Optimal. Leaf size=21 \[ -5^{\frac {2 \left (\frac {x}{e}+\log \left (x^2\right )\right )}{x}}+x \]
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Rubi [A] time = 0.22, antiderivative size = 22, normalized size of antiderivative = 1.05, number of steps used = 3, number of rules used = 2, integrand size = 45, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.044, Rules used = {14, 6706} \begin {gather*} x-5^{\frac {2 \left (e \log \left (x^2\right )+x\right )}{e x}} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 6706
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (1+\frac {2\ 5^{\frac {2 \left (x+e \log \left (x^2\right )\right )}{e x}} \log (5) \left (-2+\log \left (x^2\right )\right )}{x^2}\right ) \, dx\\ &=x+(2 \log (5)) \int \frac {5^{\frac {2 \left (x+e \log \left (x^2\right )\right )}{e x}} \left (-2+\log \left (x^2\right )\right )}{x^2} \, dx\\ &=-5^{\frac {2 \left (x+e \log \left (x^2\right )\right )}{e x}}+x\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.12, size = 21, normalized size = 1.00 \begin {gather*} -5^{\frac {2}{e}+\frac {2 \log \left (x^2\right )}{x}}+x \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.83, size = 26, normalized size = 1.24 \begin {gather*} x - e^{\left (\frac {2 \, {\left (e \log \relax (5) \log \left (x^{2}\right ) + x \log \relax (5)\right )} e^{\left (-1\right )}}{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.01, size = 26, normalized size = 1.24 \begin {gather*} x - e^{\left (\frac {2 \, {\left (e \log \relax (5) \log \left (x^{2}\right ) + x \log \relax (5)\right )} e^{\left (-1\right )}}{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.19, size = 22, normalized size = 1.05
method | result | size |
risch | \(x -5^{\frac {2 \ln \left (x^{2}\right )+2 \,{\mathrm e}^{-1} x}{x}}\) | \(22\) |
default | \(x -{\mathrm e}^{\frac {2 \left ({\mathrm e} \ln \relax (5) \ln \left (x^{2}\right )+x \ln \relax (5)\right ) {\mathrm e}^{-1}}{x}}\) | \(30\) |
norman | \(\frac {x^{2}-x \,{\mathrm e}^{\frac {2 \left ({\mathrm e} \ln \relax (5) \ln \left (x^{2}\right )+x \ln \relax (5)\right ) {\mathrm e}^{-1}}{x}}}{x}\) | \(37\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.70, size = 20, normalized size = 0.95 \begin {gather*} -5^{2 \, e^{\left (-1\right )}} e^{\left (\frac {4 \, \log \relax (5) \log \relax (x)}{x}\right )} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.83, size = 21, normalized size = 1.00 \begin {gather*} x-5^{2\,{\mathrm {e}}^{-1}}\,{\left (x^2\right )}^{\frac {2\,\ln \relax (5)}{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.33, size = 27, normalized size = 1.29 \begin {gather*} x - e^{\frac {2 \left (x \log {\relax (5 )} + e \log {\relax (5 )} \log {\left (x^{2} \right )}\right )}{e x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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