Optimal. Leaf size=31 \[ e^{e^{2 e^2 x-8 e^{-2 x} \left (x-\frac {5}{1+2 x}\right )^2}} \]
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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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Rubi steps
Aborted
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Mathematica [B] time = 1.66, size = 64, normalized size = 2.06 \begin {gather*} e^{e^{\frac {e^{-2 x} \left (-200+2 \left (40+e^{2+2 x}\right ) x+8 \left (19+e^{2+2 x}\right ) x^2+8 \left (-4+e^{2+2 x}\right ) x^3-32 x^4\right )}{(1+2 x)^2}}} \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.90, size = 234, normalized size = 7.55 \begin {gather*} e^{\left (2 \, x - \frac {{\left (8 \, {\left (4 \, x^{4} + 4 \, x^{3} - 19 \, x^{2} - 10 \, x + 25\right )} e^{2} - {\left (4 \, x^{2} + 4 \, x + 1\right )} e^{\left (2 \, x - \frac {2 \, {\left (4 \, {\left (4 \, x^{4} + 4 \, x^{3} - 19 \, x^{2} - 10 \, x + 25\right )} e^{2} - {\left (4 \, x^{3} + 4 \, x^{2} + x\right )} e^{\left (2 \, x + 4\right )}\right )} e^{\left (-2 \, x - 2\right )}}{4 \, x^{2} + 4 \, x + 1} + 2\right )} + 2 \, {\left (4 \, x^{3} + 4 \, x^{2} - {\left (4 \, x^{3} + 4 \, x^{2} + x\right )} e^{2} + x\right )} e^{\left (2 \, x + 2\right )}\right )} e^{\left (-2 \, x - 2\right )}}{4 \, x^{2} + 4 \, x + 1} + \frac {2 \, {\left (4 \, {\left (4 \, x^{4} + 4 \, x^{3} - 19 \, x^{2} - 10 \, x + 25\right )} e^{2} - {\left (4 \, x^{3} + 4 \, x^{2} + x\right )} e^{\left (2 \, x + 4\right )}\right )} e^{\left (-2 \, x - 2\right )}}{4 \, x^{2} + 4 \, x + 1}\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 {2 \, {\left (64 \, x^{5} + 32 \, x^{4} - 368 \, x^{3} - 360 \, x^{2} + {\left (8 \, x^{3} + 12 \, x^{2} + 6 \, x + 1\right )} e^{\left (2 \, x + 2\right )} + 392 \, x + 640\right )} e^{\left (-2 \, x - \frac {2 \, {\left (16 \, x^{4} + 16 \, x^{3} - 76 \, x^{2} - {\left (4 \, x^{3} + 4 \, x^{2} + x\right )} e^{\left (2 \, x + 2\right )} - 40 \, x + 100\right )} e^{\left (-2 \, x\right )}}{4 \, x^{2} + 4 \, x + 1} + e^{\left (-\frac {2 \, {\left (16 \, x^{4} + 16 \, x^{3} - 76 \, x^{2} - {\left (4 \, x^{3} + 4 \, x^{2} + x\right )} e^{\left (2 \, x + 2\right )} - 40 \, x + 100\right )} e^{\left (-2 \, x\right )}}{4 \, x^{2} + 4 \, x + 1}\right )}\right )}}{8 \, x^{3} + 12 \, x^{2} + 6 \, x + 1}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.32, size = 67, normalized size = 2.16
method | result | size |
risch | \({\mathrm e}^{{\mathrm e}^{-\frac {2 \left (-4 x^{3} {\mathrm e}^{2 x +2}+16 x^{4}-4 x^{2} {\mathrm e}^{2 x +2}+16 x^{3}-x \,{\mathrm e}^{2 x +2}-76 x^{2}-40 x +100\right ) {\mathrm e}^{-2 x}}{\left (2 x +1\right )^{2}}}}\) | \(67\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [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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mupad [B] time = 1.83, size = 165, normalized size = 5.32 \begin {gather*} {\mathrm {e}}^{{\mathrm {e}}^{\frac {80\,x\,{\mathrm {e}}^{-2\,x}}{4\,x^2+4\,x+1}}\,{\mathrm {e}}^{\frac {2\,x\,{\mathrm {e}}^2}{4\,x^2+4\,x+1}}\,{\mathrm {e}}^{-\frac {32\,x^3\,{\mathrm {e}}^{-2\,x}}{4\,x^2+4\,x+1}}\,{\mathrm {e}}^{-\frac {32\,x^4\,{\mathrm {e}}^{-2\,x}}{4\,x^2+4\,x+1}}\,{\mathrm {e}}^{\frac {152\,x^2\,{\mathrm {e}}^{-2\,x}}{4\,x^2+4\,x+1}}\,{\mathrm {e}}^{-\frac {200\,{\mathrm {e}}^{-2\,x}}{4\,x^2+4\,x+1}}\,{\mathrm {e}}^{\frac {8\,x^2\,{\mathrm {e}}^2}{4\,x^2+4\,x+1}}\,{\mathrm {e}}^{\frac {8\,x^3\,{\mathrm {e}}^2}{4\,x^2+4\,x+1}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 3.82, size = 60, normalized size = 1.94 \begin {gather*} e^{e^{\frac {2 \left (- 16 x^{4} - 16 x^{3} + 76 x^{2} + 40 x + \left (4 x^{3} + 4 x^{2} + x\right ) e^{2} e^{2 x} - 100\right ) e^{- 2 x}}{4 x^{2} + 4 x + 1}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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