Optimal. Leaf size=47 \[ \frac {a^3 x^4}{4}+\frac {9}{13} a^2 b x^{13/3}+\frac {9}{14} a b^2 x^{14/3}+\frac {b^3 x^5}{5} \]
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Rubi [A] time = 0.03, antiderivative size = 47, 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} \[ \frac {9}{13} a^2 b x^{13/3}+\frac {a^3 x^4}{4}+\frac {9}{14} a b^2 x^{14/3}+\frac {b^3 x^5}{5} \]
Antiderivative was successfully verified.
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Rule 43
Rule 266
Rubi steps
\begin {align*} \int \left (a+b \sqrt [3]{x}\right )^3 x^3 \, dx &=3 \operatorname {Subst}\left (\int x^{11} (a+b x)^3 \, dx,x,\sqrt [3]{x}\right )\\ &=3 \operatorname {Subst}\left (\int \left (a^3 x^{11}+3 a^2 b x^{12}+3 a b^2 x^{13}+b^3 x^{14}\right ) \, dx,x,\sqrt [3]{x}\right )\\ &=\frac {a^3 x^4}{4}+\frac {9}{13} a^2 b x^{13/3}+\frac {9}{14} a b^2 x^{14/3}+\frac {b^3 x^5}{5}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 47, normalized size = 1.00 \[ \frac {a^3 x^4}{4}+\frac {9}{13} a^2 b x^{13/3}+\frac {9}{14} a b^2 x^{14/3}+\frac {b^3 x^5}{5} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.57, size = 35, normalized size = 0.74 \[ \frac {1}{5} \, b^{3} x^{5} + \frac {9}{14} \, a b^{2} x^{\frac {14}{3}} + \frac {9}{13} \, a^{2} b x^{\frac {13}{3}} + \frac {1}{4} \, a^{3} x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 35, normalized size = 0.74 \[ \frac {1}{5} \, b^{3} x^{5} + \frac {9}{14} \, a b^{2} x^{\frac {14}{3}} + \frac {9}{13} \, a^{2} b x^{\frac {13}{3}} + \frac {1}{4} \, a^{3} x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 36, normalized size = 0.77 \[ \frac {b^{3} x^{5}}{5}+\frac {9 a \,b^{2} x^{\frac {14}{3}}}{14}+\frac {9 a^{2} b \,x^{\frac {13}{3}}}{13}+\frac {a^{3} x^{4}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.90, size = 200, normalized size = 4.26 \[ \frac {{\left (b x^{\frac {1}{3}} + a\right )}^{15}}{5 \, b^{12}} - \frac {33 \, {\left (b x^{\frac {1}{3}} + a\right )}^{14} a}{14 \, b^{12}} + \frac {165 \, {\left (b x^{\frac {1}{3}} + a\right )}^{13} a^{2}}{13 \, b^{12}} - \frac {165 \, {\left (b x^{\frac {1}{3}} + a\right )}^{12} a^{3}}{4 \, b^{12}} + \frac {90 \, {\left (b x^{\frac {1}{3}} + a\right )}^{11} a^{4}}{b^{12}} - \frac {693 \, {\left (b x^{\frac {1}{3}} + a\right )}^{10} a^{5}}{5 \, b^{12}} + \frac {154 \, {\left (b x^{\frac {1}{3}} + a\right )}^{9} a^{6}}{b^{12}} - \frac {495 \, {\left (b x^{\frac {1}{3}} + a\right )}^{8} a^{7}}{4 \, b^{12}} + \frac {495 \, {\left (b x^{\frac {1}{3}} + a\right )}^{7} a^{8}}{7 \, b^{12}} - \frac {55 \, {\left (b x^{\frac {1}{3}} + a\right )}^{6} a^{9}}{2 \, b^{12}} + \frac {33 \, {\left (b x^{\frac {1}{3}} + a\right )}^{5} a^{10}}{5 \, b^{12}} - \frac {3 \, {\left (b x^{\frac {1}{3}} + a\right )}^{4} a^{11}}{4 \, b^{12}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 35, normalized size = 0.74 \[ \frac {a^3\,x^4}{4}+\frac {b^3\,x^5}{5}+\frac {9\,a^2\,b\,x^{13/3}}{13}+\frac {9\,a\,b^2\,x^{14/3}}{14} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 2.09, size = 42, normalized size = 0.89 \[ \frac {a^{3} x^{4}}{4} + \frac {9 a^{2} b x^{\frac {13}{3}}}{13} + \frac {9 a b^{2} x^{\frac {14}{3}}}{14} + \frac {b^{3} x^{5}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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