Optimal. Leaf size=17 \[ e^{-24+e^{(5+(5-x) x)^2}} \]
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Rubi [F] time = 1.04, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \exp \left (1+e^{25+50 x+15 x^2-10 x^3+x^4}+50 x+15 x^2-10 x^3+x^4\right ) \left (50+30 x-30 x^2+4 x^3\right ) \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (50 \exp \left (1+e^{25+50 x+15 x^2-10 x^3+x^4}+50 x+15 x^2-10 x^3+x^4\right )+30 \exp \left (1+e^{25+50 x+15 x^2-10 x^3+x^4}+50 x+15 x^2-10 x^3+x^4\right ) x-30 \exp \left (1+e^{25+50 x+15 x^2-10 x^3+x^4}+50 x+15 x^2-10 x^3+x^4\right ) x^2+4 \exp \left (1+e^{25+50 x+15 x^2-10 x^3+x^4}+50 x+15 x^2-10 x^3+x^4\right ) x^3\right ) \, dx\\ &=4 \int \exp \left (1+e^{25+50 x+15 x^2-10 x^3+x^4}+50 x+15 x^2-10 x^3+x^4\right ) x^3 \, dx+30 \int \exp \left (1+e^{25+50 x+15 x^2-10 x^3+x^4}+50 x+15 x^2-10 x^3+x^4\right ) x \, dx-30 \int \exp \left (1+e^{25+50 x+15 x^2-10 x^3+x^4}+50 x+15 x^2-10 x^3+x^4\right ) x^2 \, dx+50 \int \exp \left (1+e^{25+50 x+15 x^2-10 x^3+x^4}+50 x+15 x^2-10 x^3+x^4\right ) \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.71, size = 16, normalized size = 0.94 \begin {gather*} e^{-24+e^{\left (-5-5 x+x^2\right )^2}} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.60, size = 22, normalized size = 1.29 \begin {gather*} e^{\left (e^{\left (x^{4} - 10 \, x^{3} + 15 \, x^{2} + 50 \, x + 25\right )} - 24\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 2 \, {\left (2 \, x^{3} - 15 \, x^{2} + 15 \, x + 25\right )} e^{\left (x^{4} - 10 \, x^{3} + 15 \, x^{2} + 50 \, x + e^{\left (x^{4} - 10 \, x^{3} + 15 \, x^{2} + 50 \, x + 25\right )} + 1\right )}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 15, normalized size = 0.88
method | result | size |
risch | \({\mathrm e}^{{\mathrm e}^{\left (x^{2}-5 x -5\right )^{2}}-24}\) | \(15\) |
derivativedivides | \({\mathrm e}^{{\mathrm e}^{x^{4}-10 x^{3}+15 x^{2}+50 x +25}-24}\) | \(23\) |
norman | \({\mathrm e}^{{\mathrm e}^{x^{4}-10 x^{3}+15 x^{2}+50 x +25}-24}\) | \(23\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.85, size = 22, normalized size = 1.29 \begin {gather*} e^{\left (e^{\left (x^{4} - 10 \, x^{3} + 15 \, x^{2} + 50 \, x + 25\right )} - 24\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.14, size = 27, normalized size = 1.59 \begin {gather*} {\mathrm {e}}^{-24}\,{\mathrm {e}}^{{\mathrm {e}}^{50\,x}\,{\mathrm {e}}^{x^4}\,{\mathrm {e}}^{25}\,{\mathrm {e}}^{-10\,x^3}\,{\mathrm {e}}^{15\,x^2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.33, size = 22, normalized size = 1.29 \begin {gather*} e^{e^{x^{4} - 10 x^{3} + 15 x^{2} + 50 x + 25} - 24} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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