Optimal. Leaf size=11 \[ 5-e^{2 x} \log (x) \]
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Rubi [A]
time = 0.04, antiderivative size = 9, normalized size of antiderivative = 0.82, number of steps
used = 6, number of rules used = 5, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.227, Rules used = {14, 2209, 2225,
2634, 12} \begin {gather*} -e^{2 x} \log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rule 2209
Rule 2225
Rule 2634
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-\frac {e^{2 x}}{x}-2 e^{2 x} \log (x)\right ) \, dx\\ &=-\left (2 \int e^{2 x} \log (x) \, dx\right )-\int \frac {e^{2 x}}{x} \, dx\\ &=-\text {Ei}(2 x)-e^{2 x} \log (x)+2 \int \frac {e^{2 x}}{2 x} \, dx\\ &=-\text {Ei}(2 x)-e^{2 x} \log (x)+\int \frac {e^{2 x}}{x} \, dx\\ &=-e^{2 x} \log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 9, normalized size = 0.82 \begin {gather*} -e^{2 x} \log (x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.49, size = 9, normalized size = 0.82
method | result | size |
norman | \(-{\mathrm e}^{2 x} \ln \left (x \right )\) | \(9\) |
risch | \(-{\mathrm e}^{2 x} \ln \left (x \right )\) | \(9\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 8, normalized size = 0.73 \begin {gather*} -e^{\left (2 \, x\right )} \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.34, size = 8, normalized size = 0.73 \begin {gather*} -e^{\left (2 \, x\right )} \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.07, size = 8, normalized size = 0.73 \begin {gather*} - e^{2 x} \log {\left (x \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 8, normalized size = 0.73 \begin {gather*} -e^{\left (2 \, x\right )} \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 3.20, size = 8, normalized size = 0.73 \begin {gather*} -{\mathrm {e}}^{2\,x}\,\ln \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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