Optimal. Leaf size=26 \[ \log \left (-e^{1+e^{2 x^2}-x}+e^{(3+\log (5))^2}\right ) \]
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Rubi [A] time = 0.28, antiderivative size = 31, normalized size of antiderivative = 1.19, number of steps used = 1, number of rules used = 1, integrand size = 54, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.019, Rules used = {6684} \begin {gather*} \log \left (-e^{1-x} \left (e^{e^{2 x^2}}-15625 e^{x+8+\log ^2(5)}\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 6684
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\log \left (-e^{1-x} \left (e^{e^{2 x^2}}-15625 e^{8+x+\log ^2(5)}\right )\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.26, size = 26, normalized size = 1.00 \begin {gather*} -x+\log \left (e^{e^{2 x^2}}-15625 e^{8+x+\log ^2(5)}\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.76, size = 27, normalized size = 1.04 \begin {gather*} \log \left (-e^{\left (\log \relax (5)^{2} + 6 \, \log \relax (5) + 9\right )} + e^{\left (-x + e^{\left (2 \, x^{2}\right )} + 1\right )}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [F(-2)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: NotImplementedError} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 26, normalized size = 1.00
method | result | size |
norman | \(\ln \left (-{\mathrm e}^{{\mathrm e}^{2 x^{2}}-x +1}+15625 \,{\mathrm e}^{\ln \relax (5)^{2}+9}\right )\) | \(26\) |
risch | \(-1+\ln \left ({\mathrm e}^{{\mathrm e}^{2 x^{2}}-x +1}-15625 \,{\mathrm e}^{\ln \relax (5)^{2}+9}\right )\) | \(26\) |
derivativedivides | \(\ln \left ({\mathrm e}^{{\mathrm e}^{2 x^{2}}-x +1}-{\mathrm e}^{\ln \relax (5)^{2}+6 \ln \relax (5)+9}\right )\) | \(28\) |
default | \(\ln \left ({\mathrm e}^{{\mathrm e}^{2 x^{2}}-x +1}-{\mathrm e}^{\ln \relax (5)^{2}+6 \ln \relax (5)+9}\right )\) | \(28\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 25, normalized size = 0.96 \begin {gather*} \log \left (15625 \, e^{\left (\log \relax (5)^{2} + 9\right )} - e^{\left (-x + e^{\left (2 \, x^{2}\right )} + 1\right )}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.22, size = 23, normalized size = 0.88 \begin {gather*} \ln \left ({\mathrm {e}}^{{\mathrm {e}}^{2\,x^2}-x+1}-15625\,{\mathrm {e}}^{{\ln \relax (5)}^2+9}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.35, size = 24, normalized size = 0.92 \begin {gather*} \log {\left (e^{- x + e^{2 x^{2}} + 1} - 15625 e^{9} e^{\log {\relax (5 )}^{2}} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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