Optimal. Leaf size=27 \[ 3-e^{-x}+\left (-1+\frac {e^4}{x}\right ) x \left (4-x^4\right ) \]
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Rubi [A]
time = 0.04, antiderivative size = 22, normalized size of antiderivative = 0.81, number of steps
used = 3, number of rules used = 2, integrand size = 27, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.074, Rules used = {6820, 2225}
\begin {gather*} x^5-e^4 x^4-4 x-e^{-x} \end {gather*}
Antiderivative was successfully verified.
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Rule 2225
Rule 6820
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-4+e^{-x}-4 e^4 x^3+5 x^4\right ) \, dx\\ &=-4 x-e^4 x^4+x^5+\int e^{-x} \, dx\\ &=-e^{-x}-4 x-e^4 x^4+x^5\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 22, normalized size = 0.81 \begin {gather*} -e^{-x}-4 x-e^4 x^4+x^5 \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.37, size = 21, normalized size = 0.78
method | result | size |
default | \(-4 x -{\mathrm e}^{-x}+x^{5}-x^{4} {\mathrm e}^{4}\) | \(21\) |
risch | \(-4 x -{\mathrm e}^{-x}+x^{5}-x^{4} {\mathrm e}^{4}\) | \(21\) |
norman | \(\left (-1+x^{5} {\mathrm e}^{x}-4 \,{\mathrm e}^{x} x -{\mathrm e}^{4} {\mathrm e}^{x} x^{4}\right ) {\mathrm e}^{-x}\) | \(28\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 20, normalized size = 0.74 \begin {gather*} x^{5} - x^{4} e^{4} - 4 \, x - e^{\left (-x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.40, size = 24, normalized size = 0.89 \begin {gather*} {\left ({\left (x^{5} - x^{4} e^{4} - 4 \, x\right )} e^{x} - 1\right )} e^{\left (-x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 17, normalized size = 0.63 \begin {gather*} x^{5} - x^{4} e^{4} - 4 x - e^{- x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 20, normalized size = 0.74 \begin {gather*} x^{5} - x^{4} e^{4} - 4 \, x - e^{\left (-x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.08, size = 20, normalized size = 0.74 \begin {gather*} x^5-{\mathrm {e}}^{-x}-x^4\,{\mathrm {e}}^4-4\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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