Optimal. Leaf size=30 \[ \log \left (6-e^x+e^{-x+\left (1+e^5-x\right ) x+x^2}-x\right ) \]
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Rubi [A] time = 0.05, antiderivative size = 18, normalized size of antiderivative = 0.60, number of steps used = 1, number of rules used = 1, integrand size = 36, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.028, Rules used = {6684} \begin {gather*} \log \left (-x-e^x+e^{e^5 x}+6\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 6684
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\log \left (6-e^x+e^{e^5 x}-x\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.16, size = 16, normalized size = 0.53 \begin {gather*} \log \left (-6+e^x-e^{e^5 x}+x\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.63, size = 22, normalized size = 0.73 \begin {gather*} \log \left (-{\left (x - 6\right )} e^{5} + e^{\left (x e^{5} + 5\right )} - e^{\left (x + 5\right )}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.18, size = 15, normalized size = 0.50 \begin {gather*} \log \left (-x + e^{\left (x e^{5}\right )} - e^{x} + 6\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 14, normalized size = 0.47
method | result | size |
norman | \(\ln \left (-{\mathrm e}^{x \,{\mathrm e}^{5}}+{\mathrm e}^{x}+x -6\right )\) | \(14\) |
derivativedivides | \(\ln \left ({\mathrm e}^{x \,{\mathrm e}^{5}}-{\mathrm e}^{x}-x +6\right )\) | \(16\) |
default | \(\ln \left ({\mathrm e}^{x \,{\mathrm e}^{5}}-{\mathrm e}^{x}-x +6\right )\) | \(16\) |
risch | \(\ln \left ({\mathrm e}^{x \,{\mathrm e}^{5}}-{\mathrm e}^{x}-x +6\right )\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 13, normalized size = 0.43 \begin {gather*} \log \left (x - e^{\left (x e^{5}\right )} + e^{x} - 6\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.13, size = 13, normalized size = 0.43 \begin {gather*} \ln \left (x-{\mathrm {e}}^{x\,{\mathrm {e}}^5}+{\mathrm {e}}^x-6\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.22, size = 14, normalized size = 0.47 \begin {gather*} \log {\left (- x - e^{x} + e^{x e^{5}} + 6 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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