Optimal. Leaf size=26 \[ \left (1+e^{20 e^{-e^{x^3}+(20-x)^2+x}}\right )^2 \]
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Rubi [A] time = 1.44, antiderivative size = 25, normalized size of antiderivative = 0.96, number of steps used = 3, number of rules used = 3, integrand size = 125, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.024, Rules used = {6688, 12, 6686} \begin {gather*} \left (e^{20 e^{-e^{x^3}+x^2-39 x+400}}+1\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 40 e^{400-e^{x^3}+20 e^{400-e^{x^3}-39 x+x^2}-39 x+x^2} \left (1+e^{20 e^{400-e^{x^3}-39 x+x^2}}\right ) \left (-39+2 x-3 e^{x^3} x^2\right ) \, dx\\ &=40 \int e^{400-e^{x^3}+20 e^{400-e^{x^3}-39 x+x^2}-39 x+x^2} \left (1+e^{20 e^{400-e^{x^3}-39 x+x^2}}\right ) \left (-39+2 x-3 e^{x^3} x^2\right ) \, dx\\ &=\left (1+e^{20 e^{400-e^{x^3}-39 x+x^2}}\right )^2\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 1.11, size = 25, normalized size = 0.96 \begin {gather*} \left (1+e^{20 e^{400-e^{x^3}-39 x+x^2}}\right )^2 \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.46, size = 39, normalized size = 1.50 \begin {gather*} e^{\left (40 \, e^{\left (x^{2} - 39 \, x - e^{\left (x^{3}\right )} + 400\right )}\right )} + 2 \, e^{\left (20 \, e^{\left (x^{2} - 39 \, x - e^{\left (x^{3}\right )} + 400\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 -40 \, {\left ({\left (3 \, x^{2} e^{\left (x^{3} + x^{2} - 39 \, x + 400\right )} - {\left (2 \, x - 39\right )} e^{\left (x^{2} - 39 \, x + 400\right )}\right )} e^{\left (40 \, e^{\left (x^{2} - 39 \, x - e^{\left (x^{3}\right )} + 400\right )}\right )} + {\left (3 \, x^{2} e^{\left (x^{3} + x^{2} - 39 \, x + 400\right )} - {\left (2 \, x - 39\right )} e^{\left (x^{2} - 39 \, x + 400\right )}\right )} e^{\left (20 \, e^{\left (x^{2} - 39 \, x - e^{\left (x^{3}\right )} + 400\right )}\right )}\right )} e^{\left (-e^{\left (x^{3}\right )}\right )}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.07, size = 40, normalized size = 1.54
method | result | size |
risch | \({\mathrm e}^{40 \,{\mathrm e}^{x^{2}-39 x +400-{\mathrm e}^{x^{3}}}}+2 \,{\mathrm e}^{20 \,{\mathrm e}^{x^{2}-39 x +400-{\mathrm e}^{x^{3}}}}\) | \(40\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.75, size = 39, normalized size = 1.50 \begin {gather*} e^{\left (40 \, e^{\left (x^{2} - 39 \, x - e^{\left (x^{3}\right )} + 400\right )}\right )} + 2 \, e^{\left (20 \, e^{\left (x^{2} - 39 \, x - e^{\left (x^{3}\right )} + 400\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.14, size = 43, normalized size = 1.65 \begin {gather*} {\mathrm {e}}^{20\,{\mathrm {e}}^{-{\mathrm {e}}^{x^3}}\,{\mathrm {e}}^{-39\,x}\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{400}}\,\left ({\mathrm {e}}^{20\,{\mathrm {e}}^{-{\mathrm {e}}^{x^3}}\,{\mathrm {e}}^{-39\,x}\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{400}}+2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 6.11, size = 41, normalized size = 1.58 \begin {gather*} e^{40 e^{x^{2} - 39 x + 400} e^{- e^{x^{3}}}} + 2 e^{20 e^{x^{2} - 39 x + 400} e^{- e^{x^{3}}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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