Optimal. Leaf size=19 \[ 2-e^{2 x}+\frac {\log ^2(2 x)}{10000} \]
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Rubi [A] time = 0.02, antiderivative size = 18, normalized size of antiderivative = 0.95, number of steps used = 5, number of rules used = 4, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {12, 14, 2194, 2301} \begin {gather*} \frac {\log ^2(2 x)}{10000}-e^{2 x} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rule 2194
Rule 2301
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \frac {-10000 e^{2 x} x+\log (2 x)}{x} \, dx}{5000}\\ &=\frac {\int \left (-10000 e^{2 x}+\frac {\log (2 x)}{x}\right ) \, dx}{5000}\\ &=\frac {\int \frac {\log (2 x)}{x} \, dx}{5000}-2 \int e^{2 x} \, dx\\ &=-e^{2 x}+\frac {\log ^2(2 x)}{10000}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 18, normalized size = 0.95 \begin {gather*} -e^{2 x}+\frac {\log ^2(2 x)}{10000} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.68, size = 15, normalized size = 0.79 \begin {gather*} \frac {1}{10000} \, \log \left (2 \, x\right )^{2} - e^{\left (2 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 15, normalized size = 0.79 \begin {gather*} \frac {1}{10000} \, \log \left (2 \, x\right )^{2} - e^{\left (2 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 16, normalized size = 0.84
method | result | size |
default | \(\frac {\ln \left (2 x \right )^{2}}{10000}-{\mathrm e}^{2 x}\) | \(16\) |
norman | \(\frac {\ln \left (2 x \right )^{2}}{10000}-{\mathrm e}^{2 x}\) | \(16\) |
risch | \(\frac {\ln \left (2 x \right )^{2}}{10000}-{\mathrm e}^{2 x}\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.41, size = 15, normalized size = 0.79 \begin {gather*} \frac {1}{10000} \, \log \left (2 \, x\right )^{2} - e^{\left (2 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.14, size = 19, normalized size = 1.00 \begin {gather*} \frac {{\ln \relax (x)}^2}{10000}+\frac {\ln \relax (2)\,\ln \relax (x)}{5000}-{\mathrm {e}}^{2\,x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.24, size = 12, normalized size = 0.63 \begin {gather*} - e^{2 x} + \frac {\log {\left (2 x \right )}^{2}}{10000} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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