Optimal. Leaf size=47 \[ \frac {a^3 x^5}{5}+\frac {9}{16} a^2 b x^{16/3}+\frac {9}{17} a b^2 x^{17/3}+\frac {b^3 x^6}{6} \]
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Rubi [A]
time = 0.02, 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 = {272, 45}
\begin {gather*} \frac {a^3 x^5}{5}+\frac {9}{16} a^2 b x^{16/3}+\frac {9}{17} a b^2 x^{17/3}+\frac {b^3 x^6}{6} \end {gather*}
Antiderivative was successfully verified.
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Rule 45
Rule 272
Rubi steps
\begin {align*} \int \left (a+b \sqrt [3]{x}\right )^3 x^4 \, dx &=3 \text {Subst}\left (\int x^{14} (a+b x)^3 \, dx,x,\sqrt [3]{x}\right )\\ &=3 \text {Subst}\left (\int \left (a^3 x^{14}+3 a^2 b x^{15}+3 a b^2 x^{16}+b^3 x^{17}\right ) \, dx,x,\sqrt [3]{x}\right )\\ &=\frac {a^3 x^5}{5}+\frac {9}{16} a^2 b x^{16/3}+\frac {9}{17} a b^2 x^{17/3}+\frac {b^3 x^6}{6}\\ \end {align*}
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Mathematica [A]
time = 0.02, size = 43, normalized size = 0.91 \begin {gather*} \frac {816 a^3 x^5+2295 a^2 b x^{16/3}+2160 a b^2 x^{17/3}+680 b^3 x^6}{4080} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.19, size = 36, normalized size = 0.77
method | result | size |
derivativedivides | \(\frac {a^{3} x^{5}}{5}+\frac {9 a^{2} b \,x^{\frac {16}{3}}}{16}+\frac {9 a \,b^{2} x^{\frac {17}{3}}}{17}+\frac {b^{3} x^{6}}{6}\) | \(36\) |
default | \(\frac {a^{3} x^{5}}{5}+\frac {9 a^{2} b \,x^{\frac {16}{3}}}{16}+\frac {9 a \,b^{2} x^{\frac {17}{3}}}{17}+\frac {b^{3} x^{6}}{6}\) | \(36\) |
trager | \(\frac {\left (5 b^{3} x^{5}+6 a^{3} x^{4}+5 b^{3} x^{4}+6 a^{3} x^{3}+5 b^{3} x^{3}+6 a^{3} x^{2}+5 b^{3} x^{2}+6 a^{3} x +5 b^{3} x +6 a^{3}+5 b^{3}\right ) \left (x -1\right )}{30}+\frac {9 a^{2} b \,x^{\frac {16}{3}}}{16}+\frac {9 a \,b^{2} x^{\frac {17}{3}}}{17}\) | \(104\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 251 vs.
\(2 (35) = 70\).
time = 0.30, size = 251, normalized size = 5.34 \begin {gather*} \frac {{\left (b x^{\frac {1}{3}} + a\right )}^{18}}{6 \, b^{15}} - \frac {42 \, {\left (b x^{\frac {1}{3}} + a\right )}^{17} a}{17 \, b^{15}} + \frac {273 \, {\left (b x^{\frac {1}{3}} + a\right )}^{16} a^{2}}{16 \, b^{15}} - \frac {364 \, {\left (b x^{\frac {1}{3}} + a\right )}^{15} a^{3}}{5 \, b^{15}} + \frac {429 \, {\left (b x^{\frac {1}{3}} + a\right )}^{14} a^{4}}{2 \, b^{15}} - \frac {462 \, {\left (b x^{\frac {1}{3}} + a\right )}^{13} a^{5}}{b^{15}} + \frac {3003 \, {\left (b x^{\frac {1}{3}} + a\right )}^{12} a^{6}}{4 \, b^{15}} - \frac {936 \, {\left (b x^{\frac {1}{3}} + a\right )}^{11} a^{7}}{b^{15}} + \frac {9009 \, {\left (b x^{\frac {1}{3}} + a\right )}^{10} a^{8}}{10 \, b^{15}} - \frac {2002 \, {\left (b x^{\frac {1}{3}} + a\right )}^{9} a^{9}}{3 \, b^{15}} + \frac {3003 \, {\left (b x^{\frac {1}{3}} + a\right )}^{8} a^{10}}{8 \, b^{15}} - \frac {156 \, {\left (b x^{\frac {1}{3}} + a\right )}^{7} a^{11}}{b^{15}} + \frac {91 \, {\left (b x^{\frac {1}{3}} + a\right )}^{6} a^{12}}{2 \, b^{15}} - \frac {42 \, {\left (b x^{\frac {1}{3}} + a\right )}^{5} a^{13}}{5 \, b^{15}} + \frac {3 \, {\left (b x^{\frac {1}{3}} + a\right )}^{4} a^{14}}{4 \, b^{15}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.34, size = 35, normalized size = 0.74 \begin {gather*} \frac {1}{6} \, b^{3} x^{6} + \frac {9}{17} \, a b^{2} x^{\frac {17}{3}} + \frac {9}{16} \, a^{2} b x^{\frac {16}{3}} + \frac {1}{5} \, a^{3} x^{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 1.08, size = 42, normalized size = 0.89 \begin {gather*} \frac {a^{3} x^{5}}{5} + \frac {9 a^{2} b x^{\frac {16}{3}}}{16} + \frac {9 a b^{2} x^{\frac {17}{3}}}{17} + \frac {b^{3} x^{6}}{6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.73, size = 35, normalized size = 0.74 \begin {gather*} \frac {1}{6} \, b^{3} x^{6} + \frac {9}{17} \, a b^{2} x^{\frac {17}{3}} + \frac {9}{16} \, a^{2} b x^{\frac {16}{3}} + \frac {1}{5} \, a^{3} x^{5} \end {gather*}
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 \begin {gather*} \frac {a^3\,x^5}{5}+\frac {b^3\,x^6}{6}+\frac {9\,a^2\,b\,x^{16/3}}{16}+\frac {9\,a\,b^2\,x^{17/3}}{17} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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