Optimal. Leaf size=13 \[ 5+x-e^{e^{143+x}} x \]
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Rubi [A] time = 0.02, antiderivative size = 12, normalized size of antiderivative = 0.92, number of steps used = 3, number of rules used = 2, integrand size = 26, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {12, 2288} \begin {gather*} x-e^{e^{x+143}} x \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2288
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \left (e+e^{e^{143+x}} \left (-e-e^{144+x} x\right )\right ) \, dx}{e}\\ &=x+\frac {\int e^{e^{143+x}} \left (-e-e^{144+x} x\right ) \, dx}{e}\\ &=x-e^{e^{143+x}} x\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.03, size = 12, normalized size = 0.92 \begin {gather*} x-e^{e^{143+x}} x \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.21, size = 10, normalized size = 0.77 \begin {gather*} -x e^{\left (e^{\left (x + 143\right )}\right )} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 18, normalized size = 1.38 \begin {gather*} {\left (x e - x e^{\left (e^{\left (x + 143\right )} + 1\right )}\right )} e^{\left (-1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.12, size = 11, normalized size = 0.85
method | result | size |
risch | \(-x \,{\mathrm e}^{{\mathrm e}^{143+x}}+x\) | \(11\) |
norman | \(x -x \,{\mathrm e}^{{\mathrm e}^{144} {\mathrm e}^{x} {\mathrm e}^{-1}}\) | \(18\) |
default | \({\mathrm e}^{-1} \left (-x \,{\mathrm e} \,{\mathrm e}^{{\mathrm e}^{144} {\mathrm e}^{x} {\mathrm e}^{-1}}+x \,{\mathrm e}\right )\) | \(28\) |
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*} {\left (x e - {\rm Ei}\left (e^{\left (x + 143\right )}\right ) e - x e^{\left (e^{\left (x + 143\right )} + 1\right )} + \int e^{\left (e^{\left (x + 143\right )} + 1\right )}\,{d x}\right )} e^{\left (-1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.07, size = 11, normalized size = 0.85 \begin {gather*} -x\,\left ({\mathrm {e}}^{{\mathrm {e}}^{143}\,{\mathrm {e}}^x}-1\right ) \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 = 0.77 \begin {gather*} - x e^{e^{143} e^{x}} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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