Optimal. Leaf size=22 \[ -3+e^3+x-e^{e^{2 x}} x^3-\log (3) \]
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Rubi [A] time = 0.02, antiderivative size = 14, normalized size of antiderivative = 0.64, number of steps used = 2, number of rules used = 1, integrand size = 26, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.038, Rules used = {2288} \begin {gather*} x-e^{e^{2 x}} x^3 \end {gather*}
Antiderivative was successfully verified.
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Rule 2288
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=x+\int e^{e^{2 x}} \left (-3 x^2-2 e^{2 x} x^3\right ) \, dx\\ &=x-e^{e^{2 x}} x^3\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 14, normalized size = 0.64 \begin {gather*} x-e^{e^{2 x}} x^3 \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.55, size = 12, normalized size = 0.55 \begin {gather*} -x^{3} e^{\left (e^{\left (2 \, x\right )}\right )} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.12, size = 12, normalized size = 0.55 \begin {gather*} -x^{3} e^{\left (e^{\left (2 \, x\right )}\right )} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 13, normalized size = 0.59
method | result | size |
default | \(x -x^{3} {\mathrm e}^{{\mathrm e}^{2 x}}\) | \(13\) |
norman | \(x -x^{3} {\mathrm e}^{{\mathrm e}^{2 x}}\) | \(13\) |
risch | \(x -x^{3} {\mathrm e}^{{\mathrm e}^{2 x}}\) | \(13\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.38, size = 12, normalized size = 0.55 \begin {gather*} -x^{3} e^{\left (e^{\left (2 \, x\right )}\right )} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.03, size = 12, normalized size = 0.55 \begin {gather*} x-x^3\,{\mathrm {e}}^{{\mathrm {e}}^{2\,x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.14, size = 10, normalized size = 0.45 \begin {gather*} - x^{3} e^{e^{2 x}} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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