Optimal. Leaf size=29 \[ \frac {e^{-e^x+5 \left (1+x+\frac {1}{4} (-1-\log (3))\right )} \log (4)}{x} \]
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Rubi [A]
time = 0.42, antiderivative size = 49, normalized size of antiderivative = 1.69, number of steps
used = 5, number of rules used = 4, integrand size = 41, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.098, Rules used = {2306, 12, 6873,
2326} \begin {gather*} \frac {e^{\frac {1}{4} \left (20 x-4 e^x+15\right )} \left (5 x-e^x x\right ) \log (4)}{3 \sqrt [4]{3} \left (5-e^x\right ) x^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2306
Rule 2326
Rule 6873
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{\frac {1}{4} \left (15-4 e^x+20 x\right )} \left (-e^x x \log (4)+(-1+5 x) \log (4)\right )}{3 \sqrt [4]{3} x^2} \, dx\\ &=\frac {\int \frac {e^{\frac {1}{4} \left (15-4 e^x+20 x\right )} \left (-e^x x \log (4)+(-1+5 x) \log (4)\right )}{x^2} \, dx}{3 \sqrt [4]{3}}\\ &=\frac {\int \frac {e^{\frac {1}{4} \left (15-4 e^x+20 x\right )} \left (-1+5 x-e^x x\right ) \log (4)}{x^2} \, dx}{3 \sqrt [4]{3}}\\ &=\frac {\log (4) \int \frac {e^{\frac {1}{4} \left (15-4 e^x+20 x\right )} \left (-1+5 x-e^x x\right )}{x^2} \, dx}{3 \sqrt [4]{3}}\\ &=\frac {e^{\frac {1}{4} \left (15-4 e^x+20 x\right )} \left (5 x-e^x x\right ) \log (4)}{3 \sqrt [4]{3} \left (5-e^x\right ) x^2}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.03, size = 28, normalized size = 0.97 \begin {gather*} \frac {e^{\frac {15}{4}-e^x+5 x} \log (4)}{3 \sqrt [4]{3} x} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.09, size = 21, normalized size = 0.72
method | result | size |
risch | \(\frac {2 \ln \left (2\right ) 3^{\frac {3}{4}} {\mathrm e}^{-{\mathrm e}^{x}+\frac {15}{4}+5 x}}{9 x}\) | \(21\) |
norman | \(\frac {2 \ln \left (2\right ) {\mathrm e}^{-{\mathrm e}^{x}-\frac {5 \ln \left (3\right )}{4}+5 x +\frac {15}{4}}}{x}\) | \(22\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.56, size = 20, normalized size = 0.69 \begin {gather*} \frac {2 \cdot 3^{\frac {3}{4}} e^{\left (5 \, x - e^{x} + \frac {15}{4}\right )} \log \left (2\right )}{9 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.40, size = 21, normalized size = 0.72 \begin {gather*} \frac {2 \, e^{\left (5 \, x - e^{x} - \frac {5}{4} \, \log \left (3\right ) + \frac {15}{4}\right )} \log \left (2\right )}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.14, size = 24, normalized size = 0.83 \begin {gather*} \frac {2 \cdot 3^{\frac {3}{4}} e^{5 x - e^{x} + \frac {15}{4}} \log {\left (2 \right )}}{9 x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F(-2)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: TypeError} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.10, size = 21, normalized size = 0.72 \begin {gather*} \frac {2\,3^{3/4}\,{\mathrm {e}}^{5\,x}\,{\mathrm {e}}^{15/4}\,{\mathrm {e}}^{-{\mathrm {e}}^x}\,\ln \left (2\right )}{9\,x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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