Optimal. Leaf size=18 \[ -5 e^{-e^x}+2 x^4 (1+x) \]
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Rubi [A]
time = 0.05, antiderivative size = 20, normalized size of antiderivative = 1.11, number of steps
used = 6, number of rules used = 4, integrand size = 31, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.129, Rules used = {6820, 2320,
2225, 45} \begin {gather*} 2 x^5+2 x^4-5 e^{-e^x} \end {gather*}
Antiderivative was successfully verified.
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Rule 45
Rule 2225
Rule 2320
Rule 6820
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (5 e^{-e^x+x}+2 x^3 (4+5 x)\right ) \, dx\\ &=2 \int x^3 (4+5 x) \, dx+5 \int e^{-e^x+x} \, dx\\ &=2 \int \left (4 x^3+5 x^4\right ) \, dx+5 \text {Subst}\left (\int e^{-x} \, dx,x,e^x\right )\\ &=-5 e^{-e^x}+2 x^4+2 x^5\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.02, size = 20, normalized size = 1.11 \begin {gather*} -5 e^{-e^x}+2 x^4+2 x^5 \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.15, size = 19, normalized size = 1.06
method | result | size |
default | \(2 x^{5}+2 x^{4}-5 \,{\mathrm e}^{-{\mathrm e}^{x}}\) | \(19\) |
risch | \(2 x^{5}+2 x^{4}-5 \,{\mathrm e}^{-{\mathrm e}^{x}}\) | \(19\) |
norman | \(\left (-5+2 x^{4} {\mathrm e}^{{\mathrm e}^{x}}+2 x^{5} {\mathrm e}^{{\mathrm e}^{x}}\right ) {\mathrm e}^{-{\mathrm e}^{x}}\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.31, size = 18, normalized size = 1.00 \begin {gather*} 2 \, x^{5} + 2 \, x^{4} - 5 \, e^{\left (-e^{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 20, normalized size = 1.11 \begin {gather*} {\left (2 \, {\left (x^{5} + x^{4}\right )} e^{\left (e^{x}\right )} - 5\right )} e^{\left (-e^{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.05, size = 15, normalized size = 0.83 \begin {gather*} 2 x^{5} + 2 x^{4} - 5 e^{- e^{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 18, normalized size = 1.00 \begin {gather*} 2 \, x^{5} + 2 \, x^{4} - 5 \, e^{\left (-e^{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.13, size = 18, normalized size = 1.00 \begin {gather*} 2\,x^4-5\,{\mathrm {e}}^{-{\mathrm {e}}^x}+2\,x^5 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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