Optimal. Leaf size=30 \[ \frac {a^2 x^2}{2}+\frac {1}{3} a b x^6+\frac {b^2 x^{10}}{10} \]
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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 = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {276}
\begin {gather*} \frac {a^2 x^2}{2}+\frac {1}{3} a b x^6+\frac {b^2 x^{10}}{10} \end {gather*}
Antiderivative was successfully verified.
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Rule 276
Rubi steps
\begin {align*} \int x \left (a+b x^4\right )^2 \, dx &=\int \left (a^2 x+2 a b x^5+b^2 x^9\right ) \, dx\\ &=\frac {a^2 x^2}{2}+\frac {1}{3} a b x^6+\frac {b^2 x^{10}}{10}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 30, normalized size = 1.00 \begin {gather*} \frac {a^2 x^2}{2}+\frac {1}{3} a b x^6+\frac {b^2 x^{10}}{10} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.15, size = 25, normalized size = 0.83
method | result | size |
gosper | \(\frac {1}{2} a^{2} x^{2}+\frac {1}{3} a b \,x^{6}+\frac {1}{10} b^{2} x^{10}\) | \(25\) |
default | \(\frac {1}{2} a^{2} x^{2}+\frac {1}{3} a b \,x^{6}+\frac {1}{10} b^{2} x^{10}\) | \(25\) |
norman | \(\frac {1}{2} a^{2} x^{2}+\frac {1}{3} a b \,x^{6}+\frac {1}{10} b^{2} x^{10}\) | \(25\) |
risch | \(\frac {1}{2} a^{2} x^{2}+\frac {1}{3} a b \,x^{6}+\frac {1}{10} b^{2} x^{10}\) | \(25\) |
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}{10} \, b^{2} x^{10} + \frac {1}{3} \, a b x^{6} + \frac {1}{2} \, a^{2} x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.34, size = 24, normalized size = 0.80 \begin {gather*} \frac {1}{10} \, b^{2} x^{10} + \frac {1}{3} \, a b x^{6} + \frac {1}{2} \, a^{2} x^{2} \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^{2}}{2} + \frac {a b x^{6}}{3} + \frac {b^{2} x^{10}}{10} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.61, size = 24, normalized size = 0.80 \begin {gather*} \frac {1}{10} \, b^{2} x^{10} + \frac {1}{3} \, a b x^{6} + \frac {1}{2} \, a^{2} x^{2} \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^2}{2}+\frac {a\,b\,x^6}{3}+\frac {b^2\,x^{10}}{10} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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