Optimal. Leaf size=32 \[ 2+5 e^{e^{(6+x)^2 \left (\frac {2 e^3}{5}+2 x\right )^2}} (2-x) \]
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Rubi [B] time = 0.86, antiderivative size = 139, normalized size of antiderivative = 4.34, number of steps used = 2, number of rules used = 2, integrand size = 164, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.012, Rules used = {12, 2288} \begin {gather*} \frac {5 \left (-50 x^4-350 x^3+e^6 \left (-x^2-4 x+12\right )+15 e^3 \left (-x^3-6 x^2+4 x+24\right )+1800 x\right ) \exp \left (\exp \left (\frac {4}{25} \left (25 x^4+300 x^3+900 x^2+e^6 \left (x^2+12 x+36\right )+10 e^3 \left (x^3+12 x^2+36 x\right )\right )\right )\right )}{50 x^3+450 x^2+15 e^3 \left (x^2+8 x+12\right )+900 x+e^6 (x+6)} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2288
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{5} \int \exp \left (\exp \left (\frac {1}{25} \left (3600 x^2+1200 x^3+100 x^4+e^6 \left (144+48 x+4 x^2\right )+e^3 \left (1440 x+480 x^2+40 x^3\right )\right )\right )\right ) \left (-25+\exp \left (\frac {1}{25} \left (3600 x^2+1200 x^3+100 x^4+e^6 \left (144+48 x+4 x^2\right )+e^3 \left (1440 x+480 x^2+40 x^3\right )\right )\right ) \left (14400 x-2800 x^3-400 x^4+e^6 \left (96-32 x-8 x^2\right )+e^3 \left (2880+480 x-720 x^2-120 x^3\right )\right )\right ) \, dx\\ &=\frac {5 \exp \left (\exp \left (\frac {4}{25} \left (900 x^2+300 x^3+25 x^4+e^6 \left (36+12 x+x^2\right )+10 e^3 \left (36 x+12 x^2+x^3\right )\right )\right )\right ) \left (1800 x-350 x^3-50 x^4+e^6 \left (12-4 x-x^2\right )+15 e^3 \left (24+4 x-6 x^2-x^3\right )\right )}{900 x+450 x^2+50 x^3+e^6 (6+x)+15 e^3 \left (12+8 x+x^2\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.18, size = 27, normalized size = 0.84 \begin {gather*} -5 e^{e^{\frac {4}{25} (6+x)^2 \left (e^3+5 x\right )^2}} (-2+x) \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.86, size = 51, normalized size = 1.59 \begin {gather*} -5 \, {\left (x - 2\right )} e^{\left (e^{\left (4 \, x^{4} + 48 \, x^{3} + 144 \, x^{2} + \frac {4}{25} \, {\left (x^{2} + 12 \, x + 36\right )} e^{6} + \frac {8}{5} \, {\left (x^{3} + 12 \, x^{2} + 36 \, x\right )} e^{3}\right )}\right )} \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*} \int -\frac {1}{5} \, {\left (8 \, {\left (50 \, x^{4} + 350 \, x^{3} + {\left (x^{2} + 4 \, x - 12\right )} e^{6} + 15 \, {\left (x^{3} + 6 \, x^{2} - 4 \, x - 24\right )} e^{3} - 1800 \, x\right )} e^{\left (4 \, x^{4} + 48 \, x^{3} + 144 \, x^{2} + \frac {4}{25} \, {\left (x^{2} + 12 \, x + 36\right )} e^{6} + \frac {8}{5} \, {\left (x^{3} + 12 \, x^{2} + 36 \, x\right )} e^{3}\right )} + 25\right )} e^{\left (e^{\left (4 \, x^{4} + 48 \, x^{3} + 144 \, x^{2} + \frac {4}{25} \, {\left (x^{2} + 12 \, x + 36\right )} e^{6} + \frac {8}{5} \, {\left (x^{3} + 12 \, x^{2} + 36 \, x\right )} e^{3}\right )}\right )}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.46, size = 30, normalized size = 0.94
method | result | size |
risch | \(\frac {\left (-25 x +50\right ) {\mathrm e}^{{\mathrm e}^{\frac {4 \left (x +6\right )^{2} \left (10 x \,{\mathrm e}^{3}+25 x^{2}+{\mathrm e}^{6}\right )}{25}}}}{5}\) | \(30\) |
norman | \(-5 x \,{\mathrm e}^{{\mathrm e}^{\frac {\left (4 x^{2}+48 x +144\right ) {\mathrm e}^{6}}{25}+\frac {\left (40 x^{3}+480 x^{2}+1440 x \right ) {\mathrm e}^{3}}{25}+4 x^{4}+48 x^{3}+144 x^{2}}}+10 \,{\mathrm e}^{{\mathrm e}^{\frac {\left (4 x^{2}+48 x +144\right ) {\mathrm e}^{6}}{25}+\frac {\left (40 x^{3}+480 x^{2}+1440 x \right ) {\mathrm e}^{3}}{25}+4 x^{4}+48 x^{3}+144 x^{2}}}\) | \(111\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.44, size = 58, normalized size = 1.81 \begin {gather*} -5 \, {\left (x - 2\right )} e^{\left (e^{\left (4 \, x^{4} + \frac {8}{5} \, x^{3} e^{3} + 48 \, x^{3} + \frac {4}{25} \, x^{2} e^{6} + \frac {96}{5} \, x^{2} e^{3} + 144 \, x^{2} + \frac {48}{25} \, x e^{6} + \frac {288}{5} \, x e^{3} + \frac {144}{25} \, e^{6}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.51, size = 66, normalized size = 2.06 \begin {gather*} -5\,{\mathrm {e}}^{{\mathrm {e}}^{\frac {8\,x^3\,{\mathrm {e}}^3}{5}}\,{\mathrm {e}}^{\frac {4\,x^2\,{\mathrm {e}}^6}{25}}\,{\mathrm {e}}^{\frac {96\,x^2\,{\mathrm {e}}^3}{5}}\,{\mathrm {e}}^{\frac {144\,{\mathrm {e}}^6}{25}}\,{\mathrm {e}}^{4\,x^4}\,{\mathrm {e}}^{48\,x^3}\,{\mathrm {e}}^{144\,x^2}\,{\mathrm {e}}^{\frac {48\,x\,{\mathrm {e}}^6}{25}}\,{\mathrm {e}}^{\frac {288\,x\,{\mathrm {e}}^3}{5}}}\,\left (x-2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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