Optimal. Leaf size=51 \[ \frac {3}{7} a^3 x^{7/3}+\frac {9}{10} a^2 b x^{10/3}+\frac {9}{13} a b^2 x^{13/3}+\frac {3}{16} b^3 x^{16/3} \]
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Rubi [A]
time = 0.01, antiderivative size = 51, 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 = {45}
\begin {gather*} \frac {3}{7} a^3 x^{7/3}+\frac {9}{10} a^2 b x^{10/3}+\frac {9}{13} a b^2 x^{13/3}+\frac {3}{16} b^3 x^{16/3} \end {gather*}
Antiderivative was successfully verified.
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Rule 45
Rubi steps
\begin {align*} \int x^{4/3} (a+b x)^3 \, dx &=\int \left (a^3 x^{4/3}+3 a^2 b x^{7/3}+3 a b^2 x^{10/3}+b^3 x^{13/3}\right ) \, dx\\ &=\frac {3}{7} a^3 x^{7/3}+\frac {9}{10} a^2 b x^{10/3}+\frac {9}{13} a b^2 x^{13/3}+\frac {3}{16} b^3 x^{16/3}\\ \end {align*}
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Mathematica [A]
time = 0.02, size = 39, normalized size = 0.76 \begin {gather*} \frac {3 x^{7/3} \left (1040 a^3+2184 a^2 b x+1680 a b^2 x^2+455 b^3 x^3\right )}{7280} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.12, size = 36, normalized size = 0.71
method | result | size |
gosper | \(\frac {3 x^{\frac {7}{3}} \left (455 b^{3} x^{3}+1680 a \,b^{2} x^{2}+2184 a^{2} b x +1040 a^{3}\right )}{7280}\) | \(36\) |
derivativedivides | \(\frac {3 a^{3} x^{\frac {7}{3}}}{7}+\frac {9 a^{2} b \,x^{\frac {10}{3}}}{10}+\frac {9 a \,b^{2} x^{\frac {13}{3}}}{13}+\frac {3 b^{3} x^{\frac {16}{3}}}{16}\) | \(36\) |
default | \(\frac {3 a^{3} x^{\frac {7}{3}}}{7}+\frac {9 a^{2} b \,x^{\frac {10}{3}}}{10}+\frac {9 a \,b^{2} x^{\frac {13}{3}}}{13}+\frac {3 b^{3} x^{\frac {16}{3}}}{16}\) | \(36\) |
trager | \(\frac {3 x^{\frac {7}{3}} \left (455 b^{3} x^{3}+1680 a \,b^{2} x^{2}+2184 a^{2} b x +1040 a^{3}\right )}{7280}\) | \(36\) |
risch | \(\frac {3 x^{\frac {7}{3}} \left (455 b^{3} x^{3}+1680 a \,b^{2} x^{2}+2184 a^{2} b x +1040 a^{3}\right )}{7280}\) | \(36\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 35, normalized size = 0.69 \begin {gather*} \frac {3}{16} \, b^{3} x^{\frac {16}{3}} + \frac {9}{13} \, a b^{2} x^{\frac {13}{3}} + \frac {9}{10} \, a^{2} b x^{\frac {10}{3}} + \frac {3}{7} \, a^{3} x^{\frac {7}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.76, size = 40, normalized size = 0.78 \begin {gather*} \frac {3}{7280} \, {\left (455 \, b^{3} x^{5} + 1680 \, a b^{2} x^{4} + 2184 \, a^{2} b x^{3} + 1040 \, a^{3} x^{2}\right )} x^{\frac {1}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.47, size = 49, normalized size = 0.96 \begin {gather*} \frac {3 a^{3} x^{\frac {7}{3}}}{7} + \frac {9 a^{2} b x^{\frac {10}{3}}}{10} + \frac {9 a b^{2} x^{\frac {13}{3}}}{13} + \frac {3 b^{3} x^{\frac {16}{3}}}{16} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.75, size = 35, normalized size = 0.69 \begin {gather*} \frac {3}{16} \, b^{3} x^{\frac {16}{3}} + \frac {9}{13} \, a b^{2} x^{\frac {13}{3}} + \frac {9}{10} \, a^{2} b x^{\frac {10}{3}} + \frac {3}{7} \, a^{3} x^{\frac {7}{3}} \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 = 0.69 \begin {gather*} \frac {3\,a^3\,x^{7/3}}{7}+\frac {3\,b^3\,x^{16/3}}{16}+\frac {9\,a^2\,b\,x^{10/3}}{10}+\frac {9\,a\,b^2\,x^{13/3}}{13} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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