Optimal. Leaf size=17 \[ 4 \left (-5+e^{e^{4-x}}\right )-4 x \]
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Rubi [A]
time = 0.01, antiderivative size = 15, normalized size of antiderivative = 0.88, number of steps
used = 3, number of rules used = 2, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {2320, 2225}
\begin {gather*} 4 e^{e^{4-x}}-4 x \end {gather*}
Antiderivative was successfully verified.
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Rule 2225
Rule 2320
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-4 x-4 \int e^{4+e^{4-x}-x} \, dx\\ &=-4 x+4 \text {Subst}\left (\int e^{4+e^4 x} \, dx,x,e^{-x}\right )\\ &=4 e^{e^{4-x}}-4 x\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.04, size = 15, normalized size = 0.88 \begin {gather*} 4 e^{e^{4-x}}-4 x \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.09, size = 14, normalized size = 0.82
method | result | size |
default | \(-4 x +4 \,{\mathrm e}^{{\mathrm e}^{-x +4}}\) | \(14\) |
norman | \(-4 x +4 \,{\mathrm e}^{{\mathrm e}^{-x +4}}\) | \(14\) |
risch | \(-4 x +4 \,{\mathrm e}^{{\mathrm e}^{-x +4}}\) | \(14\) |
derivativedivides | \(4 \ln \left ({\mathrm e}^{-x +4}\right )+4 \,{\mathrm e}^{{\mathrm e}^{-x +4}}\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 13, normalized size = 0.76 \begin {gather*} -4 \, x + 4 \, e^{\left (e^{\left (-x + 4\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 29 vs.
\(2 (14) = 28\).
time = 0.30, size = 29, normalized size = 1.71 \begin {gather*} -4 \, {\left (x e^{\left (-x + 4\right )} - e^{\left (-x + e^{\left (-x + 4\right )} + 4\right )}\right )} e^{\left (x - 4\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 10, normalized size = 0.59 \begin {gather*} - 4 x + 4 e^{e^{4 - x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 13, normalized size = 0.76 \begin {gather*} -4 \, x + 4 \, e^{\left (e^{\left (-x + 4\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.09, size = 13, normalized size = 0.76 \begin {gather*} 4\,{\mathrm {e}}^{{\mathrm {e}}^{4-x}}-4\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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