Optimal. Leaf size=26 \[ \frac {1}{3} e^{1+e^x} (1-x) \left (e^x-e^9 x\right ) \]
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Rubi [F]
time = 0.37, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps
used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {}
\begin {gather*} \int \frac {1}{3} e^{e^x} \left (e^{1+2 x} (1-x)+e^{10} (-1+2 x)+e^x \left (-e x+e^{10} \left (-x+x^2\right )\right )\right ) \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{3} \int e^{e^x} \left (e^{1+2 x} (1-x)+e^{10} (-1+2 x)+e^x \left (-e x+e^{10} \left (-x+x^2\right )\right )\right ) \, dx\\ &=\frac {1}{3} \int \left (-e^{1+e^x+2 x} (-1+x)+e^{10+e^x} (-1+2 x)+e^{1+e^x+x} x \left (-1-e^9+e^9 x\right )\right ) \, dx\\ &=-\left (\frac {1}{3} \int e^{1+e^x+2 x} (-1+x) \, dx\right )+\frac {1}{3} \int e^{10+e^x} (-1+2 x) \, dx+\frac {1}{3} \int e^{1+e^x+x} x \left (-1-e^9+e^9 x\right ) \, dx\\ &=\frac {1}{3} \int \left (-e^{10+e^x}+2 e^{10+e^x} x\right ) \, dx-\frac {1}{3} \int \left (-e^{1+e^x+2 x}+e^{1+e^x+2 x} x\right ) \, dx+\frac {1}{3} \int \left (-e^{1+e^x+x} \left (1+e^9\right ) x+e^{10+e^x+x} x^2\right ) \, dx\\ &=-\left (\frac {1}{3} \int e^{10+e^x} \, dx\right )+\frac {1}{3} \int e^{1+e^x+2 x} \, dx-\frac {1}{3} \int e^{1+e^x+2 x} x \, dx+\frac {1}{3} \int e^{10+e^x+x} x^2 \, dx+\frac {2}{3} \int e^{10+e^x} x \, dx+\frac {1}{3} \left (-1-e^9\right ) \int e^{1+e^x+x} x \, dx\\ &=-\left (\frac {1}{3} \int e^{1+e^x+2 x} x \, dx\right )+\frac {1}{3} \int e^{10+e^x+x} x^2 \, dx-\frac {1}{3} \text {Subst}\left (\int \frac {e^{10+x}}{x} \, dx,x,e^x\right )+\frac {1}{3} \text {Subst}\left (\int e^{1+x} x \, dx,x,e^x\right )+\frac {2}{3} \int e^{10+e^x} x \, dx+\frac {1}{3} \left (-1-e^9\right ) \int e^{1+e^x+x} x \, dx\\ &=\frac {1}{3} e^{1+e^x+x}-\frac {e^{10} \text {Ei}\left (e^x\right )}{3}-\frac {1}{3} \int e^{1+e^x+2 x} x \, dx+\frac {1}{3} \int e^{10+e^x+x} x^2 \, dx-\frac {1}{3} \text {Subst}\left (\int e^{1+x} \, dx,x,e^x\right )+\frac {2}{3} \int e^{10+e^x} x \, dx+\frac {1}{3} \left (-1-e^9\right ) \int e^{1+e^x+x} x \, dx\\ &=-\frac {1}{3} e^{1+e^x}+\frac {1}{3} e^{1+e^x+x}-\frac {e^{10} \text {Ei}\left (e^x\right )}{3}-\frac {1}{3} \int e^{1+e^x+2 x} x \, dx+\frac {1}{3} \int e^{10+e^x+x} x^2 \, dx+\frac {2}{3} \int e^{10+e^x} x \, dx+\frac {1}{3} \left (-1-e^9\right ) \int e^{1+e^x+x} x \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.06, size = 25, normalized size = 0.96 \begin {gather*} \frac {1}{3} e^{1+e^x} (-1+x) \left (-e^x+e^9 x\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.54, size = 29, normalized size = 1.12
method | result | size |
risch | \(\frac {\left ({\mathrm e}^{10} x^{2}-x \,{\mathrm e}^{10}-x \,{\mathrm e}^{x +1}+{\mathrm e}^{x +1}\right ) {\mathrm e}^{{\mathrm e}^{x}}}{3}\) | \(29\) |
norman | \(\frac {{\mathrm e} \,{\mathrm e}^{x} {\mathrm e}^{{\mathrm e}^{x}}}{3}+\frac {{\mathrm e} \,{\mathrm e}^{9} x^{2} {\mathrm e}^{{\mathrm e}^{x}}}{3}-\frac {{\mathrm e}^{{\mathrm e}^{x}} x \,{\mathrm e} \,{\mathrm e}^{x}}{3}-\frac {{\mathrm e}^{{\mathrm e}^{x}} {\mathrm e} \,{\mathrm e}^{9} x}{3}\) | \(43\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.39, size = 25, normalized size = 0.96 \begin {gather*} \frac {1}{3} \, {\left ({\left (x^{2} - x\right )} e^{10} - {\left (x - 1\right )} e^{\left (x + 1\right )}\right )} e^{\left (e^{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.13, size = 32, normalized size = 1.23 \begin {gather*} \frac {\left (x^{2} e^{10} - e x e^{x} - x e^{10} + e e^{x}\right ) e^{e^{x}}}{3} \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. 45 vs.
\(2 (19) = 38\).
time = 0.41, size = 45, normalized size = 1.73 \begin {gather*} \frac {1}{3} \, {\left (x^{2} e^{\left (x + e^{x} + 10\right )} - x e^{\left (2 \, x + e^{x} + 1\right )} - x e^{\left (x + e^{x} + 10\right )} + e^{\left (2 \, x + e^{x} + 1\right )}\right )} e^{\left (-x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.08, size = 18, normalized size = 0.69 \begin {gather*} -\frac {{\mathrm {e}}^{{\mathrm {e}}^x+1}\,\left ({\mathrm {e}}^x-x\,{\mathrm {e}}^9\right )\,\left (x-1\right )}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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