Optimal. Leaf size=19 \[ \frac {a x^4}{4}+\frac {3}{13} b x^{13/3} \]
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Rubi [A]
time = 0.00, antiderivative size = 19, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {14}
\begin {gather*} \frac {a x^4}{4}+\frac {3}{13} b x^{13/3} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin {align*} \int \left (a+b \sqrt [3]{x}\right ) x^3 \, dx &=\int \left (a x^3+b x^{10/3}\right ) \, dx\\ &=\frac {a x^4}{4}+\frac {3}{13} b x^{13/3}\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 19, normalized size = 1.00 \begin {gather*} \frac {1}{52} \left (13 a+12 b \sqrt [3]{x}\right ) x^4 \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.03, size = 14, normalized size = 0.74
method | result | size |
derivativedivides | \(\frac {a \,x^{4}}{4}+\frac {3 b \,x^{\frac {13}{3}}}{13}\) | \(14\) |
default | \(\frac {a \,x^{4}}{4}+\frac {3 b \,x^{\frac {13}{3}}}{13}\) | \(14\) |
trager | \(\frac {a \left (x^{3}+x^{2}+x +1\right ) \left (x -1\right )}{4}+\frac {3 b \,x^{\frac {13}{3}}}{13}\) | \(23\) |
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. 200 vs.
\(2 (13) = 26\).
time = 0.30, size = 200, normalized size = 10.53 \begin {gather*} \frac {3 \, {\left (b x^{\frac {1}{3}} + a\right )}^{13}}{13 \, b^{12}} - \frac {11 \, {\left (b x^{\frac {1}{3}} + a\right )}^{12} a}{4 \, b^{12}} + \frac {15 \, {\left (b x^{\frac {1}{3}} + a\right )}^{11} a^{2}}{b^{12}} - \frac {99 \, {\left (b x^{\frac {1}{3}} + a\right )}^{10} a^{3}}{2 \, b^{12}} + \frac {110 \, {\left (b x^{\frac {1}{3}} + a\right )}^{9} a^{4}}{b^{12}} - \frac {693 \, {\left (b x^{\frac {1}{3}} + a\right )}^{8} a^{5}}{4 \, b^{12}} + \frac {198 \, {\left (b x^{\frac {1}{3}} + a\right )}^{7} a^{6}}{b^{12}} - \frac {165 \, {\left (b x^{\frac {1}{3}} + a\right )}^{6} a^{7}}{b^{12}} + \frac {99 \, {\left (b x^{\frac {1}{3}} + a\right )}^{5} a^{8}}{b^{12}} - \frac {165 \, {\left (b x^{\frac {1}{3}} + a\right )}^{4} a^{9}}{4 \, b^{12}} + \frac {11 \, {\left (b x^{\frac {1}{3}} + a\right )}^{3} a^{10}}{b^{12}} - \frac {3 \, {\left (b x^{\frac {1}{3}} + a\right )}^{2} a^{11}}{2 \, b^{12}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 13, normalized size = 0.68 \begin {gather*} \frac {3}{13} \, b x^{\frac {13}{3}} + \frac {1}{4} \, a x^{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.69, size = 15, normalized size = 0.79 \begin {gather*} \frac {a x^{4}}{4} + \frac {3 b x^{\frac {13}{3}}}{13} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.35, size = 13, normalized size = 0.68 \begin {gather*} \frac {3}{13} \, b x^{\frac {13}{3}} + \frac {1}{4} \, a x^{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 13, normalized size = 0.68 \begin {gather*} \frac {a\,x^4}{4}+\frac {3\,b\,x^{13/3}}{13} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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