Optimal. Leaf size=34 \[ \frac{a^2 x^5}{5}+\frac{3}{8} a b x^{16/3}+\frac{3}{17} b^2 x^{17/3} \]
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Rubi [A] time = 0.0301086, antiderivative size = 34, 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, Rules used = {266, 43} \[ \frac{a^2 x^5}{5}+\frac{3}{8} a b x^{16/3}+\frac{3}{17} b^2 x^{17/3} \]
Antiderivative was successfully verified.
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Rule 266
Rule 43
Rubi steps
\begin{align*} \int \left (a+b \sqrt [3]{x}\right )^2 x^4 \, dx &=3 \operatorname{Subst}\left (\int x^{14} (a+b x)^2 \, dx,x,\sqrt [3]{x}\right )\\ &=3 \operatorname{Subst}\left (\int \left (a^2 x^{14}+2 a b x^{15}+b^2 x^{16}\right ) \, dx,x,\sqrt [3]{x}\right )\\ &=\frac{a^2 x^5}{5}+\frac{3}{8} a b x^{16/3}+\frac{3}{17} b^2 x^{17/3}\\ \end{align*}
Mathematica [A] time = 0.0245209, size = 34, normalized size = 1. \[ \frac{a^2 x^5}{5}+\frac{3}{8} a b x^{16/3}+\frac{3}{17} b^2 x^{17/3} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 25, normalized size = 0.7 \begin{align*}{\frac{{x}^{5}{a}^{2}}{5}}+{\frac{3\,ab}{8}{x}^{{\frac{16}{3}}}}+{\frac{3\,{b}^{2}}{17}{x}^{{\frac{17}{3}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 0.957662, size = 338, normalized size = 9.94 \begin{align*} \frac{3 \,{\left (b x^{\frac{1}{3}} + a\right )}^{17}}{17 \, b^{15}} - \frac{21 \,{\left (b x^{\frac{1}{3}} + a\right )}^{16} a}{8 \, b^{15}} + \frac{91 \,{\left (b x^{\frac{1}{3}} + a\right )}^{15} a^{2}}{5 \, b^{15}} - \frac{78 \,{\left (b x^{\frac{1}{3}} + a\right )}^{14} a^{3}}{b^{15}} + \frac{231 \,{\left (b x^{\frac{1}{3}} + a\right )}^{13} a^{4}}{b^{15}} - \frac{1001 \,{\left (b x^{\frac{1}{3}} + a\right )}^{12} a^{5}}{2 \, b^{15}} + \frac{819 \,{\left (b x^{\frac{1}{3}} + a\right )}^{11} a^{6}}{b^{15}} - \frac{5148 \,{\left (b x^{\frac{1}{3}} + a\right )}^{10} a^{7}}{5 \, b^{15}} + \frac{1001 \,{\left (b x^{\frac{1}{3}} + a\right )}^{9} a^{8}}{b^{15}} - \frac{3003 \,{\left (b x^{\frac{1}{3}} + a\right )}^{8} a^{9}}{4 \, b^{15}} + \frac{429 \,{\left (b x^{\frac{1}{3}} + a\right )}^{7} a^{10}}{b^{15}} - \frac{182 \,{\left (b x^{\frac{1}{3}} + a\right )}^{6} a^{11}}{b^{15}} + \frac{273 \,{\left (b x^{\frac{1}{3}} + a\right )}^{5} a^{12}}{5 \, b^{15}} - \frac{21 \,{\left (b x^{\frac{1}{3}} + a\right )}^{4} a^{13}}{2 \, b^{15}} + \frac{{\left (b x^{\frac{1}{3}} + a\right )}^{3} a^{14}}{b^{15}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.42351, size = 70, normalized size = 2.06 \begin{align*} \frac{3}{17} \, b^{2} x^{\frac{17}{3}} + \frac{3}{8} \, a b x^{\frac{16}{3}} + \frac{1}{5} \, a^{2} x^{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 2.98734, size = 31, normalized size = 0.91 \begin{align*} \frac{a^{2} x^{5}}{5} + \frac{3 a b x^{\frac{16}{3}}}{8} + \frac{3 b^{2} x^{\frac{17}{3}}}{17} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.13648, size = 32, normalized size = 0.94 \begin{align*} \frac{3}{17} \, b^{2} x^{\frac{17}{3}} + \frac{3}{8} \, a b x^{\frac{16}{3}} + \frac{1}{5} \, a^{2} x^{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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