Optimal. Leaf size=20 \[ 5 e^{-5+e^{1+x+e^5 x}-2 x} x \]
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Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(62\) vs. \(2(20)=40\).
time = 0.11, antiderivative size = 62, normalized size of antiderivative = 3.10, number of steps
used = 2, number of rules used = 2, integrand size = 42, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.048, Rules used = {12, 2326}
\begin {gather*} \frac {5 e^{-2 x+e^{e^5 x+x+1}-5} \left (2 x-\left (1+e^5\right ) e^{e^5 x+x+1} x\right )}{2-\left (1+e^5\right ) e^{e^5 x+x+1}} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2326
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=5 \int e^{-5+e^{1+x+e^5 x}-2 x} \left (1-2 x+e^{1+x+e^5 x} \left (x+e^5 x\right )\right ) \, dx\\ &=\frac {5 e^{-5+e^{1+x+e^5 x}-2 x} \left (2 x-e^{1+x+e^5 x} \left (1+e^5\right ) x\right )}{2-e^{1+x+e^5 x} \left (1+e^5\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.09, size = 20, normalized size = 1.00 \begin {gather*} 5 e^{-5+e^{1+x+e^5 x}-2 x} x \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.14, size = 18, normalized size = 0.90
method | result | size |
risch | \(5 x \,{\mathrm e}^{{\mathrm e}^{x \,{\mathrm e}^{5}+x +1}-2 x -5}\) | \(18\) |
norman | \(x \,{\mathrm e}^{{\mathrm e}^{x \,{\mathrm e}^{5}+x +1}+\ln \left (5\right )-2 x -5}\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.34, size = 17, normalized size = 0.85 \begin {gather*} 5 \, x e^{\left (-2 \, x + e^{\left (x e^{5} + x + 1\right )} - 5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.45, size = 18, normalized size = 0.90 \begin {gather*} x e^{\left (-2 \, x + e^{\left (x e^{5} + x + 1\right )} + \log \left (5\right ) - 5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.11, size = 19, normalized size = 0.95 \begin {gather*} 5 x e^{- 2 x + e^{x + x e^{5} + 1} - 5} \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 = 0.76, size = 20, normalized size = 1.00 \begin {gather*} 5\,x\,{\mathrm {e}}^{-2\,x}\,{\mathrm {e}}^{-5}\,{\mathrm {e}}^{\mathrm {e}\,{\mathrm {e}}^{x\,{\mathrm {e}}^5}\,{\mathrm {e}}^x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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