Optimal. Leaf size=30 \[ e^{-e^{e+x}+x+\frac {e^2}{x \log ^2(x)}}+(4-x)^2 \]
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Rubi [A] time = 1.87, antiderivative size = 29, normalized size of antiderivative = 0.97, number of steps used = 3, number of rules used = 2, integrand size = 89, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.022, Rules used = {6688, 6706} \begin {gather*} x^2-8 x+e^{x-e^{x+e}+\frac {e^2}{x \log ^2(x)}} \end {gather*}
Antiderivative was successfully verified.
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Rule 6688
Rule 6706
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-8+2 x+\frac {e^{-e^{e+x}+x+\frac {e^2}{x \log ^2(x)}} \left (-2 e^2-e^2 \log (x)-\left (-1+e^{e+x}\right ) x^2 \log ^3(x)\right )}{x^2 \log ^3(x)}\right ) \, dx\\ &=-8 x+x^2+\int \frac {e^{-e^{e+x}+x+\frac {e^2}{x \log ^2(x)}} \left (-2 e^2-e^2 \log (x)-\left (-1+e^{e+x}\right ) x^2 \log ^3(x)\right )}{x^2 \log ^3(x)} \, dx\\ &=e^{-e^{e+x}+x+\frac {e^2}{x \log ^2(x)}}-8 x+x^2\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 1.12, size = 29, normalized size = 0.97 \begin {gather*} e^{-e^{e+x}+x+\frac {e^2}{x \log ^2(x)}}-8 x+x^2 \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.82, size = 36, normalized size = 1.20 \begin {gather*} x^{2} - 8 \, x + e^{\left (\frac {{\left (x^{2} - x e^{\left (x + e\right )}\right )} \log \relax (x)^{2} + e^{2}}{x \log \relax (x)^{2}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \mathit {undef} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.16, size = 40, normalized size = 1.33
method | result | size |
risch | \(x^{2}-8 x +{\mathrm e}^{\frac {-\ln \relax (x )^{2} {\mathrm e}^{x +{\mathrm e}} x +x^{2} \ln \relax (x )^{2}+{\mathrm e}^{2}}{\ln \relax (x )^{2} x}}\) | \(40\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.47, size = 27, normalized size = 0.90 \begin {gather*} x^{2} - 8 \, x + e^{\left (x + \frac {e^{2}}{x \log \relax (x)^{2}} - e^{\left (x + e\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.25, size = 29, normalized size = 0.97 \begin {gather*} x^2-8\,x+{\mathrm {e}}^{\frac {{\mathrm {e}}^2}{x\,{\ln \relax (x)}^2}}\,{\mathrm {e}}^{-{\mathrm {e}}^{\mathrm {e}}\,{\mathrm {e}}^x}\,{\mathrm {e}}^x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.55, size = 34, normalized size = 1.13 \begin {gather*} x^{2} - 8 x + e^{\frac {\left (x^{2} - x e^{x + e}\right ) \log {\relax (x )}^{2} + e^{2}}{x \log {\relax (x )}^{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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