Optimal. Leaf size=21 \[ \frac {3}{5} a x^{5/3}+\frac {3}{8} b x^{8/3} \]
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Rubi [A]
time = 0.00, antiderivative size = 21, 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 = {45}
\begin {gather*} \frac {3}{5} a x^{5/3}+\frac {3}{8} b x^{8/3} \end {gather*}
Antiderivative was successfully verified.
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Rule 45
Rubi steps
\begin {align*} \int x^{2/3} (a+b x) \, dx &=\int \left (a x^{2/3}+b x^{5/3}\right ) \, dx\\ &=\frac {3}{5} a x^{5/3}+\frac {3}{8} b x^{8/3}\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 17, normalized size = 0.81 \begin {gather*} \frac {3}{40} x^{5/3} (8 a+5 b x) \end {gather*}
Antiderivative was successfully verified.
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Mathics [A]
time = 1.64, size = 13, normalized size = 0.62 \begin {gather*} \frac {3 x^{\frac {5}{3}} \left (8 a+5 b x\right )}{40} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.05, size = 14, normalized size = 0.67
method | result | size |
gosper | \(\frac {3 x^{\frac {5}{3}} \left (5 b x +8 a \right )}{40}\) | \(14\) |
derivativedivides | \(\frac {3 a \,x^{\frac {5}{3}}}{5}+\frac {3 b \,x^{\frac {8}{3}}}{8}\) | \(14\) |
default | \(\frac {3 a \,x^{\frac {5}{3}}}{5}+\frac {3 b \,x^{\frac {8}{3}}}{8}\) | \(14\) |
trager | \(\frac {3 x^{\frac {5}{3}} \left (5 b x +8 a \right )}{40}\) | \(14\) |
risch | \(\frac {3 x^{\frac {5}{3}} \left (5 b x +8 a \right )}{40}\) | \(14\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 13, normalized size = 0.62 \begin {gather*} \frac {3}{8} \, b x^{\frac {8}{3}} + \frac {3}{5} \, a x^{\frac {5}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.30, size = 16, normalized size = 0.76 \begin {gather*} \frac {3}{40} \, {\left (5 \, b x^{2} + 8 \, a x\right )} x^{\frac {2}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.14, size = 19, normalized size = 0.90 \begin {gather*} \frac {3 a x^{\frac {5}{3}}}{5} + \frac {3 b x^{\frac {8}{3}}}{8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.00, size = 31, normalized size = 1.48 \begin {gather*} \frac {3 b \left (x^{\frac {1}{3}}\right )^{2} x^{2}}{2\cdot 4}+\frac {3}{5} a \left (x^{\frac {1}{3}}\right )^{2} x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.02, size = 13, normalized size = 0.62 \begin {gather*} \frac {3\,x^{5/3}\,\left (8\,a+5\,b\,x\right )}{40} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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