Optimal. Leaf size=43 \[ \frac {a^3 x^{12}}{12}+\frac {1}{5} a^2 b x^{15}+\frac {1}{6} a b^2 x^{18}+\frac {b^3 x^{21}}{21} \]
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Rubi [A]
time = 0.02, antiderivative size = 43, normalized size of antiderivative = 1.00, number of steps
used = 3, number of rules used = 2, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {272, 45}
\begin {gather*} \frac {a^3 x^{12}}{12}+\frac {1}{5} a^2 b x^{15}+\frac {1}{6} a b^2 x^{18}+\frac {b^3 x^{21}}{21} \end {gather*}
Antiderivative was successfully verified.
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Rule 45
Rule 272
Rubi steps
\begin {align*} \int x^{11} \left (a+b x^3\right )^3 \, dx &=\frac {1}{3} \text {Subst}\left (\int x^3 (a+b x)^3 \, dx,x,x^3\right )\\ &=\frac {1}{3} \text {Subst}\left (\int \left (a^3 x^3+3 a^2 b x^4+3 a b^2 x^5+b^3 x^6\right ) \, dx,x,x^3\right )\\ &=\frac {a^3 x^{12}}{12}+\frac {1}{5} a^2 b x^{15}+\frac {1}{6} a b^2 x^{18}+\frac {b^3 x^{21}}{21}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 43, normalized size = 1.00 \begin {gather*} \frac {a^3 x^{12}}{12}+\frac {1}{5} a^2 b x^{15}+\frac {1}{6} a b^2 x^{18}+\frac {b^3 x^{21}}{21} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.13, size = 36, normalized size = 0.84
method | result | size |
gosper | \(\frac {1}{12} a^{3} x^{12}+\frac {1}{5} a^{2} b \,x^{15}+\frac {1}{6} a \,b^{2} x^{18}+\frac {1}{21} b^{3} x^{21}\) | \(36\) |
default | \(\frac {1}{12} a^{3} x^{12}+\frac {1}{5} a^{2} b \,x^{15}+\frac {1}{6} a \,b^{2} x^{18}+\frac {1}{21} b^{3} x^{21}\) | \(36\) |
norman | \(\frac {1}{12} a^{3} x^{12}+\frac {1}{5} a^{2} b \,x^{15}+\frac {1}{6} a \,b^{2} x^{18}+\frac {1}{21} b^{3} x^{21}\) | \(36\) |
risch | \(\frac {1}{12} a^{3} x^{12}+\frac {1}{5} a^{2} b \,x^{15}+\frac {1}{6} a \,b^{2} x^{18}+\frac {1}{21} b^{3} x^{21}\) | \(36\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.31, size = 35, normalized size = 0.81 \begin {gather*} \frac {1}{21} \, b^{3} x^{21} + \frac {1}{6} \, a b^{2} x^{18} + \frac {1}{5} \, a^{2} b x^{15} + \frac {1}{12} \, a^{3} x^{12} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.34, size = 35, normalized size = 0.81 \begin {gather*} \frac {1}{21} \, b^{3} x^{21} + \frac {1}{6} \, a b^{2} x^{18} + \frac {1}{5} \, a^{2} b x^{15} + \frac {1}{12} \, a^{3} x^{12} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 36, normalized size = 0.84 \begin {gather*} \frac {a^{3} x^{12}}{12} + \frac {a^{2} b x^{15}}{5} + \frac {a b^{2} x^{18}}{6} + \frac {b^{3} x^{21}}{21} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 2.32, size = 35, normalized size = 0.81 \begin {gather*} \frac {1}{21} \, b^{3} x^{21} + \frac {1}{6} \, a b^{2} x^{18} + \frac {1}{5} \, a^{2} b x^{15} + \frac {1}{12} \, a^{3} x^{12} \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^{12}}{12}+\frac {a^2\,b\,x^{15}}{5}+\frac {a\,b^2\,x^{18}}{6}+\frac {b^3\,x^{21}}{21} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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