Optimal. Leaf size=28 \[ 1+\frac {3}{\log \left (e^{e^{40} \left (1+\left (2+\frac {e^x}{5}\right ) x\right )}+x\right )} \]
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Rubi [A]
time = 0.39, antiderivative size = 31, normalized size of antiderivative = 1.11, number of steps
used = 1, number of rules used = 1, integrand size = 103, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.010, Rules used = {6818}
\begin {gather*} \frac {3}{\log \left (x+e^{\frac {1}{5} \left (e^{x+40} x+5 e^{40} (2 x+1)\right )}\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 6818
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {3}{\log \left (e^{\frac {1}{5} \left (e^{40+x} x+5 e^{40} (1+2 x)\right )}+x\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.20, size = 29, normalized size = 1.04 \begin {gather*} \frac {3}{\log \left (e^{e^{40}+2 e^{40} x+\frac {1}{5} e^{40+x} x}+x\right )} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.48, size = 24, normalized size = 0.86
method | result | size |
risch | \(\frac {3}{\ln \left ({\mathrm e}^{\frac {x \,{\mathrm e}^{40+x}}{5}+2 \,{\mathrm e}^{40} x +{\mathrm e}^{40}}+x \right )}\) | \(24\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.34, size = 23, normalized size = 0.82 \begin {gather*} \frac {3}{\log \left (x + e^{\left (2 \, x e^{40} + \frac {1}{5} \, x e^{\left (x + 40\right )} + e^{40}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 24, normalized size = 0.86 \begin {gather*} \frac {3}{\log \left (x + e^{\left ({\left (2 \, x + 1\right )} e^{40} + \frac {1}{5} \, x e^{\left (x + 40\right )}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.49, size = 24, normalized size = 0.86 \begin {gather*} \frac {3}{\log {\left (x + e^{\frac {x e^{40} e^{x}}{5} + \left (2 x + 1\right ) e^{40}} \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 4.23, size = 25, normalized size = 0.89 \begin {gather*} \frac {3}{\ln \left (x+{\mathrm {e}}^{\frac {x\,{\mathrm {e}}^{40}\,{\mathrm {e}}^x}{5}}\,{\mathrm {e}}^{2\,x\,{\mathrm {e}}^{40}}\,{\mathrm {e}}^{{\mathrm {e}}^{40}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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