Optimal. Leaf size=19 \[ \frac {3}{5} b x^{5/3}+\frac {a x^2}{2} \]
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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}{5} b x^{5/3} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin {align*} \int \left (a+\frac {b}{\sqrt [3]{x}}\right ) x \, dx &=\int \left (b x^{2/3}+a x\right ) \, dx\\ &=\frac {3}{5} b x^{5/3}+\frac {a x^2}{2}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 19, normalized size = 1.00 \begin {gather*} \frac {3}{5} b x^{5/3}+\frac {a x^2}{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 | \(\frac {3 b \,x^{\frac {5}{3}}}{5}+\frac {a \,x^{2}}{2}\) | \(14\) |
default | \(\frac {3 b \,x^{\frac {5}{3}}}{5}+\frac {a \,x^{2}}{2}\) | \(14\) |
trager | \(\frac {\left (x -1\right ) a \left (x +1\right )}{2}+\frac {3 b \,x^{\frac {5}{3}}}{5}\) | \(17\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 15, normalized size = 0.79 \begin {gather*} \frac {1}{10} \, {\left (5 \, a + \frac {6 \, b}{x^{\frac {1}{3}}}\right )} x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 13, normalized size = 0.68 \begin {gather*} \frac {1}{2} \, a x^{2} + \frac {3}{5} \, b x^{\frac {5}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.07, size = 15, normalized size = 0.79 \begin {gather*} \frac {a x^{2}}{2} + \frac {3 b x^{\frac {5}{3}}}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.56, size = 13, normalized size = 0.68 \begin {gather*} \frac {1}{2} \, a x^{2} + \frac {3}{5} \, b x^{\frac {5}{3}} \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^{5/3}}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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