Optimal. Leaf size=47 \[ \frac {a^3 x^3}{3}+\frac {9}{8} a^2 b x^{8/3}+\frac {9}{7} a b^2 x^{7/3}+\frac {b^3 x^2}{2} \]
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Rubi [A] time = 0.03, antiderivative size = 47, 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} \[ \frac {9}{8} a^2 b x^{8/3}+\frac {a^3 x^3}{3}+\frac {9}{7} a b^2 x^{7/3}+\frac {b^3 x^2}{2} \]
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 )^3 x^2 \, dx &=\int \left (b+a \sqrt [3]{x}\right )^3 x \, dx\\ &=3 \operatorname {Subst}\left (\int x^5 (b+a x)^3 \, dx,x,\sqrt [3]{x}\right )\\ &=3 \operatorname {Subst}\left (\int \left (b^3 x^5+3 a b^2 x^6+3 a^2 b x^7+a^3 x^8\right ) \, dx,x,\sqrt [3]{x}\right )\\ &=\frac {b^3 x^2}{2}+\frac {9}{7} a b^2 x^{7/3}+\frac {9}{8} a^2 b x^{8/3}+\frac {a^3 x^3}{3}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 47, normalized size = 1.00 \[ \frac {a^3 x^3}{3}+\frac {9}{8} a^2 b x^{8/3}+\frac {9}{7} a b^2 x^{7/3}+\frac {b^3 x^2}{2} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.89, size = 35, normalized size = 0.74 \[ \frac {1}{3} \, a^{3} x^{3} + \frac {9}{8} \, a^{2} b x^{\frac {8}{3}} + \frac {9}{7} \, a b^{2} x^{\frac {7}{3}} + \frac {1}{2} \, b^{3} x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.19, size = 35, normalized size = 0.74 \[ \frac {1}{3} \, a^{3} x^{3} + \frac {9}{8} \, a^{2} b x^{\frac {8}{3}} + \frac {9}{7} \, a b^{2} x^{\frac {7}{3}} + \frac {1}{2} \, b^{3} x^{2} \]
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 \[ \frac {a^{3} x^{3}}{3}+\frac {9 a^{2} b \,x^{\frac {8}{3}}}{8}+\frac {9 a \,b^{2} x^{\frac {7}{3}}}{7}+\frac {b^{3} x^{2}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.57, size = 37, normalized size = 0.79 \[ \frac {1}{168} \, {\left (56 \, a^{3} + \frac {189 \, a^{2} b}{x^{\frac {1}{3}}} + \frac {216 \, a b^{2}}{x^{\frac {2}{3}}} + \frac {84 \, b^{3}}{x}\right )} x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 35, normalized size = 0.74 \[ \frac {a^3\,x^3}{3}+\frac {b^3\,x^2}{2}+\frac {9\,a\,b^2\,x^{7/3}}{7}+\frac {9\,a^2\,b\,x^{8/3}}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 1.22, size = 42, normalized size = 0.89 \[ \frac {a^{3} x^{3}}{3} + \frac {9 a^{2} b x^{\frac {8}{3}}}{8} + \frac {9 a b^{2} x^{\frac {7}{3}}}{7} + \frac {b^{3} x^{2}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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