Optimal. Leaf size=28 \[ \frac {5 e^{e^{e^x}}}{(3-x) \left (e^x-x\right ) x} \]
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Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(100\) vs. \(2(28)=56\).
time = 0.29, antiderivative size = 100, normalized size of antiderivative = 3.57, number of steps
used = 1, number of rules used = 1, integrand size = 124, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.008, Rules used = {2326}
\begin {gather*} \frac {5 e^{e^{e^x}-x} \left (e^{2 x} \left (3 x-x^2\right )-e^x \left (3 x^2-x^3\right )\right )}{x^6-6 x^5+9 x^4-2 e^x \left (x^5-6 x^4+9 x^3\right )+e^{2 x} \left (x^4-6 x^3+9 x^2\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 2326
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {5 e^{e^{e^x}-x} \left (e^{2 x} \left (3 x-x^2\right )-e^x \left (3 x^2-x^3\right )\right )}{9 x^4-6 x^5+x^6+e^{2 x} \left (9 x^2-6 x^3+x^4\right )-2 e^x \left (9 x^3-6 x^4+x^5\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.18, size = 26, normalized size = 0.93 \begin {gather*} -\frac {5 e^{e^{e^x}}}{\left (e^x-x\right ) (-3+x) x} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.26, size = 28, normalized size = 1.00
method | result | size |
risch | \(\frac {5 \,{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x}}}}{x \left (x^{2}-{\mathrm e}^{x} x -3 x +3 \,{\mathrm e}^{x}\right )}\) | \(28\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.34, size = 28, normalized size = 1.00 \begin {gather*} \frac {5 \, e^{\left (e^{\left (e^{x}\right )}\right )}}{x^{3} - 3 \, x^{2} - {\left (x^{2} - 3 \, x\right )} e^{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.39, size = 28, normalized size = 1.00 \begin {gather*} \frac {5 \, e^{\left (e^{\left (e^{x}\right )}\right )}}{x^{3} - 3 \, x^{2} - {\left (x^{2} - 3 \, x\right )} e^{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.15, size = 29, normalized size = 1.04 \begin {gather*} \frac {5 e^{e^{e^{x}}}}{x^{3} - x^{2} e^{x} - 3 x^{2} + 3 x e^{x}} \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 = 0.44, size = 30, normalized size = 1.07 \begin {gather*} -\frac {5\,{\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^x}}}{x^2\,{\mathrm {e}}^x-3\,x\,{\mathrm {e}}^x+3\,x^2-x^3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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