Optimal. Leaf size=34 \[ \frac {a^2 x^4}{4}+\frac {6}{11} a b x^{11/3}+\frac {3}{10} b^2 x^{10/3} \]
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Rubi [A] time = 0.03, antiderivative size = 34, normalized size of antiderivative = 1.00, number of steps used = 4, number of rules used = 3, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {263, 266, 43} \[ \frac {a^2 x^4}{4}+\frac {6}{11} a b x^{11/3}+\frac {3}{10} b^2 x^{10/3} \]
Antiderivative was successfully verified.
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Rule 43
Rule 263
Rule 266
Rubi steps
\begin {align*} \int \left (a+\frac {b}{\sqrt [3]{x}}\right )^2 x^3 \, dx &=\int \left (b+a \sqrt [3]{x}\right )^2 x^{7/3} \, dx\\ &=3 \operatorname {Subst}\left (\int x^9 (b+a x)^2 \, dx,x,\sqrt [3]{x}\right )\\ &=3 \operatorname {Subst}\left (\int \left (b^2 x^9+2 a b x^{10}+a^2 x^{11}\right ) \, dx,x,\sqrt [3]{x}\right )\\ &=\frac {3}{10} b^2 x^{10/3}+\frac {6}{11} a b x^{11/3}+\frac {a^2 x^4}{4}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 34, normalized size = 1.00 \[ \frac {a^2 x^4}{4}+\frac {6}{11} a b x^{11/3}+\frac {3}{10} b^2 x^{10/3} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.77, size = 24, normalized size = 0.71 \[ \frac {1}{4} \, a^{2} x^{4} + \frac {6}{11} \, a b x^{\frac {11}{3}} + \frac {3}{10} \, b^{2} x^{\frac {10}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 24, normalized size = 0.71 \[ \frac {1}{4} \, a^{2} x^{4} + \frac {6}{11} \, a b x^{\frac {11}{3}} + \frac {3}{10} \, b^{2} x^{\frac {10}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 25, normalized size = 0.74 \[ \frac {a^{2} x^{4}}{4}+\frac {6 a b \,x^{\frac {11}{3}}}{11}+\frac {3 b^{2} x^{\frac {10}{3}}}{10} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.59, size = 26, normalized size = 0.76 \[ \frac {1}{220} \, {\left (55 \, a^{2} + \frac {120 \, a b}{x^{\frac {1}{3}}} + \frac {66 \, b^{2}}{x^{\frac {2}{3}}}\right )} x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.14, size = 24, normalized size = 0.71 \[ \frac {a^2\,x^4}{4}+\frac {3\,b^2\,x^{10/3}}{10}+\frac {6\,a\,b\,x^{11/3}}{11} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 1.79, size = 31, normalized size = 0.91 \[ \frac {a^{2} x^{4}}{4} + \frac {6 a b x^{\frac {11}{3}}}{11} + \frac {3 b^{2} x^{\frac {10}{3}}}{10} \]
Verification of antiderivative is not currently implemented for this CAS.
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