Optimal. Leaf size=166 \[ -\frac{3 a^{11} \log \left (a+b \sqrt [3]{x}\right )}{b^{12}}+\frac{3 a^{10} \sqrt [3]{x}}{b^{11}}-\frac{3 a^9 x^{2/3}}{2 b^{10}}+\frac{a^8 x}{b^9}-\frac{3 a^7 x^{4/3}}{4 b^8}+\frac{3 a^6 x^{5/3}}{5 b^7}-\frac{a^5 x^2}{2 b^6}+\frac{3 a^4 x^{7/3}}{7 b^5}-\frac{3 a^3 x^{8/3}}{8 b^4}+\frac{a^2 x^3}{3 b^3}-\frac{3 a x^{10/3}}{10 b^2}+\frac{3 x^{11/3}}{11 b} \]
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Rubi [A] time = 0.24773, antiderivative size = 166, 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 \[ -\frac{3 a^{11} \log \left (a+b \sqrt [3]{x}\right )}{b^{12}}+\frac{3 a^{10} \sqrt [3]{x}}{b^{11}}-\frac{3 a^9 x^{2/3}}{2 b^{10}}+\frac{a^8 x}{b^9}-\frac{3 a^7 x^{4/3}}{4 b^8}+\frac{3 a^6 x^{5/3}}{5 b^7}-\frac{a^5 x^2}{2 b^6}+\frac{3 a^4 x^{7/3}}{7 b^5}-\frac{3 a^3 x^{8/3}}{8 b^4}+\frac{a^2 x^3}{3 b^3}-\frac{3 a x^{10/3}}{10 b^2}+\frac{3 x^{11/3}}{11 b} \]
Antiderivative was successfully verified.
[In] Int[x^3/(a + b*x^(1/3)),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{3 a^{11} \log{\left (a + b \sqrt [3]{x} \right )}}{b^{12}} - \frac{3 a^{9} \int ^{\sqrt [3]{x}} x\, dx}{b^{10}} + \frac{a^{8} x}{b^{9}} - \frac{3 a^{7} x^{\frac{4}{3}}}{4 b^{8}} + \frac{3 a^{6} x^{\frac{5}{3}}}{5 b^{7}} - \frac{a^{5} x^{2}}{2 b^{6}} + \frac{3 a^{4} x^{\frac{7}{3}}}{7 b^{5}} - \frac{3 a^{3} x^{\frac{8}{3}}}{8 b^{4}} + \frac{a^{2} x^{3}}{3 b^{3}} - \frac{3 a x^{\frac{10}{3}}}{10 b^{2}} + \frac{3 x^{\frac{11}{3}}}{11 b} + \frac{3 \int ^{\sqrt [3]{x}} a^{10}\, dx}{b^{11}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**3/(a+b*x**(1/3)),x)
[Out]
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Mathematica [A] time = 0.11852, size = 166, normalized size = 1. \[ -\frac{3 a^{11} \log \left (a+b \sqrt [3]{x}\right )}{b^{12}}+\frac{3 a^{10} \sqrt [3]{x}}{b^{11}}-\frac{3 a^9 x^{2/3}}{2 b^{10}}+\frac{a^8 x}{b^9}-\frac{3 a^7 x^{4/3}}{4 b^8}+\frac{3 a^6 x^{5/3}}{5 b^7}-\frac{a^5 x^2}{2 b^6}+\frac{3 a^4 x^{7/3}}{7 b^5}-\frac{3 a^3 x^{8/3}}{8 b^4}+\frac{a^2 x^3}{3 b^3}-\frac{3 a x^{10/3}}{10 b^2}+\frac{3 x^{11/3}}{11 b} \]
Antiderivative was successfully verified.
