Optimal. Leaf size=17 \[ 25 e^{6+e^8+e^{1-x}} x \]
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Rubi [A] time = 0.02, antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 28, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.071, Rules used = {12, 2288} \begin {gather*} 25 e^{e^{1-x}+6+e^8} x \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2288
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=25 \int e^{6+e^8+e^{1-x}} \left (1-e^{1-x} x\right ) \, dx\\ &=25 e^{6+e^8+e^{1-x}} x\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.14, size = 17, normalized size = 1.00 \begin {gather*} 25 e^{6+e^8+e^{1-x}} x \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.84, size = 17, normalized size = 1.00 \begin {gather*} x e^{\left (e^{8} + e^{\left (-x + 1\right )} + 2 \, \log \relax (5) + 6\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.22, size = 14, normalized size = 0.82 \begin {gather*} 25 \, x e^{\left (e^{8} + e^{\left (-x + 1\right )} + 6\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 15, normalized size = 0.88
method | result | size |
risch | \(25 x \,{\mathrm e}^{{\mathrm e}^{1-x}+6+{\mathrm e}^{8}}\) | \(15\) |
norman | \(x \,{\mathrm e}^{{\mathrm e}^{1-x}+2 \ln \relax (5)+{\mathrm e}^{8}+6}\) | \(20\) |
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*} 25 \, {\left (x e^{\left (e^{8} + 7\right )} + e^{\left (e^{8} + 7\right )}\right )} e^{\left (-x + e^{\left (-x + 1\right )}\right )} - 25 \, {\rm Ei}\left (e^{\left (-x + 1\right )}\right ) e^{\left (e^{8} + 6\right )} + 25 \, \int {\left (x e^{\left (e^{8} + 8\right )} + e^{\left (e^{8} + 8\right )}\right )} e^{\left (-2 \, x + e^{\left (-x + 1\right )}\right )}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.08, size = 16, normalized size = 0.94 \begin {gather*} 25\,x\,{\mathrm {e}}^6\,{\mathrm {e}}^{{\mathrm {e}}^{-x}\,\mathrm {e}}\,{\mathrm {e}}^{{\mathrm {e}}^8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.14, size = 14, normalized size = 0.82 \begin {gather*} 25 x e^{e^{1 - x} + 6 + e^{8}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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