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 = 0.03, 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} \[ \frac {a^2 x^5}{5}+\frac {3}{8} a b x^{16/3}+\frac {3}{17} b^2 x^{17/3} \]
Antiderivative was successfully verified.
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Rule 43
Rule 266
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*}
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Mathematica [A] time = 0.04, size = 34, normalized size = 1.00 \[ \frac {a^2 x^5}{5}+\frac {3}{8} a b x^{16/3}+\frac {3}{17} b^2 x^{17/3} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.68, size = 24, normalized size = 0.71 \[ \frac {3}{17} \, b^{2} x^{\frac {17}{3}} + \frac {3}{8} \, a b x^{\frac {16}{3}} + \frac {1}{5} \, a^{2} x^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.20, size = 24, normalized size = 0.71 \[ \frac {3}{17} \, b^{2} x^{\frac {17}{3}} + \frac {3}{8} \, a b x^{\frac {16}{3}} + \frac {1}{5} \, a^{2} x^{5} \]
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 \[ \frac {3 b^{2} x^{\frac {17}{3}}}{17}+\frac {3 a b \,x^{\frac {16}{3}}}{8}+\frac {a^{2} x^{5}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.92, size = 250, normalized size = 7.35 \[ \frac {3 \, {\left (b x^{\frac {1}{3}} + a\right )}^{17}}{17 \, b^{15}} - \frac {21 \, {\left (b x^{\frac {1}{3}} + a\right )}^{16} a}{8 \, b^{15}} + \frac {91 \, {\left (b x^{\frac {1}{3}} + a\right )}^{15} a^{2}}{5 \, b^{15}} - \frac {78 \, {\left (b x^{\frac {1}{3}} + a\right )}^{14} a^{3}}{b^{15}} + \frac {231 \, {\left (b x^{\frac {1}{3}} + a\right )}^{13} a^{4}}{b^{15}} - \frac {1001 \, {\left (b x^{\frac {1}{3}} + a\right )}^{12} a^{5}}{2 \, b^{15}} + \frac {819 \, {\left (b x^{\frac {1}{3}} + a\right )}^{11} a^{6}}{b^{15}} - \frac {5148 \, {\left (b x^{\frac {1}{3}} + a\right )}^{10} a^{7}}{5 \, b^{15}} + \frac {1001 \, {\left (b x^{\frac {1}{3}} + a\right )}^{9} a^{8}}{b^{15}} - \frac {3003 \, {\left (b x^{\frac {1}{3}} + a\right )}^{8} a^{9}}{4 \, b^{15}} + \frac {429 \, {\left (b x^{\frac {1}{3}} + a\right )}^{7} a^{10}}{b^{15}} - \frac {182 \, {\left (b x^{\frac {1}{3}} + a\right )}^{6} a^{11}}{b^{15}} + \frac {273 \, {\left (b x^{\frac {1}{3}} + a\right )}^{5} a^{12}}{5 \, b^{15}} - \frac {21 \, {\left (b x^{\frac {1}{3}} + a\right )}^{4} a^{13}}{2 \, b^{15}} + \frac {{\left (b x^{\frac {1}{3}} + a\right )}^{3} a^{14}}{b^{15}} \]
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 \[ \frac {a^2\,x^5}{5}+\frac {3\,b^2\,x^{17/3}}{17}+\frac {3\,a\,b\,x^{16/3}}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 2.02, size = 31, normalized size = 0.91 \[ \frac {a^{2} x^{5}}{5} + \frac {3 a b x^{\frac {16}{3}}}{8} + \frac {3 b^{2} x^{\frac {17}{3}}}{17} \]
Verification of antiderivative is not currently implemented for this CAS.
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