Optimal. Leaf size=29 \[ 2+\frac {2 e^{e^4}}{3 (5+x) \left (-e^{e^e}+2 x\right )} \]
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Rubi [A] time = 0.09, antiderivative size = 33, normalized size of antiderivative = 1.14, number of steps used = 3, number of rules used = 3, integrand size = 80, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.038, Rules used = {1680, 12, 261} \begin {gather*} -\frac {2 e^{e^4}}{3 \left (-2 x^2+\left (e^{e^e}-10\right ) x+5 e^{e^e}\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 261
Rule 1680
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\operatorname {Subst}\left (\int -\frac {512 e^{e^4} x}{3 \left (100+20 e^{e^e}+e^{2 e^e}-16 x^2\right )^2} \, dx,x,\frac {1}{48} \left (120-12 e^{e^e}\right )+x\right )\\ &=-\left (\frac {1}{3} \left (512 e^{e^4}\right ) \operatorname {Subst}\left (\int \frac {x}{\left (100+20 e^{e^e}+e^{2 e^e}-16 x^2\right )^2} \, dx,x,\frac {1}{48} \left (120-12 e^{e^e}\right )+x\right )\right )\\ &=-\frac {2 e^{e^4}}{3 \left (5 e^{e^e}-\left (10-e^{e^e}\right ) x-2 x^2\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.03, size = 25, normalized size = 0.86 \begin {gather*} -\frac {2 e^{e^4}}{3 \left (e^{e^e}-2 x\right ) (5+x)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.81, size = 33, normalized size = 1.14 \begin {gather*} -\frac {2 \, e^{\left (2 \, e^{4}\right )}}{3 \, {\left ({\left (x + 5\right )} e^{\left (e^{4} + e^{e}\right )} - 2 \, {\left (x^{2} + 5 \, x\right )} e^{\left (e^{4}\right )}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [F(-2)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: NotImplementedError} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.16, size = 21, normalized size = 0.72
method | result | size |
norman | \(-\frac {2 \,{\mathrm e}^{{\mathrm e}^{4}}}{3 \left (5+x \right ) \left (-2 x +{\mathrm e}^{{\mathrm e}^{{\mathrm e}}}\right )}\) | \(21\) |
gosper | \(-\frac {2 \,{\mathrm e}^{{\mathrm e}^{4}}}{3 \left ({\mathrm e}^{{\mathrm e}^{{\mathrm e}}} x -2 x^{2}+5 \,{\mathrm e}^{{\mathrm e}^{{\mathrm e}}}-10 x \right )}\) | \(29\) |
risch | \(-\frac {2 \,{\mathrm e}^{{\mathrm e}^{4}}}{3 \left ({\mathrm e}^{{\mathrm e}^{{\mathrm e}}} x -2 x^{2}+5 \,{\mathrm e}^{{\mathrm e}^{{\mathrm e}}}-10 x \right )}\) | \(29\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 28, normalized size = 0.97 \begin {gather*} \frac {2 \, e^{\left (e^{4}\right )}}{3 \, {\left (2 \, x^{2} - x {\left (e^{\left (e^{e}\right )} - 10\right )} - 5 \, e^{\left (e^{e}\right )}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.28, size = 86, normalized size = 2.97 \begin {gather*} \frac {4\,\left ({\mathrm {e}}^{{\mathrm {e}}^4+2\,{\mathrm {e}}^{\mathrm {e}}}+100\,{\mathrm {e}}^{{\mathrm {e}}^4}+20\,{\mathrm {e}}^{{\mathrm {e}}^4+{\mathrm {e}}^{\mathrm {e}}}\right )}{3\,{\left ({\mathrm {e}}^{{\mathrm {e}}^{\mathrm {e}}}+10\right )}^3\,\left (2\,x-{\mathrm {e}}^{{\mathrm {e}}^{\mathrm {e}}}\right )}-\frac {2\,\left ({\mathrm {e}}^{{\mathrm {e}}^4+2\,{\mathrm {e}}^{\mathrm {e}}}+100\,{\mathrm {e}}^{{\mathrm {e}}^4}+20\,{\mathrm {e}}^{{\mathrm {e}}^4+{\mathrm {e}}^{\mathrm {e}}}\right )}{3\,{\left ({\mathrm {e}}^{{\mathrm {e}}^{\mathrm {e}}}+10\right )}^3\,\left (x+5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.55, size = 31, normalized size = 1.07 \begin {gather*} \frac {2 e^{e^{4}}}{6 x^{2} + x \left (30 - 3 e^{e^{e}}\right ) - 15 e^{e^{e}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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