[In] Integrate[x^3/(a + b*x^(1/3)),x]
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Maple [A] time = 0.007, size = 131, normalized size = 0.8 \[ 3\,{\frac{{a}^{10}\sqrt [3]{x}}{{b}^{11}}}-{\frac{3\,{a}^{9}}{2\,{b}^{10}}{x}^{{\frac{2}{3}}}}+{\frac{{a}^{8}x}{{b}^{9}}}-{\frac{3\,{a}^{7}}{4\,{b}^{8}}{x}^{{\frac{4}{3}}}}+{\frac{3\,{a}^{6}}{5\,{b}^{7}}{x}^{{\frac{5}{3}}}}-{\frac{{a}^{5}{x}^{2}}{2\,{b}^{6}}}+{\frac{3\,{a}^{4}}{7\,{b}^{5}}{x}^{{\frac{7}{3}}}}-{\frac{3\,{a}^{3}}{8\,{b}^{4}}{x}^{{\frac{8}{3}}}}+{\frac{{x}^{3}{a}^{2}}{3\,{b}^{3}}}-{\frac{3\,a}{10\,{b}^{2}}{x}^{{\frac{10}{3}}}}+{\frac{3}{11\,b}{x}^{{\frac{11}{3}}}}-3\,{\frac{{a}^{11}\ln \left ( a+b\sqrt [3]{x} \right ) }{{b}^{12}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^3/(a+b*x^(1/3)),x)
[Out]
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Maxima [A] time = 1.42504, size = 266, normalized size = 1.6 \[ -\frac{3 \, a^{11} \log \left (b x^{\frac{1}{3}} + a\right )}{b^{12}} + \frac{3 \,{\left (b x^{\frac{1}{3}} + a\right )}^{11}}{11 \, b^{12}} - \frac{33 \,{\left (b x^{\frac{1}{3}} + a\right )}^{10} a}{10 \, b^{12}} + \frac{55 \,{\left (b x^{\frac{1}{3}} + a\right )}^{9} a^{2}}{3 \, b^{12}} - \frac{495 \,{\left (b x^{\frac{1}{3}} + a\right )}^{8} a^{3}}{8 \, b^{12}} + \frac{990 \,{\left (b x^{\frac{1}{3}} + a\right )}^{7} a^{4}}{7 \, b^{12}} - \frac{231 \,{\left (b x^{\frac{1}{3}} + a\right )}^{6} a^{5}}{b^{12}} + \frac{1386 \,{\left (b x^{\frac{1}{3}} + a\right )}^{5} a^{6}}{5 \, b^{12}} - \frac{495 \,{\left (b x^{\frac{1}{3}} + a\right )}^{4} a^{7}}{2 \, b^{12}} + \frac{165 \,{\left (b x^{\frac{1}{3}} + a\right )}^{3} a^{8}}{b^{12}} - \frac{165 \,{\left (b x^{\frac{1}{3}} + a\right )}^{2} a^{9}}{2 \, b^{12}} + \frac{33 \,{\left (b x^{\frac{1}{3}} + a\right )} a^{10}}{b^{12}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3/(b*x^(1/3) + a),x, algorithm="maxima")
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Fricas [A] time = 0.219047, size = 180, normalized size = 1.08 \[ \frac{3080 \, a^{2} b^{9} x^{3} - 4620 \, a^{5} b^{6} x^{2} + 9240 \, a^{8} b^{3} x - 27720 \, a^{11} \log \left (b x^{\frac{1}{3}} + a\right ) + 63 \,{\left (40 \, b^{11} x^{3} - 55 \, a^{3} b^{8} x^{2} + 88 \, a^{6} b^{5} x - 220 \, a^{9} b^{2}\right )} x^{\frac{2}{3}} - 198 \,{\left (14 \, a b^{10} x^{3} - 20 \, a^{4} b^{7} x^{2} + 35 \, a^{7} b^{4} x - 140 \, a^{10} b\right )} x^{\frac{1}{3}}}{9240 \, b^{12}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3/(b*x^(1/3) + a),x, algorithm="fricas")
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Sympy [A] time = 129.273, size = 165, normalized size = 0.99 \[ - \frac{3 a^{11} \log{\left (1 + \frac{b \sqrt [3]{x}}{a} \right )}}{b^{12}} + \frac{3 a^{10} \sqrt [3]{x}}{b^{11}} - \frac{3 a^{9} x^{\frac{2}{3}}}{2 b^{10}} + \frac{a^{8} x}{b^{9}} - \frac{3 a^{7} x^{\frac{4}{3}}}{4 b^{8}} + \frac{3 a^{6} x^{\frac{5}{3}}}{5 b^{7}} - \frac{a^{5} x^{2}}{2 b^{6}} + \frac{3 a^{4} x^{\frac{7}{3}}}{7 b^{5}} - \frac{3 a^{3} x^{\frac{8}{3}}}{8 b^{4}} + \frac{a^{2} x^{3}}{3 b^{3}} - \frac{3 a x^{\frac{10}{3}}}{10 b^{2}} + \frac{3 x^{\frac{11}{3}}}{11 b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**3/(a+b*x**(1/3)),x)
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GIAC/XCAS [A] time = 0.219318, size = 180, normalized size = 1.08 \[ -\frac{3 \, a^{11}{\rm ln}\left ({\left | b x^{\frac{1}{3}} + a \right |}\right )}{b^{12}} + \frac{2520 \, b^{10} x^{\frac{11}{3}} - 2772 \, a b^{9} x^{\frac{10}{3}} + 3080 \, a^{2} b^{8} x^{3} - 3465 \, a^{3} b^{7} x^{\frac{8}{3}} + 3960 \, a^{4} b^{6} x^{\frac{7}{3}} - 4620 \, a^{5} b^{5} x^{2} + 5544 \, a^{6} b^{4} x^{\frac{5}{3}} - 6930 \, a^{7} b^{3} x^{\frac{4}{3}} + 9240 \, a^{8} b^{2} x - 13860 \, a^{9} b x^{\frac{2}{3}} + 27720 \, a^{10} x^{\frac{1}{3}}}{9240 \, b^{11}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3/(b*x^(1/3) + a),x, algorithm="giac")
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