Optimal. Leaf size=18 \[ 1-e^{-6 e^{1+3 x}}+x+\log (x) \]
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Rubi [A]
time = 0.02, 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, 2320, 2225,
45} \begin {gather*} x-e^{-6 e^{3 x+1}}+\log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 45
Rule 2225
Rule 2320
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 \text {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 = 0.02, 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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Maple [A]
time = 0.05, size = 17, normalized size = 0.94
method | result | size |
norman | \(x -{\mathrm e}^{-6 \,{\mathrm e}^{3 x +1}}+\ln \left (x \right )\) | \(16\) |
risch | \(x -{\mathrm e}^{-6 \,{\mathrm e}^{3 x +1}}+\ln \left (x \right )\) | \(16\) |
default | \(x -{\mathrm e}^{-6 \,{\mathrm e}^{3 x +1}}+\ln \left (x \right )\) | \(17\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 15, normalized size = 0.83 \begin {gather*} x - e^{\left (-6 \, e^{\left (3 \, x + 1\right )}\right )} + \log \left (x\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. 41 vs.
\(2 (16) = 32\).
time = 0.31, size = 41, normalized size = 2.28 \begin {gather*} {\left (x e^{\left (3 \, x + 1\right )} + e^{\left (3 \, x + 1\right )} \log \left (x\right ) - 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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Sympy [A]
time = 0.06, size = 15, normalized size = 0.83 \begin {gather*} x + \log {\left (x \right )} - e^{- 6 e^{3 x + 1}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 41 vs.
\(2 (16) = 32\).
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 \left (x\right ) - 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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Mupad [B]
time = 0.45, size = 15, normalized size = 0.83 \begin {gather*} x-{\mathrm {e}}^{-6\,{\mathrm {e}}^{3\,x}\,\mathrm {e}}+\ln \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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