Optimal. Leaf size=24 \[ e^{\frac {e^{2 e^{2 x}+x+\frac {8}{1+x}}}{x}} \]
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Rubi [F] time = 15.50, 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*} \int \frac {e^{2 e^{2 x}+\frac {e^{2 e^{2 x}+x+\frac {8}{1+x}}}{x}+\frac {8}{1+x}} \left (e^x \left (-1-9 x+x^2+x^3\right )+e^{3 x} \left (4 x+8 x^2+4 x^3\right )\right )}{x^2+2 x^3+x^4} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{2 e^{2 x}+\frac {e^{2 e^{2 x}+x+\frac {8}{1+x}}}{x}+\frac {8}{1+x}} \left (e^x \left (-1-9 x+x^2+x^3\right )+e^{3 x} \left (4 x+8 x^2+4 x^3\right )\right )}{x^2 \left (1+2 x+x^2\right )} \, dx\\ &=\int \frac {e^{2 e^{2 x}+\frac {e^{2 e^{2 x}+x+\frac {8}{1+x}}}{x}+\frac {8}{1+x}} \left (e^x \left (-1-9 x+x^2+x^3\right )+e^{3 x} \left (4 x+8 x^2+4 x^3\right )\right )}{x^2 (1+x)^2} \, dx\\ &=\int \left (\frac {4 \exp \left (2 e^{2 x}+\frac {e^{2 e^{2 x}+x+\frac {8}{1+x}}}{x}+3 x+\frac {8}{1+x}\right )}{x}+\frac {\exp \left (2 e^{2 x}+\frac {e^{2 e^{2 x}+x+\frac {8}{1+x}}}{x}+x+\frac {8}{1+x}\right ) \left (-1-9 x+x^2+x^3\right )}{x^2 (1+x)^2}\right ) \, dx\\ &=4 \int \frac {\exp \left (2 e^{2 x}+\frac {e^{2 e^{2 x}+x+\frac {8}{1+x}}}{x}+3 x+\frac {8}{1+x}\right )}{x} \, dx+\int \frac {\exp \left (2 e^{2 x}+\frac {e^{2 e^{2 x}+x+\frac {8}{1+x}}}{x}+x+\frac {8}{1+x}\right ) \left (-1-9 x+x^2+x^3\right )}{x^2 (1+x)^2} \, dx\\ &=4 \int \frac {\exp \left (2 e^{2 x}+\frac {e^{2 e^{2 x}+x+\frac {8}{1+x}}}{x}+3 x+\frac {8}{1+x}\right )}{x} \, dx+\int \left (-\frac {\exp \left (2 e^{2 x}+\frac {e^{2 e^{2 x}+x+\frac {8}{1+x}}}{x}+x+\frac {8}{1+x}\right )}{x^2}-\frac {7 \exp \left (2 e^{2 x}+\frac {e^{2 e^{2 x}+x+\frac {8}{1+x}}}{x}+x+\frac {8}{1+x}\right )}{x}+\frac {8 \exp \left (2 e^{2 x}+\frac {e^{2 e^{2 x}+x+\frac {8}{1+x}}}{x}+x+\frac {8}{1+x}\right )}{(1+x)^2}+\frac {8 \exp \left (2 e^{2 x}+\frac {e^{2 e^{2 x}+x+\frac {8}{1+x}}}{x}+x+\frac {8}{1+x}\right )}{1+x}\right ) \, dx\\ &=4 \int \frac {\exp \left (2 e^{2 x}+\frac {e^{2 e^{2 x}+x+\frac {8}{1+x}}}{x}+3 x+\frac {8}{1+x}\right )}{x} \, dx-7 \int \frac {\exp \left (2 e^{2 x}+\frac {e^{2 e^{2 x}+x+\frac {8}{1+x}}}{x}+x+\frac {8}{1+x}\right )}{x} \, dx+8 \int \frac {\exp \left (2 e^{2 x}+\frac {e^{2 e^{2 x}+x+\frac {8}{1+x}}}{x}+x+\frac {8}{1+x}\right )}{(1+x)^2} \, dx+8 \int \frac {\exp \left (2 e^{2 x}+\frac {e^{2 e^{2 x}+x+\frac {8}{1+x}}}{x}+x+\frac {8}{1+x}\right )}{1+x} \, dx-\int \frac {\exp \left (2 e^{2 x}+\frac {e^{2 e^{2 x}+x+\frac {8}{1+x}}}{x}+x+\frac {8}{1+x}\right )}{x^2} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.20, size = 24, normalized size = 1.00 \begin {gather*} e^{\frac {e^{2 e^{2 x}+x+\frac {8}{1+x}}}{x}} \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.65, size = 74, normalized size = 3.08 \begin {gather*} e^{\left (x + \frac {2 \, {\left (x^{2} + x\right )} e^{\left (2 \, x\right )} + {\left (x + 1\right )} e^{\left (\frac {x^{2} + 2 \, {\left (x + 1\right )} e^{\left (2 \, x\right )} + x + 8}{x + 1}\right )} + 8 \, x}{x^{2} + x} - \frac {x^{2} + 2 \, {\left (x + 1\right )} e^{\left (2 \, x\right )} + x + 8}{x + 1}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 21, normalized size = 0.88 \begin {gather*} e^{\left (\frac {e^{\left (x + \frac {8}{x + 1} + 2 \, e^{\left (2 \, x\right )}\right )}}{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.08, size = 32, normalized size = 1.33
method | result | size |
risch | \({\mathrm e}^{\frac {{\mathrm e}^{\frac {2 x \,{\mathrm e}^{2 x}+x^{2}+2 \,{\mathrm e}^{2 x}+x +8}{x +1}}}{x}}\) | \(32\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.64, size = 21, normalized size = 0.88 \begin {gather*} e^{\left (\frac {e^{\left (x + \frac {8}{x + 1} + 2 \, e^{\left (2 \, x\right )}\right )}}{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.75, size = 22, normalized size = 0.92 \begin {gather*} {\mathrm {e}}^{\frac {{\mathrm {e}}^{2\,{\mathrm {e}}^{2\,x}}\,{\mathrm {e}}^x\,{\mathrm {e}}^{\frac {8}{x+1}}}{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 2.17, size = 20, normalized size = 0.83 \begin {gather*} e^{\frac {e^{x} e^{\frac {8}{x + 1}} e^{2 e^{2 x}}}{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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