Optimal. Leaf size=19 \[ \frac {a x^2}{2}+\frac {3}{7} b x^{7/3} \]
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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 = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {14}
\begin {gather*} \frac {a x^2}{2}+\frac {3}{7} b x^{7/3} \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 \, dx &=\int \left (a x+b x^{4/3}\right ) \, dx\\ &=\frac {a x^2}{2}+\frac {3}{7} b x^{7/3}\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 19, normalized size = 1.00 \begin {gather*} \frac {1}{14} \left (7 a+6 b \sqrt [3]{x}\right ) x^2 \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.02, size = 14, normalized size = 0.74
method | result | size |
derivativedivides | \(\frac {a \,x^{2}}{2}+\frac {3 b \,x^{\frac {7}{3}}}{7}\) | \(14\) |
default | \(\frac {a \,x^{2}}{2}+\frac {3 b \,x^{\frac {7}{3}}}{7}\) | \(14\) |
trager | \(\frac {\left (x -1\right ) a \left (x +1\right )}{2}+\frac {3 b \,x^{\frac {7}{3}}}{7}\) | \(17\) |
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. 98 vs.
\(2 (13) = 26\).
time = 0.31, size = 98, normalized size = 5.16 \begin {gather*} \frac {3 \, {\left (b x^{\frac {1}{3}} + a\right )}^{7}}{7 \, b^{6}} - \frac {5 \, {\left (b x^{\frac {1}{3}} + a\right )}^{6} a}{2 \, b^{6}} + \frac {6 \, {\left (b x^{\frac {1}{3}} + a\right )}^{5} a^{2}}{b^{6}} - \frac {15 \, {\left (b x^{\frac {1}{3}} + a\right )}^{4} a^{3}}{2 \, b^{6}} + \frac {5 \, {\left (b x^{\frac {1}{3}} + a\right )}^{3} a^{4}}{b^{6}} - \frac {3 \, {\left (b x^{\frac {1}{3}} + a\right )}^{2} a^{5}}{2 \, b^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.34, size = 13, normalized size = 0.68 \begin {gather*} \frac {3}{7} \, b x^{\frac {7}{3}} + \frac {1}{2} \, a x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.56, size = 15, normalized size = 0.79 \begin {gather*} \frac {a x^{2}}{2} + \frac {3 b x^{\frac {7}{3}}}{7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.09, size = 13, normalized size = 0.68 \begin {gather*} \frac {3}{7} \, b x^{\frac {7}{3}} + \frac {1}{2} \, a x^{2} \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^2}{2}+\frac {3\,b\,x^{7/3}}{7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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