Optimal. Leaf size=30 \[ \frac {a^2 x^6}{6}+\frac {1}{5} a b x^{10}+\frac {b^2 x^{14}}{14} \]
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Rubi [A]
time = 0.01, antiderivative size = 30, 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 = {276}
\begin {gather*} \frac {a^2 x^6}{6}+\frac {1}{5} a b x^{10}+\frac {b^2 x^{14}}{14} \end {gather*}
Antiderivative was successfully verified.
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Rule 276
Rubi steps
\begin {align*} \int x^5 \left (a+b x^4\right )^2 \, dx &=\int \left (a^2 x^5+2 a b x^9+b^2 x^{13}\right ) \, dx\\ &=\frac {a^2 x^6}{6}+\frac {1}{5} a b x^{10}+\frac {b^2 x^{14}}{14}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 30, normalized size = 1.00 \begin {gather*} \frac {a^2 x^6}{6}+\frac {1}{5} a b x^{10}+\frac {b^2 x^{14}}{14} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.14, size = 25, normalized size = 0.83
method | result | size |
gosper | \(\frac {1}{6} a^{2} x^{6}+\frac {1}{5} a b \,x^{10}+\frac {1}{14} b^{2} x^{14}\) | \(25\) |
default | \(\frac {1}{6} a^{2} x^{6}+\frac {1}{5} a b \,x^{10}+\frac {1}{14} b^{2} x^{14}\) | \(25\) |
norman | \(\frac {1}{6} a^{2} x^{6}+\frac {1}{5} a b \,x^{10}+\frac {1}{14} b^{2} x^{14}\) | \(25\) |
risch | \(\frac {1}{6} a^{2} x^{6}+\frac {1}{5} a b \,x^{10}+\frac {1}{14} b^{2} x^{14}\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 24, normalized size = 0.80 \begin {gather*} \frac {1}{14} \, b^{2} x^{14} + \frac {1}{5} \, a b x^{10} + \frac {1}{6} \, a^{2} x^{6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 24, normalized size = 0.80 \begin {gather*} \frac {1}{14} \, b^{2} x^{14} + \frac {1}{5} \, a b x^{10} + \frac {1}{6} \, a^{2} x^{6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 24, normalized size = 0.80 \begin {gather*} \frac {a^{2} x^{6}}{6} + \frac {a b x^{10}}{5} + \frac {b^{2} x^{14}}{14} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.79, size = 24, normalized size = 0.80 \begin {gather*} \frac {1}{14} \, b^{2} x^{14} + \frac {1}{5} \, a b x^{10} + \frac {1}{6} \, a^{2} x^{6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 24, normalized size = 0.80 \begin {gather*} \frac {a^2\,x^6}{6}+\frac {a\,b\,x^{10}}{5}+\frac {b^2\,x^{14}}{14} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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