Optimal. Leaf size=28 \[ \frac {e^{e^{4+x^2 \left (e^{e^4}+(4+x)^4\right )}} (-2+x)}{x} \]
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Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(119\) vs. \(2(28)=56\).
time = 0.56, antiderivative size = 119, normalized size of antiderivative = 4.25, 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 {\left (-3 x^7-34 x^6-112 x^5+512 x^3+512 x^2+e^{e^4} \left (2 x^2-x^3\right )\right ) \exp \left (\exp \left (x^6+16 x^5+96 x^4+256 x^3+e^{e^4} x^2+256 x^2+4\right )\right )}{x^2 \left (3 x^5+40 x^4+192 x^3+384 x^2+e^{e^4} x+256 x\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 2326
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\frac {\exp \left (\exp \left (4+256 x^2+e^{e^4} x^2+256 x^3+96 x^4+16 x^5+x^6\right )\right ) \left (512 x^2+512 x^3-112 x^5-34 x^6-3 x^7+e^{e^4} \left (2 x^2-x^3\right )\right )}{x^2 \left (256 x+e^{e^4} x+384 x^2+192 x^3+40 x^4+3 x^5\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.12, size = 43, normalized size = 1.54 \begin {gather*} e^{e^{4+\left (256+e^{e^4}\right ) x^2+256 x^3+96 x^4+16 x^5+x^6}} \left (1-\frac {2}{x}\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.39, size = 42, normalized size = 1.50
method | result | size |
risch | \(\frac {\left (x -2\right ) {\mathrm e}^{{\mathrm e}^{x^{2} {\mathrm e}^{{\mathrm e}^{4}}+x^{6}+16 x^{5}+96 x^{4}+256 x^{3}+256 x^{2}+4}}}{x}\) | \(42\) |
norman | \(\frac {x \,{\mathrm e}^{{\mathrm e}^{x^{2} {\mathrm e}^{{\mathrm e}^{4}}+x^{6}+16 x^{5}+96 x^{4}+256 x^{3}+256 x^{2}+4}}-2 \,{\mathrm e}^{{\mathrm e}^{x^{2} {\mathrm e}^{{\mathrm e}^{4}}+x^{6}+16 x^{5}+96 x^{4}+256 x^{3}+256 x^{2}+4}}}{x}\) | \(78\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.34, size = 41, normalized size = 1.46 \begin {gather*} \frac {{\left (x - 2\right )} e^{\left (e^{\left (x^{6} + 16 \, x^{5} + 96 \, x^{4} + 256 \, x^{3} + x^{2} e^{\left (e^{4}\right )} + 256 \, x^{2} + 4\right )}\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 41, normalized size = 1.46 \begin {gather*} \frac {{\left (x - 2\right )} e^{\left (e^{\left (x^{6} + 16 \, x^{5} + 96 \, x^{4} + 256 \, x^{3} + x^{2} e^{\left (e^{4}\right )} + 256 \, x^{2} + 4\right )}\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.13, size = 41, normalized size = 1.46 \begin {gather*} \frac {\left (x - 2\right ) e^{e^{x^{6} + 16 x^{5} + 96 x^{4} + 256 x^{3} + 256 x^{2} + x^{2} e^{e^{4}} + 4}}}{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 = 2.36, size = 47, normalized size = 1.68 \begin {gather*} \frac {{\mathrm {e}}^{{\mathrm {e}}^{x^6}\,{\mathrm {e}}^4\,{\mathrm {e}}^{x^2\,{\mathrm {e}}^{{\mathrm {e}}^4}}\,{\mathrm {e}}^{16\,x^5}\,{\mathrm {e}}^{96\,x^4}\,{\mathrm {e}}^{256\,x^2}\,{\mathrm {e}}^{256\,x^3}}\,\left (x-2\right )}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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