Optimal. Leaf size=20 \[ e^{-20+5 x \log \left (-1-e+e^{e^x+x}\right )} \]
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Rubi [A]
time = 0.38, antiderivative size = 20, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 82, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.012, Rules used = {6838}
\begin {gather*} \frac {\left (e^{x+e^x}-1-e\right )^{5 x}}{e^{20}} \end {gather*}
Antiderivative was successfully verified.
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Rule 6838
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\left (-1-e+e^{e^x+x}\right )^{5 x}}{e^{20}}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.07, size = 20, normalized size = 1.00 \begin {gather*} \frac {\left (-1-e+e^{e^x+x}\right )^{5 x}}{e^{20}} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.19, size = 19, normalized size = 0.95
method | result | size |
risch | \(\left ({\mathrm e}^{{\mathrm e}^{x}+x}-{\mathrm e}-1\right )^{5 x} {\mathrm e}^{-20}\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.37, size = 18, normalized size = 0.90 \begin {gather*} e^{\left (5 \, x \log \left (-e + e^{\left (x + e^{x}\right )} - 1\right ) - 20\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 18, normalized size = 0.90 \begin {gather*} e^{\left (5 \, x \log \left (-e + e^{\left (x + e^{x}\right )} - 1\right ) - 20\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] Timed out
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.60, size = 18, normalized size = 0.90 \begin {gather*} e^{\left (5 \, x \log \left (-e + e^{\left (x + e^{x}\right )} - 1\right ) - 20\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.52, size = 18, normalized size = 0.90 \begin {gather*} {\mathrm {e}}^{-20}\,{\left ({\mathrm {e}}^{x+{\mathrm {e}}^x}-\mathrm {e}-1\right )}^{5\,x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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