Optimal. Leaf size=21 \[ -e^x+\left (6+x+4 \left (1-x+x^2\right )\right )^2 \]
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Rubi [A]
time = 0.00, antiderivative size = 24, normalized size of antiderivative = 1.14, number of steps
used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {2225}
\begin {gather*} 16 x^4-24 x^3+89 x^2-60 x-e^x \end {gather*}
Antiderivative was successfully verified.
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Rule 2225
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-60 x+89 x^2-24 x^3+16 x^4-\int e^x \, dx\\ &=-e^x-60 x+89 x^2-24 x^3+16 x^4\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 24, normalized size = 1.14 \begin {gather*} -e^x-60 x+89 x^2-24 x^3+16 x^4 \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.25, size = 24, normalized size = 1.14
method | result | size |
default | \(16 x^{4}-24 x^{3}+89 x^{2}-60 x -{\mathrm e}^{x}\) | \(24\) |
norman | \(16 x^{4}-24 x^{3}+89 x^{2}-60 x -{\mathrm e}^{x}\) | \(24\) |
risch | \(16 x^{4}-24 x^{3}+89 x^{2}-60 x -{\mathrm e}^{x}\) | \(24\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 23, normalized size = 1.10 \begin {gather*} 16 \, x^{4} - 24 \, x^{3} + 89 \, x^{2} - 60 \, x - e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.40, size = 23, normalized size = 1.10 \begin {gather*} 16 \, x^{4} - 24 \, x^{3} + 89 \, x^{2} - 60 \, x - e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 20, normalized size = 0.95 \begin {gather*} 16 x^{4} - 24 x^{3} + 89 x^{2} - 60 x - e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.43, size = 23, normalized size = 1.10 \begin {gather*} 16 \, x^{4} - 24 \, x^{3} + 89 \, x^{2} - 60 \, x - e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.05, size = 23, normalized size = 1.10 \begin {gather*} 89\,x^2-{\mathrm {e}}^x-60\,x-24\,x^3+16\,x^4 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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