Optimal. Leaf size=43 \[ \frac {a^3 x^2}{2}+\frac {3}{5} a^2 b x^5+\frac {3}{8} a b^2 x^8+\frac {b^3 x^{11}}{11} \]
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Rubi [A]
time = 0.01, antiderivative size = 43, 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 = {276}
\begin {gather*} \frac {a^3 x^2}{2}+\frac {3}{5} a^2 b x^5+\frac {3}{8} a b^2 x^8+\frac {b^3 x^{11}}{11} \end {gather*}
Antiderivative was successfully verified.
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Rule 276
Rubi steps
\begin {align*} \int x \left (a+b x^3\right )^3 \, dx &=\int \left (a^3 x+3 a^2 b x^4+3 a b^2 x^7+b^3 x^{10}\right ) \, dx\\ &=\frac {a^3 x^2}{2}+\frac {3}{5} a^2 b x^5+\frac {3}{8} a b^2 x^8+\frac {b^3 x^{11}}{11}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 43, normalized size = 1.00 \begin {gather*} \frac {a^3 x^2}{2}+\frac {3}{5} a^2 b x^5+\frac {3}{8} a b^2 x^8+\frac {b^3 x^{11}}{11} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.14, size = 36, normalized size = 0.84
method | result | size |
gosper | \(\frac {1}{2} a^{3} x^{2}+\frac {3}{5} a^{2} b \,x^{5}+\frac {3}{8} a \,b^{2} x^{8}+\frac {1}{11} b^{3} x^{11}\) | \(36\) |
default | \(\frac {1}{2} a^{3} x^{2}+\frac {3}{5} a^{2} b \,x^{5}+\frac {3}{8} a \,b^{2} x^{8}+\frac {1}{11} b^{3} x^{11}\) | \(36\) |
norman | \(\frac {1}{2} a^{3} x^{2}+\frac {3}{5} a^{2} b \,x^{5}+\frac {3}{8} a \,b^{2} x^{8}+\frac {1}{11} b^{3} x^{11}\) | \(36\) |
risch | \(\frac {1}{2} a^{3} x^{2}+\frac {3}{5} a^{2} b \,x^{5}+\frac {3}{8} a \,b^{2} x^{8}+\frac {1}{11} b^{3} x^{11}\) | \(36\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 35, normalized size = 0.81 \begin {gather*} \frac {1}{11} \, b^{3} x^{11} + \frac {3}{8} \, a b^{2} x^{8} + \frac {3}{5} \, a^{2} b x^{5} + \frac {1}{2} \, a^{3} x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.33, size = 35, normalized size = 0.81 \begin {gather*} \frac {1}{11} \, b^{3} x^{11} + \frac {3}{8} \, a b^{2} x^{8} + \frac {3}{5} \, a^{2} b x^{5} + \frac {1}{2} \, a^{3} x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 39, normalized size = 0.91 \begin {gather*} \frac {a^{3} x^{2}}{2} + \frac {3 a^{2} b x^{5}}{5} + \frac {3 a b^{2} x^{8}}{8} + \frac {b^{3} x^{11}}{11} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.79, size = 35, normalized size = 0.81 \begin {gather*} \frac {1}{11} \, b^{3} x^{11} + \frac {3}{8} \, a b^{2} x^{8} + \frac {3}{5} \, a^{2} b x^{5} + \frac {1}{2} \, a^{3} x^{2} \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 = 0.81 \begin {gather*} \frac {a^3\,x^2}{2}+\frac {3\,a^2\,b\,x^5}{5}+\frac {3\,a\,b^2\,x^8}{8}+\frac {b^3\,x^{11}}{11} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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