Optimal. Leaf size=23 \[ \frac {1}{2} e^{2 x} \log \left (e^x\right )-\frac {e^{2 x}}{4} \]
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Rubi [A] time = 0.01, antiderivative size = 23, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 3, integrand size = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.300, Rules used = {2194, 2554, 12} \[ \frac {1}{2} e^{2 x} \log \left (e^x\right )-\frac {e^{2 x}}{4} \]
Antiderivative was successfully verified.
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Rule 12
Rule 2194
Rule 2554
Rubi steps
\begin {align*} \int e^{2 x} \log \left (e^x\right ) \, dx &=\frac {1}{2} e^{2 x} \log \left (e^x\right )-\int \frac {e^{2 x}}{2} \, dx\\ &=\frac {1}{2} e^{2 x} \log \left (e^x\right )-\frac {1}{2} \int e^{2 x} \, dx\\ &=-\frac {e^{2 x}}{4}+\frac {1}{2} e^{2 x} \log \left (e^x\right )\\ \end {align*}
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Mathematica [A] time = 0.01, size = 17, normalized size = 0.74 \[ \frac {1}{4} e^{2 x} \left (2 \log \left (e^x\right )-1\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.41, size = 11, normalized size = 0.48 \[ \frac {1}{4} \, {\left (2 \, x - 1\right )} e^{\left (2 \, x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.22, size = 11, normalized size = 0.48 \[ \frac {1}{4} \, {\left (2 \, x - 1\right )} e^{\left (2 \, x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 28, normalized size = 1.22 \[ \frac {x \,{\mathrm e}^{2 x}}{2}-\frac {{\mathrm e}^{2 x}}{4}+\frac {\left (-x +\ln \left ({\mathrm e}^{x}\right )\right ) {\mathrm e}^{2 x}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.44, size = 11, normalized size = 0.48 \[ \frac {1}{4} \, {\left (2 \, x - 1\right )} e^{\left (2 \, x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 11, normalized size = 0.48 \[ \frac {{\mathrm {e}}^{2\,x}\,\left (2\,x-1\right )}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 10, normalized size = 0.43 \[ \frac {\left (2 x - 1\right ) e^{2 x}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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