Optimal. Leaf size=21 \[ 5-\frac {3 \left (e^{2 x}-x (2+x+\log (x))\right )}{x} \]
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Rubi [A] time = 0.04, antiderivative size = 18, normalized size of antiderivative = 0.86, number of steps used = 5, number of rules used = 3, integrand size = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {14, 43, 2197} \begin {gather*} 3 x-\frac {3 e^{2 x}}{x}+3 \log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 43
Rule 2197
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {3 (1+x)}{x}-\frac {3 e^{2 x} (-1+2 x)}{x^2}\right ) \, dx\\ &=3 \int \frac {1+x}{x} \, dx-3 \int \frac {e^{2 x} (-1+2 x)}{x^2} \, dx\\ &=-\frac {3 e^{2 x}}{x}+3 \int \left (1+\frac {1}{x}\right ) \, dx\\ &=-\frac {3 e^{2 x}}{x}+3 x+3 \log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.02, size = 16, normalized size = 0.76 \begin {gather*} 3 \left (-\frac {e^{2 x}}{x}+x+\log (x)\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.97, size = 19, normalized size = 0.90 \begin {gather*} \frac {3 \, {\left (x^{2} + x \log \relax (x) - e^{\left (2 \, x\right )}\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.18, size = 19, normalized size = 0.90 \begin {gather*} \frac {3 \, {\left (x^{2} + x \log \relax (x) - e^{\left (2 \, x\right )}\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.10, size = 18, normalized size = 0.86
method | result | size |
risch | \(3 x +3 \ln \relax (x )-\frac {3 \,{\mathrm e}^{2 x}}{x}\) | \(18\) |
derivativedivides | \(3 x +3 \ln \left (2 x \right )-\frac {3 \,{\mathrm e}^{2 x}}{x}\) | \(20\) |
default | \(3 x +3 \ln \left (2 x \right )-\frac {3 \,{\mathrm e}^{2 x}}{x}\) | \(20\) |
norman | \(\frac {3 x^{2}-3 \,{\mathrm e}^{2 x}}{x}+3 \ln \relax (x )\) | \(22\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [C] time = 0.38, size = 21, normalized size = 1.00 \begin {gather*} 3 \, x - 6 \, {\rm Ei}\left (2 \, x\right ) + 6 \, \Gamma \left (-1, -2 \, x\right ) + 3 \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 22, normalized size = 1.05 \begin {gather*} 3\,\ln \relax (x)-\frac {3\,{\mathrm {e}}^{2\,x}-3\,x^2}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.12, size = 15, normalized size = 0.71 \begin {gather*} 3 x + 3 \log {\relax (x )} - \frac {3 e^{2 x}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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