Optimal. Leaf size=30 \[ e^{e^{4+x \left (4+\frac {e^x x^2}{3+\frac {3}{4+x}}\right )^2}} \]
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Rubi [F] time = 180.00, 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*} \text {\$Aborted} \end {gather*}
Verification is not applicable to the result.
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Aborted
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Mathematica [A] time = 1.93, size = 49, normalized size = 1.63 \begin {gather*} e^{e^{4+16 x+\frac {e^{2 x} x^5 (4+x)^2}{9 (5+x)^2}+\frac {8 e^x x^3 (4+x)}{3 (5+x)}}} \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.56, size = 205, normalized size = 6.83 \begin {gather*} e^{\left (\frac {144 \, x^{3} + 1476 \, x^{2} + {\left (x^{7} + 8 \, x^{6} + 16 \, x^{5}\right )} e^{\left (2 \, x\right )} + 24 \, {\left (x^{5} + 9 \, x^{4} + 20 \, x^{3}\right )} e^{x} + 9 \, {\left (x^{2} + 10 \, x + 25\right )} e^{\left (\frac {144 \, x^{3} + 1476 \, x^{2} + {\left (x^{7} + 8 \, x^{6} + 16 \, x^{5}\right )} e^{\left (2 \, x\right )} + 24 \, {\left (x^{5} + 9 \, x^{4} + 20 \, x^{3}\right )} e^{x} + 3960 \, x + 900}{9 \, {\left (x^{2} + 10 \, x + 25\right )}}\right )} + 3960 \, x + 900}{9 \, {\left (x^{2} + 10 \, x + 25\right )}} - \frac {144 \, x^{3} + 1476 \, x^{2} + {\left (x^{7} + 8 \, x^{6} + 16 \, x^{5}\right )} e^{\left (2 \, x\right )} + 24 \, {\left (x^{5} + 9 \, x^{4} + 20 \, x^{3}\right )} e^{x} + 3960 \, x + 900}{9 \, {\left (x^{2} + 10 \, x + 25\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 {{\left (144 \, x^{3} + 2160 \, x^{2} + {\left (2 \, x^{8} + 31 \, x^{7} + 179 \, x^{6} + 448 \, x^{5} + 400 \, x^{4}\right )} e^{\left (2 \, x\right )} + 24 \, {\left (x^{6} + 17 \, x^{5} + 108 \, x^{4} + 300 \, x^{3} + 300 \, x^{2}\right )} e^{x} + 10800 \, x + 18000\right )} e^{\left (\frac {144 \, x^{3} + 1476 \, x^{2} + {\left (x^{7} + 8 \, x^{6} + 16 \, x^{5}\right )} e^{\left (2 \, x\right )} + 24 \, {\left (x^{5} + 9 \, x^{4} + 20 \, x^{3}\right )} e^{x} + 3960 \, x + 900}{9 \, {\left (x^{2} + 10 \, x + 25\right )}} + e^{\left (\frac {144 \, x^{3} + 1476 \, x^{2} + {\left (x^{7} + 8 \, x^{6} + 16 \, x^{5}\right )} e^{\left (2 \, x\right )} + 24 \, {\left (x^{5} + 9 \, x^{4} + 20 \, x^{3}\right )} e^{x} + 3960 \, x + 900}{9 \, {\left (x^{2} + 10 \, x + 25\right )}}\right )}\right )}}{9 \, {\left (x^{3} + 15 \, x^{2} + 75 \, x + 125\right )}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.34, size = 72, normalized size = 2.40
method | result | size |
risch | \({\mathrm e}^{{\mathrm e}^{\frac {{\mathrm e}^{2 x} x^{7}+8 \,{\mathrm e}^{2 x} x^{6}+16 x^{5} {\mathrm e}^{2 x}+24 x^{5} {\mathrm e}^{x}+216 \,{\mathrm e}^{x} x^{4}+480 \,{\mathrm e}^{x} x^{3}+144 x^{3}+1476 x^{2}+3960 x +900}{9 \left (5+x \right )^{2}}}}\) | \(72\) |
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*} \frac {1}{9} \, \int \frac {{\left (144 \, x^{3} + 2160 \, x^{2} + {\left (2 \, x^{8} + 31 \, x^{7} + 179 \, x^{6} + 448 \, x^{5} + 400 \, x^{4}\right )} e^{\left (2 \, x\right )} + 24 \, {\left (x^{6} + 17 \, x^{5} + 108 \, x^{4} + 300 \, x^{3} + 300 \, x^{2}\right )} e^{x} + 10800 \, x + 18000\right )} e^{\left (\frac {144 \, x^{3} + 1476 \, x^{2} + {\left (x^{7} + 8 \, x^{6} + 16 \, x^{5}\right )} e^{\left (2 \, x\right )} + 24 \, {\left (x^{5} + 9 \, x^{4} + 20 \, x^{3}\right )} e^{x} + 3960 \, x + 900}{9 \, {\left (x^{2} + 10 \, x + 25\right )}} + e^{\left (\frac {144 \, x^{3} + 1476 \, x^{2} + {\left (x^{7} + 8 \, x^{6} + 16 \, x^{5}\right )} e^{\left (2 \, x\right )} + 24 \, {\left (x^{5} + 9 \, x^{4} + 20 \, x^{3}\right )} e^{x} + 3960 \, x + 900}{9 \, {\left (x^{2} + 10 \, x + 25\right )}}\right )}\right )}}{x^{3} + 15 \, x^{2} + 75 \, x + 125}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.92, size = 184, normalized size = 6.13 \begin {gather*} {\mathrm {e}}^{{\mathrm {e}}^{\frac {16\,x^3}{x^2+10\,x+25}}\,{\mathrm {e}}^{\frac {164\,x^2}{x^2+10\,x+25}}\,{\mathrm {e}}^{\frac {100}{x^2+10\,x+25}}\,{\mathrm {e}}^{\frac {8\,x^5\,{\mathrm {e}}^x}{3\,x^2+30\,x+75}}\,{\mathrm {e}}^{\frac {160\,x^3\,{\mathrm {e}}^x}{3\,x^2+30\,x+75}}\,{\mathrm {e}}^{\frac {x^7\,{\mathrm {e}}^{2\,x}}{9\,x^2+90\,x+225}}\,{\mathrm {e}}^{\frac {8\,x^6\,{\mathrm {e}}^{2\,x}}{9\,x^2+90\,x+225}}\,{\mathrm {e}}^{\frac {16\,x^5\,{\mathrm {e}}^{2\,x}}{9\,x^2+90\,x+225}}\,{\mathrm {e}}^{\frac {440\,x}{x^2+10\,x+25}}\,{\mathrm {e}}^{\frac {24\,x^4\,{\mathrm {e}}^x}{x^2+10\,x+25}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 10.41, size = 65, normalized size = 2.17 \begin {gather*} e^{e^{\frac {144 x^{3} + 1476 x^{2} + 3960 x + \left (24 x^{5} + 216 x^{4} + 480 x^{3}\right ) e^{x} + \left (x^{7} + 8 x^{6} + 16 x^{5}\right ) e^{2 x} + 900}{9 x^{2} + 90 x + 225}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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