Optimal. Leaf size=25 \[ 5 \left (-3 e^{5-e^x-x} x-x^2\right )^2 \]
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Rubi [B] time = 0.12, antiderivative size = 70, normalized size of antiderivative = 2.80, number of steps used = 3, number of rules used = 1, integrand size = 70, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.014, Rules used = {2288} \begin {gather*} 5 x^4+\frac {30 e^{-x-e^x+5} \left (e^x x^3+x^3\right )}{e^x+1}+\frac {45 e^{-2 x-2 e^x+10} \left (e^x x^2+x^2\right )}{e^x+1} \end {gather*}
Antiderivative was successfully verified.
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Rule 2288
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=5 x^4+3 \int e^{5-e^x-x} \left (30 x^2-10 x^3-10 e^x x^3\right ) \, dx+9 \int e^{10-2 e^x-2 x} \left (10 x-10 x^2-10 e^x x^2\right ) \, dx\\ &=5 x^4+\frac {45 e^{10-2 e^x-2 x} \left (x^2+e^x x^2\right )}{1+e^x}+\frac {30 e^{5-e^x-x} \left (x^3+e^x x^3\right )}{1+e^x}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.98, size = 31, normalized size = 1.24 \begin {gather*} 5 e^{-2 \left (e^x+x\right )} x^2 \left (3 e^5+e^{e^x+x} x\right )^2 \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.84, size = 42, normalized size = 1.68 \begin {gather*} 5 \, x^{4} + 10 \, x^{3} e^{\left (-x - e^{x} + \log \relax (3) + 5\right )} + 5 \, x^{2} e^{\left (-2 \, x - 2 \, e^{x} + 2 \, \log \relax (3) + 10\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.20, size = 36, normalized size = 1.44 \begin {gather*} 5 \, x^{4} + 30 \, x^{3} e^{\left (-x - e^{x} + 5\right )} + 45 \, x^{2} e^{\left (-2 \, x - 2 \, e^{x} + 10\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.18, size = 37, normalized size = 1.48
method | result | size |
risch | \(45 \,{\mathrm e}^{-2 \,{\mathrm e}^{x}+10-2 x} x^{2}+30 \,{\mathrm e}^{-{\mathrm e}^{x}+5-x} x^{3}+5 x^{4}\) | \(37\) |
default | \(45 \,{\mathrm e}^{-2 \,{\mathrm e}^{x}+10-2 x} x^{2}+10 \,{\mathrm e}^{-{\mathrm e}^{x}+\ln \relax (3)-x +5} x^{3}+5 x^{4}\) | \(43\) |
norman | \(45 \,{\mathrm e}^{-2 \,{\mathrm e}^{x}+10-2 x} x^{2}+10 \,{\mathrm e}^{-{\mathrm e}^{x}+\ln \relax (3)-x +5} x^{3}+5 x^{4}\) | \(43\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.42, size = 36, normalized size = 1.44 \begin {gather*} 5 \, x^{4} + 30 \, x^{3} e^{\left (-x - e^{x} + 5\right )} + 45 \, x^{2} e^{\left (-2 \, x - 2 \, e^{x} + 10\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.19, size = 28, normalized size = 1.12 \begin {gather*} 5\,x^2\,{\mathrm {e}}^{-2\,x-2\,{\mathrm {e}}^x}\,{\left (3\,{\mathrm {e}}^5+x\,{\mathrm {e}}^{x+{\mathrm {e}}^x}\right )}^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.21, size = 34, normalized size = 1.36 \begin {gather*} 5 x^{4} + 30 x^{3} e^{- x - e^{x} + 5} + 45 x^{2} e^{- 2 x - 2 e^{x} + 10} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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