Optimal. Leaf size=24 \[ 3-\frac {289}{4} \left (-\frac {4 e^{2 x}}{x}+x-\log (3 x)\right ) \]
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Rubi [A] time = 0.05, antiderivative size = 22, normalized size of antiderivative = 0.92, number of steps used = 6, number of rules used = 4, integrand size = 27, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.148, Rules used = {12, 14, 43, 2197} \begin {gather*} -\frac {289 x}{4}+\frac {289 e^{2 x}}{x}+\frac {289 \log (x)}{4} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rule 43
Rule 2197
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{4} \int \frac {289 x-289 x^2+e^{2 x} (-1156+2312 x)}{x^2} \, dx\\ &=\frac {1}{4} \int \left (-\frac {289 (-1+x)}{x}+\frac {1156 e^{2 x} (-1+2 x)}{x^2}\right ) \, dx\\ &=-\left (\frac {289}{4} \int \frac {-1+x}{x} \, dx\right )+289 \int \frac {e^{2 x} (-1+2 x)}{x^2} \, dx\\ &=\frac {289 e^{2 x}}{x}-\frac {289}{4} \int \left (1-\frac {1}{x}\right ) \, dx\\ &=\frac {289 e^{2 x}}{x}-\frac {289 x}{4}+\frac {289 \log (x)}{4}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.02, size = 20, normalized size = 0.83 \begin {gather*} \frac {289}{4} \left (\frac {4 e^{2 x}}{x}-x+\log (x)\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.01, size = 20, normalized size = 0.83 \begin {gather*} -\frac {289 \, {\left (x^{2} - x \log \relax (x) - 4 \, e^{\left (2 \, x\right )}\right )}}{4 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 20, normalized size = 0.83 \begin {gather*} -\frac {289 \, {\left (x^{2} - x \log \relax (x) - 4 \, e^{\left (2 \, x\right )}\right )}}{4 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 18, normalized size = 0.75
method | result | size |
default | \(-\frac {289 x}{4}+\frac {289 \ln \relax (x )}{4}+\frac {289 \,{\mathrm e}^{2 x}}{x}\) | \(18\) |
risch | \(-\frac {289 x}{4}+\frac {289 \ln \relax (x )}{4}+\frac {289 \,{\mathrm e}^{2 x}}{x}\) | \(18\) |
norman | \(\frac {-\frac {289 x^{2}}{4}+289 \,{\mathrm e}^{2 x}}{x}+\frac {289 \ln \relax (x )}{4}\) | \(22\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [C] time = 0.39, size = 21, normalized size = 0.88 \begin {gather*} -\frac {289}{4} \, x + 578 \, {\rm Ei}\left (2 \, x\right ) - 578 \, \Gamma \left (-1, -2 \, x\right ) + \frac {289}{4} \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.14, size = 22, normalized size = 0.92 \begin {gather*} \frac {289\,\ln \relax (x)}{4}+\frac {1156\,{\mathrm {e}}^{2\,x}-289\,x^2}{4\,x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.15, size = 19, normalized size = 0.79 \begin {gather*} - \frac {289 x}{4} + \frac {289 \log {\relax (x )}}{4} + \frac {289 e^{2 x}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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