Optimal. Leaf size=24 \[ 6+\frac {4 e^{2 e^x-2 i \pi }}{x \log ^2(5)} \]
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Rubi [A]
time = 0.03, antiderivative size = 22, normalized size of antiderivative = 0.92, number of steps
used = 2, number of rules used = 2, integrand size = 29, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.069, Rules used = {12, 2326}
\begin {gather*} \frac {4 e^{2 e^x-2 i \pi }}{x \log ^2(5)} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2326
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \frac {e^{2 e^x-2 i \pi } \left (-4+8 e^x x\right )}{x^2} \, dx}{\log ^2(5)}\\ &=\frac {4 e^{2 e^x-2 i \pi }}{x \log ^2(5)}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 16, normalized size = 0.67 \begin {gather*} \frac {4 e^{2 e^x}}{x \log ^2(5)} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.07, size = 15, normalized size = 0.62
method | result | size |
risch | \(\frac {4 \,{\mathrm e}^{2 \,{\mathrm e}^{x}}}{x \ln \left (5\right )^{2}}\) | \(15\) |
norman | \(\frac {4 \,{\mathrm e}^{2 \,{\mathrm e}^{x}}}{x \ln \left (5\right )^{2}}\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 14, normalized size = 0.58 \begin {gather*} \frac {4 \, e^{\left (2 \, e^{x}\right )}}{x \log \left (5\right )^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.30, size = 18, normalized size = 0.75 \begin {gather*} \frac {4 \, e^{\left (2 \, e^{x} - 2 \, \log \left (-\log \left (5\right )\right )\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.05, size = 14, normalized size = 0.58 \begin {gather*} \frac {4 e^{2 e^{x}}}{x \log {\left (5 \right )}^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 14, normalized size = 0.58 \begin {gather*} \frac {4 \, e^{\left (2 \, e^{x}\right )}}{x \log \left (5\right )^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.32, size = 14, normalized size = 0.58 \begin {gather*} \frac {4\,{\mathrm {e}}^{2\,{\mathrm {e}}^x}}{x\,{\ln \left (5\right )}^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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