Gamma \left (- \frac{10}{3}\right )}{27 a^{5} b^{4} x^{9} \Gamma \left (- \frac{1}{3}\right ) + 54 a^{4} b^{5} x^{12} \Gamma \left (- \frac{1}{3}\right ) + 27 a^{3} b^{6} x^{15} \Gamma \left (- \frac{1}{3}\right )} + \frac{30 a b^{\frac{25}{3}} x^{12} \sqrt [3]{\frac{a}{b x^{3}} + 1} \Gamma \left (- \frac{10}{3}\right )}{27 a^{5} b^{4} x^{9} \Gamma \left (- \frac{1}{3}\right ) + 54 a^{4} b^{5} x^{12} \Gamma \left (- \frac{1}{3}\right ) + 27 a^{3} b^{6} x^{15} \Gamma \left (- \frac{1}{3}\right )} + \frac{18 b^{\frac{28}{3}} x^{15} \sqrt [3]{\frac{a}{b x^{3}} + 1} \Gamma \left (- \frac{10}{3}\right )}{27 a^{5} b^{4} x^{9} \Gamma \left (- \frac{1}{3}\right ) + 54 a^{4} b^{5} x^{12} \Gamma \left (- \frac{1}{3}\right ) + 27 a^{3} b^{6} x^{15} \Gamma \left (- \frac{1}{3}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**3+a)**(1/3)/x**11,x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{{\left (b x^{3} + a\right )}^{\frac{1}{3}}}{x^{11}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^(1/3)/x^11,x, algorithm="giac")
[Out]