Optimal. Leaf size=23 \[ \left (-x+\log \left (-1+x+\frac {\left (2+e^4\right )^2 \log (5)}{x^2}\right )\right )^2 \]
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Rubi [A] time = 0.37, antiderivative size = 32, normalized size of antiderivative = 1.39, number of steps used = 3, number of rules used = 3, integrand size = 144, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.021, Rules used = {6688, 12, 6686} \begin {gather*} \left (x-\log \left (-\frac {-x^3+x^2-\left (2+e^4\right )^2 \log (5)}{x^2}\right )\right )^2 \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6686
Rule 6688
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {2 \left (2 x^3-x^4-2 \left (2+e^4\right )^2 \log (5)-\left (2+e^4\right )^2 x \log (5)\right ) \left (x-\log \left (\frac {-x^2+x^3+\left (2+e^4\right )^2 \log (5)}{x^2}\right )\right )}{x \left (x^2-x^3-\left (2+e^4\right )^2 \log (5)\right )} \, dx\\ &=2 \int \frac {\left (2 x^3-x^4-2 \left (2+e^4\right )^2 \log (5)-\left (2+e^4\right )^2 x \log (5)\right ) \left (x-\log \left (\frac {-x^2+x^3+\left (2+e^4\right )^2 \log (5)}{x^2}\right )\right )}{x \left (x^2-x^3-\left (2+e^4\right )^2 \log (5)\right )} \, dx\\ &=\left (x-\log \left (-\frac {x^2-x^3-\left (2+e^4\right )^2 \log (5)}{x^2}\right )\right )^2\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.06, size = 30, normalized size = 1.30 \begin {gather*} \left (x-\log \left (\frac {-x^2+x^3+\left (2+e^4\right )^2 \log (5)}{x^2}\right )\right )^2 \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.57, size = 59, normalized size = 2.57 \begin {gather*} x^{2} - 2 \, x \log \left (\frac {x^{3} - x^{2} + {\left (e^{8} + 4 \, e^{4} + 4\right )} \log \relax (5)}{x^{2}}\right ) + \log \left (\frac {x^{3} - x^{2} + {\left (e^{8} + 4 \, e^{4} + 4\right )} \log \relax (5)}{x^{2}}\right )^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.33, size = 72, normalized size = 3.13 \begin {gather*} x^{2} - 2 \, x \log \left (x^{3} - x^{2} + e^{8} \log \relax (5) + 4 \, e^{4} \log \relax (5) + 4 \, \log \relax (5)\right ) + 4 \, x \log \relax (x) - 4 \, \log \left (x^{3} - x^{2} + e^{8} \log \relax (5) + 4 \, e^{4} \log \relax (5) + 4 \, \log \relax (5)\right ) \log \relax (x) + 4 \, \log \relax (x)^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.44, size = 64, normalized size = 2.78
method | result | size |
norman | \(x^{2}+\ln \left (\frac {\left ({\mathrm e}^{8}+4 \,{\mathrm e}^{4}+4\right ) \ln \relax (5)+x^{3}-x^{2}}{x^{2}}\right )^{2}-2 x \ln \left (\frac {\left ({\mathrm e}^{8}+4 \,{\mathrm e}^{4}+4\right ) \ln \relax (5)+x^{3}-x^{2}}{x^{2}}\right )\) | \(64\) |
default | error in gcdex: invalid arguments\ | N/A |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.45, size = 67, normalized size = 2.91 \begin {gather*} x^{2} - 2 \, {\left (x + 2 \, \log \relax (x)\right )} \log \left (x^{3} - x^{2} + {\left (e^{8} + 4 \, e^{4} + 4\right )} \log \relax (5)\right ) + \log \left (x^{3} - x^{2} + {\left (e^{8} + 4 \, e^{4} + 4\right )} \log \relax (5)\right )^{2} + 4 \, x \log \relax (x) + 4 \, \log \relax (x)^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 10.41, size = 31, normalized size = 1.35 \begin {gather*} {\left (x-\ln \left (\frac {x^3-x^2+\ln \relax (5)\,\left (4\,{\mathrm {e}}^4+{\mathrm {e}}^8+4\right )}{x^2}\right )\right )}^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.34, size = 58, normalized size = 2.52 \begin {gather*} x^{2} - 2 x \log {\left (\frac {x^{3} - x^{2} + \left (4 + 4 e^{4} + e^{8}\right ) \log {\relax (5 )}}{x^{2}} \right )} + \log {\left (\frac {x^{3} - x^{2} + \left (4 + 4 e^{4} + e^{8}\right ) \log {\relax (5 )}}{x^{2}} \right )}^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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