Optimal. Leaf size=25 \[ \frac {1}{4} (-5+x)+\frac {e^{5-e^3}}{x^2 \log (4)} \]
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Rubi [A] time = 0.01, antiderivative size = 23, normalized size of antiderivative = 0.92, number of steps used = 3, number of rules used = 2, integrand size = 27, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.074, Rules used = {12, 14} \begin {gather*} \frac {e^{5-e^3}}{x^2 \log (4)}+\frac {x}{4} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{4} \int \frac {x-\frac {8 e^{5-e^3}}{x^2 \log (4)}}{x} \, dx\\ &=\frac {1}{4} \int \left (1-\frac {8 e^{5-e^3}}{x^3 \log (4)}\right ) \, dx\\ &=\frac {x}{4}+\frac {e^{5-e^3}}{x^2 \log (4)}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 23, normalized size = 0.92 \begin {gather*} \frac {x}{4}+\frac {e^{5-e^3}}{x^2 \log (4)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.95, size = 29, normalized size = 1.16 \begin {gather*} \frac {{\left (x^{3} e^{\left (e^{3} - 5\right )} \log \relax (2) + 2\right )} e^{\left (-e^{3} + 5\right )}}{4 \, x^{2} \log \relax (2)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.13, size = 20, normalized size = 0.80 \begin {gather*} \frac {1}{4} \, x + \frac {e^{\left (-e^{3} + 5\right )}}{2 \, x^{2} \log \relax (2)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 21, normalized size = 0.84
method | result | size |
risch | \(\frac {x}{4}+\frac {{\mathrm e}^{-{\mathrm e}^{3}+5}}{2 x^{2} \ln \relax (2)}\) | \(21\) |
default | \(\frac {x}{4}+{\mathrm e}^{-\ln \left (2 x^{2} \ln \relax (2)\right )-{\mathrm e}^{3}+5}\) | \(22\) |
norman | \(\frac {\frac {x^{3}}{4}+\frac {{\mathrm e}^{-{\mathrm e}^{3}} {\mathrm e}^{5}}{2 \ln \relax (2)}}{x^{2}}\) | \(24\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.49, size = 20, normalized size = 0.80 \begin {gather*} \frac {1}{4} \, x + \frac {e^{\left (-e^{3} + 5\right )}}{2 \, x^{2} \log \relax (2)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.18, size = 20, normalized size = 0.80 \begin {gather*} \frac {x}{4}+\frac {{\mathrm {e}}^{5-{\mathrm {e}}^3}}{2\,x^2\,\ln \relax (2)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 27, normalized size = 1.08 \begin {gather*} \frac {x e^{e^{3}} \log {\relax (2 )} + \frac {2 e^{5}}{x^{2}}}{4 e^{e^{3}} \log {\relax (2 )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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