Optimal. Leaf size=17 \[ \frac {1}{5} x^2 \left (-3+256 e^4 x^2\right ) \]
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Rubi [A] time = 0.00, antiderivative size = 18, normalized size of antiderivative = 1.06, number of steps used = 2, number of rules used = 1, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {12} \begin {gather*} \frac {256 e^4 x^4}{5}-\frac {3 x^2}{5} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{5} \int \left (-6 x+1024 e^4 x^3\right ) \, dx\\ &=-\frac {3 x^2}{5}+\frac {256 e^4 x^4}{5}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 20, normalized size = 1.18 \begin {gather*} \frac {2}{5} \left (-\frac {3 x^2}{2}+128 e^4 x^4\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.85, size = 13, normalized size = 0.76 \begin {gather*} \frac {256}{5} \, x^{4} e^{4} - \frac {3}{5} \, x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 13, normalized size = 0.76 \begin {gather*} \frac {256}{5} \, x^{4} e^{4} - \frac {3}{5} \, x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 14, normalized size = 0.82
method | result | size |
risch | \(\frac {256 x^{4} {\mathrm e}^{4}}{5}-\frac {3 x^{2}}{5}\) | \(14\) |
default | \(\frac {256 x^{4} {\mathrm e}^{4}}{5}-\frac {3 x^{2}}{5}\) | \(16\) |
norman | \(\frac {256 x^{4} {\mathrm e}^{4}}{5}-\frac {3 x^{2}}{5}\) | \(16\) |
gosper | \(\frac {\left (256 x^{2} {\mathrm e}^{4}-3\right ) x^{2}}{5}\) | \(17\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.35, size = 13, normalized size = 0.76 \begin {gather*} \frac {256}{5} \, x^{4} e^{4} - \frac {3}{5} \, x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 14, normalized size = 0.82 \begin {gather*} \frac {x^2\,\left (256\,x^2\,{\mathrm {e}}^4-3\right )}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.05, size = 15, normalized size = 0.88 \begin {gather*} \frac {256 x^{4} e^{4}}{5} - \frac {3 x^{2}}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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