Optimal. Leaf size=18 \[ 1-e^{-6 e^{1+3 x}}+x+\log (x) \]
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Rubi [A] time = 0.03, antiderivative size = 17, normalized size of antiderivative = 0.94, number of steps used = 6, number of rules used = 4, integrand size = 26, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {14, 2282, 2194, 43} \begin {gather*} x-e^{-6 e^{3 x+1}}+\log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 43
Rule 2194
Rule 2282
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (18 e^{1-6 e^{1+3 x}+3 x}+\frac {1+x}{x}\right ) \, dx\\ &=18 \int e^{1-6 e^{1+3 x}+3 x} \, dx+\int \frac {1+x}{x} \, dx\\ &=6 \operatorname {Subst}\left (\int e^{1-6 e x} \, dx,x,e^{3 x}\right )+\int \left (1+\frac {1}{x}\right ) \, dx\\ &=-e^{-6 e^{1+3 x}}+x+\log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.03, size = 17, normalized size = 0.94 \begin {gather*} -e^{-6 e^{1+3 x}}+x+\log (x) \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.72, size = 41, normalized size = 2.28 \begin {gather*} {\left (x e^{\left (3 \, x + 1\right )} + e^{\left (3 \, x + 1\right )} \log \relax (x) - e^{\left (3 \, x - 6 \, e^{\left (3 \, x + 1\right )} + 1\right )}\right )} e^{\left (-3 \, x - 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.43, size = 41, normalized size = 2.28 \begin {gather*} {\left (x e^{\left (3 \, x + 1\right )} + e^{\left (3 \, x + 1\right )} \log \relax (x) - e^{\left (3 \, x - 6 \, e^{\left (3 \, x + 1\right )} + 1\right )}\right )} e^{\left (-3 \, x - 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 16, normalized size = 0.89
method | result | size |
norman | \(x -{\mathrm e}^{-6 \,{\mathrm e}^{3 x +1}}+\ln \relax (x )\) | \(16\) |
risch | \(x -{\mathrm e}^{-6 \,{\mathrm e}^{3 x +1}}+\ln \relax (x )\) | \(16\) |
default | \(x -{\mathrm e}^{-6 \,{\mathrm e}^{3 x +1}}+\ln \relax (x )\) | \(17\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.37, size = 15, normalized size = 0.83 \begin {gather*} x - e^{\left (-6 \, e^{\left (3 \, x + 1\right )}\right )} + \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.45, size = 15, normalized size = 0.83 \begin {gather*} x-{\mathrm {e}}^{-6\,{\mathrm {e}}^{3\,x}\,\mathrm {e}}+\ln \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.14, size = 15, normalized size = 0.83 \begin {gather*} x + \log {\relax (x )} - e^{- 6 e^{3 x + 1}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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