Optimal. Leaf size=20 \[ -e^{e^x} \left (16+\frac {x}{4}\right )+10 x^2 \]
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Rubi [A] time = 0.02, antiderivative size = 18, normalized size of antiderivative = 0.90, number of steps used = 3, number of rules used = 2, integrand size = 25, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.080, Rules used = {12, 2288} \begin {gather*} 10 x^2-\frac {1}{4} e^{e^x} (x+64) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2288
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{4} \int \left (e^{e^x} \left (-1+e^x (-64-x)\right )+80 x\right ) \, dx\\ &=10 x^2+\frac {1}{4} \int e^{e^x} \left (-1+e^x (-64-x)\right ) \, dx\\ &=10 x^2-\frac {1}{4} e^{e^x} (64+x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.02, size = 18, normalized size = 0.90 \begin {gather*} 10 x^2-\frac {1}{4} e^{e^x} (64+x) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.59, size = 14, normalized size = 0.70 \begin {gather*} 10 \, x^{2} - \frac {1}{4} \, {\left (x + 64\right )} e^{\left (e^{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.53, size = 27, normalized size = 1.35 \begin {gather*} 10 \, x^{2} - \frac {1}{4} \, {\left (x e^{\left (x + e^{x}\right )} + 64 \, e^{\left (x + e^{x}\right )}\right )} e^{\left (-x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 17, normalized size = 0.85
method | result | size |
risch | \(\frac {\left (-x -64\right ) {\mathrm e}^{{\mathrm e}^{x}}}{4}+10 x^{2}\) | \(17\) |
default | \(10 x^{2}-\frac {x \,{\mathrm e}^{{\mathrm e}^{x}}}{4}-16 \,{\mathrm e}^{{\mathrm e}^{x}}\) | \(18\) |
norman | \(10 x^{2}-\frac {x \,{\mathrm e}^{{\mathrm e}^{x}}}{4}-16 \,{\mathrm e}^{{\mathrm e}^{x}}\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} 10 \, x^{2} - \frac {1}{4} \, x e^{\left (e^{x}\right )} - \frac {1}{4} \, {\rm Ei}\left (e^{x}\right ) - 16 \, e^{\left (e^{x}\right )} + \frac {1}{4} \, \int e^{\left (e^{x}\right )}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.06, size = 17, normalized size = 0.85 \begin {gather*} 10\,x^2-\frac {x\,{\mathrm {e}}^{{\mathrm {e}}^x}}{4}-16\,{\mathrm {e}}^{{\mathrm {e}}^x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.14, size = 15, normalized size = 0.75 \begin {gather*} 10 x^{2} + \frac {\left (- x - 64\right ) e^{e^{x}}}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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