Optimal. Leaf size=20 \[ e^x-x-e^3 (23-x) x^2 \]
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Rubi [A]
time = 0.01, antiderivative size = 22, normalized size of antiderivative = 1.10, number of steps
used = 3, number of rules used = 1, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {2225}
\begin {gather*} e^3 x^3-23 e^3 x^2-x+e^x \end {gather*}
Antiderivative was successfully verified.
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Rule 2225
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-x+e^3 \int \left (-46 x+3 x^2\right ) \, dx+\int e^x \, dx\\ &=e^x-x-23 e^3 x^2+e^3 x^3\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 22, normalized size = 1.10 \begin {gather*} e^x-x-23 e^3 x^2+e^3 x^3 \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.18, size = 19, normalized size = 0.95
method | result | size |
default | \(-x +{\mathrm e}^{3} \left (x^{3}-23 x^{2}\right )+{\mathrm e}^{x}\) | \(19\) |
norman | \(x^{3} {\mathrm e}^{3}-x -23 x^{2} {\mathrm e}^{3}+{\mathrm e}^{x}\) | \(20\) |
risch | \(x^{3} {\mathrm e}^{3}-x -23 x^{2} {\mathrm e}^{3}+{\mathrm e}^{x}\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 18, normalized size = 0.90 \begin {gather*} {\left (x^{3} - 23 \, x^{2}\right )} e^{3} - x + e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 18, normalized size = 0.90 \begin {gather*} {\left (x^{3} - 23 \, x^{2}\right )} e^{3} - 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 = 19, normalized size = 0.95 \begin {gather*} x^{3} e^{3} - 23 x^{2} e^{3} - x + e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 18, normalized size = 0.90 \begin {gather*} {\left (x^{3} - 23 \, x^{2}\right )} e^{3} - x + e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.06, size = 19, normalized size = 0.95 \begin {gather*} {\mathrm {e}}^x-x-23\,x^2\,{\mathrm {e}}^3+x^3\,{\mathrm {e}}^3 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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