Optimal. Leaf size=25 \[ e^{e^{x \left (e^x x+\left (23+5 e^{e^4}\right ) x\right )}} x \]
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Rubi [B] time = 0.20, antiderivative size = 84, normalized size of antiderivative = 3.36, number of steps used = 1, number of rules used = 1, integrand size = 85, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.012, Rules used = {2288} \begin {gather*} \frac {e^{e^{e^x x^2+5 e^{e^4} x^2+23 x^2}} \left (10 e^{e^4} x^2+46 x^2+e^x \left (x^3+2 x^2\right )\right )}{e^x x^2+2 e^x x+10 e^{e^4} x+46 x} \end {gather*}
Antiderivative was successfully verified.
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Rule 2288
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {e^{e^{23 x^2+5 e^{e^4} x^2+e^x x^2}} \left (46 x^2+10 e^{e^4} x^2+e^x \left (2 x^2+x^3\right )\right )}{46 x+10 e^{e^4} x+2 e^x x+e^x x^2}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.16, size = 22, normalized size = 0.88 \begin {gather*} e^{e^{\left (23+5 e^{e^4}+e^x\right ) x^2}} x \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.58, size = 24, normalized size = 0.96 \begin {gather*} x e^{\left (e^{\left (x^{2} e^{x} + 5 \, x^{2} e^{\left (e^{4}\right )} + 23 \, x^{2}\right )}\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*} \int {\left ({\left (10 \, x^{2} e^{\left (e^{4}\right )} + 46 \, x^{2} + {\left (x^{3} + 2 \, x^{2}\right )} e^{x}\right )} e^{\left (x^{2} e^{x} + 5 \, x^{2} e^{\left (e^{4}\right )} + 23 \, x^{2}\right )} + 1\right )} e^{\left (e^{\left (x^{2} e^{x} + 5 \, x^{2} e^{\left (e^{4}\right )} + 23 \, x^{2}\right )}\right )}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.08, size = 18, normalized size = 0.72
method | result | size |
risch | \(x \,{\mathrm e}^{{\mathrm e}^{x^{2} \left ({\mathrm e}^{x}+5 \,{\mathrm e}^{{\mathrm e}^{4}}+23\right )}}\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.56, size = 24, normalized size = 0.96 \begin {gather*} x e^{\left (e^{\left (x^{2} e^{x} + 5 \, x^{2} e^{\left (e^{4}\right )} + 23 \, x^{2}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.99, size = 26, normalized size = 1.04 \begin {gather*} x\,{\mathrm {e}}^{{\mathrm {e}}^{5\,x^2\,{\mathrm {e}}^{{\mathrm {e}}^4}}\,{\mathrm {e}}^{x^2\,{\mathrm {e}}^x}\,{\mathrm {e}}^{23\,x^2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 4.76, size = 26, normalized size = 1.04 \begin {gather*} x e^{e^{x^{2} e^{x} + 23 x^{2} + 5 x^{2} e^{e^{4}}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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