Optimal. Leaf size=14 \[ \frac {e^{3 e^3 (-3+x)}}{x^2} \]
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Rubi [A] time = 0.04, antiderivative size = 16, normalized size of antiderivative = 1.14, number of steps used = 1, number of rules used = 1, integrand size = 23, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.043, Rules used = {2197} \begin {gather*} \frac {e^{-3 e^3 (3-x)}}{x^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 2197
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {e^{-3 e^3 (3-x)}}{x^2}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 14, normalized size = 1.00 \begin {gather*} \frac {e^{3 e^3 (-3+x)}}{x^2} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.42, size = 12, normalized size = 0.86 \begin {gather*} \frac {e^{\left (3 \, {\left (x - 3\right )} e^{3}\right )}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.33, size = 15, normalized size = 1.07 \begin {gather*} \frac {e^{\left (3 \, x e^{3} - 9 \, e^{3}\right )}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.16, size = 13, normalized size = 0.93
method | result | size |
gosper | \(\frac {{\mathrm e}^{3 \,{\mathrm e}^{3} \left (x -3\right )}}{x^{2}}\) | \(13\) |
risch | \(\frac {{\mathrm e}^{3 \,{\mathrm e}^{3} \left (x -3\right )}}{x^{2}}\) | \(13\) |
norman | \(\frac {{\mathrm e}^{\left (3 x -9\right ) {\mathrm e}^{3}}}{x^{2}}\) | \(14\) |
derivativedivides | \(\frac {{\mathrm e}^{3 x \,{\mathrm e}^{3}-9 \,{\mathrm e}^{3}}}{x^{2}}\) | \(16\) |
default | \(\frac {{\mathrm e}^{3 x \,{\mathrm e}^{3}-9 \,{\mathrm e}^{3}}}{x^{2}}\) | \(16\) |
meijerg | \(-9 \,{\mathrm e}^{6-9 \,{\mathrm e}^{3}} \left (\frac {{\mathrm e}^{-3}}{3 x}-2-\ln \relax (x )-\ln \relax (3)-i \pi -\frac {{\mathrm e}^{-3} \left (6 x \,{\mathrm e}^{3}+2\right )}{6 x}+\frac {{\mathrm e}^{3 x \,{\mathrm e}^{3}-3}}{3 x}+\ln \left (-3 x \,{\mathrm e}^{3}\right )+\expIntegralEi \left (1, -3 x \,{\mathrm e}^{3}\right )\right )-18 \,{\mathrm e}^{6-9 \,{\mathrm e}^{3}} \left (-\frac {{\mathrm e}^{-6}}{18 x^{2}}-\frac {{\mathrm e}^{-3}}{3 x}+\frac {3}{4}+\frac {\ln \relax (x )}{2}+\frac {\ln \relax (3)}{2}+\frac {i \pi }{2}+\frac {{\mathrm e}^{-6} \left (81 x^{2} {\mathrm e}^{6}+36 x \,{\mathrm e}^{3}+6\right )}{108 x^{2}}-\frac {{\mathrm e}^{-6+3 x \,{\mathrm e}^{3}} \left (9 x \,{\mathrm e}^{3}+3\right )}{54 x^{2}}-\frac {\ln \left (-3 x \,{\mathrm e}^{3}\right )}{2}-\frac {\expIntegralEi \left (1, -3 x \,{\mathrm e}^{3}\right )}{2}\right )\) | \(167\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [C] time = 0.71, size = 33, normalized size = 2.36 \begin {gather*} 9 \, e^{\left (-9 \, e^{3} + 6\right )} \Gamma \left (-1, -3 \, x e^{3}\right ) + 18 \, e^{\left (-9 \, e^{3} + 6\right )} \Gamma \left (-2, -3 \, x e^{3}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.09, size = 15, normalized size = 1.07 \begin {gather*} \frac {{\mathrm {e}}^{-9\,{\mathrm {e}}^3}\,{\mathrm {e}}^{3\,x\,{\mathrm {e}}^3}}{x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 12, normalized size = 0.86 \begin {gather*} \frac {e^{\left (3 x - 9\right ) e^{3}}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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