Optimal. Leaf size=27 \[ \frac {e^{1+e^{3+x}} (4+x (4+x))^2}{x^4 (2+x)^2} \]
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Rubi [A] time = 0.09, antiderivative size = 25, normalized size of antiderivative = 0.93, number of steps used = 1, number of rules used = 1, integrand size = 41, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.024, Rules used = {2288} \begin {gather*} \frac {e^{e^{x+3}+1} \left (x^3+4 x^2+4 x\right )}{x^5} \end {gather*}
Antiderivative was successfully verified.
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Rule 2288
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {e^{1+e^{3+x}} \left (4 x+4 x^2+x^3\right )}{x^5}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.25, size = 18, normalized size = 0.67 \begin {gather*} \frac {e^{1+e^{3+x}} (2+x)^2}{x^4} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.71, size = 19, normalized size = 0.70 \begin {gather*} \frac {{\left (x^{2} + 4 \, x + 4\right )} e^{\left (e^{\left (x + 3\right )} + 1\right )}}{x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.14, size = 44, normalized size = 1.63 \begin {gather*} \frac {{\left (x^{2} e^{\left (x + e^{\left (x + 3\right )} + 4\right )} + 4 \, x e^{\left (x + e^{\left (x + 3\right )} + 4\right )} + 4 \, e^{\left (x + e^{\left (x + 3\right )} + 4\right )}\right )} e^{\left (-x - 3\right )}}{x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 20, normalized size = 0.74
method | result | size |
risch | \(\frac {\left (x^{2}+4 x +4\right ) {\mathrm e}^{{\mathrm e}^{3+x}+1}}{x^{4}}\) | \(20\) |
norman | \(\frac {x^{2} {\mathrm e}^{{\mathrm e}^{3+x}+1}+4 x \,{\mathrm e}^{{\mathrm e}^{3+x}+1}+4 \,{\mathrm e}^{{\mathrm e}^{3+x}+1}}{x^{4}}\) | \(36\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.55, size = 25, normalized size = 0.93 \begin {gather*} \frac {{\left (x^{2} e + 4 \, x e + 4 \, e\right )} e^{\left (e^{\left (x + 3\right )}\right )}}{x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.60, size = 17, normalized size = 0.63 \begin {gather*} \frac {{\mathrm {e}}^{{\mathrm {e}}^3\,{\mathrm {e}}^x+1}\,{\left (x+2\right )}^2}{x^4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.15, size = 19, normalized size = 0.70 \begin {gather*} \frac {\left (x^{2} + 4 x + 4\right ) e^{e^{x + 3} + 1}}{x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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