Optimal. Leaf size=34 \[ \frac {a^2 x^4}{4}+\frac {6}{13} a b x^{13/3}+\frac {3}{14} b^2 x^{14/3} \]
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Rubi [A] time = 0.03, antiderivative size = 34, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.133, Rules used = {266, 43} \[ \frac {a^2 x^4}{4}+\frac {6}{13} a b x^{13/3}+\frac {3}{14} b^2 x^{14/3} \]
Antiderivative was successfully verified.
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Rule 43
Rule 266
Rubi steps
\begin {align*} \int \left (a+b \sqrt [3]{x}\right )^2 x^3 \, dx &=3 \operatorname {Subst}\left (\int x^{11} (a+b x)^2 \, dx,x,\sqrt [3]{x}\right )\\ &=3 \operatorname {Subst}\left (\int \left (a^2 x^{11}+2 a b x^{12}+b^2 x^{13}\right ) \, dx,x,\sqrt [3]{x}\right )\\ &=\frac {a^2 x^4}{4}+\frac {6}{13} a b x^{13/3}+\frac {3}{14} b^2 x^{14/3}\\ \end {align*}
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Mathematica [A] time = 0.03, size = 34, normalized size = 1.00 \[ \frac {a^2 x^4}{4}+\frac {6}{13} a b x^{13/3}+\frac {3}{14} b^2 x^{14/3} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.52, size = 24, normalized size = 0.71 \[ \frac {3}{14} \, b^{2} x^{\frac {14}{3}} + \frac {6}{13} \, a b x^{\frac {13}{3}} + \frac {1}{4} \, a^{2} x^{4} \]
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 \[ \frac {3}{14} \, b^{2} x^{\frac {14}{3}} + \frac {6}{13} \, a b x^{\frac {13}{3}} + \frac {1}{4} \, a^{2} x^{4} \]
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 \[ \frac {3 b^{2} x^{\frac {14}{3}}}{14}+\frac {6 a b \,x^{\frac {13}{3}}}{13}+\frac {a^{2} x^{4}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.92, size = 200, normalized size = 5.88 \[ \frac {3 \, {\left (b x^{\frac {1}{3}} + a\right )}^{14}}{14 \, b^{12}} - \frac {33 \, {\left (b x^{\frac {1}{3}} + a\right )}^{13} a}{13 \, b^{12}} + \frac {55 \, {\left (b x^{\frac {1}{3}} + a\right )}^{12} a^{2}}{4 \, b^{12}} - \frac {45 \, {\left (b x^{\frac {1}{3}} + a\right )}^{11} a^{3}}{b^{12}} + \frac {99 \, {\left (b x^{\frac {1}{3}} + a\right )}^{10} a^{4}}{b^{12}} - \frac {154 \, {\left (b x^{\frac {1}{3}} + a\right )}^{9} a^{5}}{b^{12}} + \frac {693 \, {\left (b x^{\frac {1}{3}} + a\right )}^{8} a^{6}}{4 \, b^{12}} - \frac {990 \, {\left (b x^{\frac {1}{3}} + a\right )}^{7} a^{7}}{7 \, b^{12}} + \frac {165 \, {\left (b x^{\frac {1}{3}} + a\right )}^{6} a^{8}}{2 \, b^{12}} - \frac {33 \, {\left (b x^{\frac {1}{3}} + a\right )}^{5} a^{9}}{b^{12}} + \frac {33 \, {\left (b x^{\frac {1}{3}} + a\right )}^{4} a^{10}}{4 \, b^{12}} - \frac {{\left (b x^{\frac {1}{3}} + a\right )}^{3} a^{11}}{b^{12}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 24, normalized size = 0.71 \[ \frac {a^2\,x^4}{4}+\frac {3\,b^2\,x^{14/3}}{14}+\frac {6\,a\,b\,x^{13/3}}{13} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 1.73, size = 31, normalized size = 0.91 \[ \frac {a^{2} x^{4}}{4} + \frac {6 a b x^{\frac {13}{3}}}{13} + \frac {3 b^{2} x^{\frac {14}{3}}}{14} \]
Verification of antiderivative is not currently implemented for this CAS.
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