Optimal. Leaf size=31 \[ 3+\frac {625}{256} x^2 \left (-e^5+x\right ) \left (x-\frac {5-x+x^2}{x}\right ) \]
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Rubi [A] time = 0.01, antiderivative size = 29, normalized size of antiderivative = 0.94, number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {12} \begin {gather*} \frac {625 x^3}{256}-\frac {3125 x^2}{256}-\frac {625 e^5 (5-2 x)^2}{1024} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{256} \int \left (e^5 (3125-1250 x)-6250 x+1875 x^2\right ) \, dx\\ &=-\frac {625 e^5 (5-2 x)^2}{1024}-\frac {3125 x^2}{256}+\frac {625 x^3}{256}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 27, normalized size = 0.87 \begin {gather*} \frac {625}{256} \left (5 e^5 x-5 x^2-e^5 x^2+x^3\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.48, size = 22, normalized size = 0.71 \begin {gather*} \frac {625}{256} \, x^{3} - \frac {3125}{256} \, x^{2} - \frac {625}{256} \, {\left (x^{2} - 5 \, x\right )} e^{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.21, size = 22, normalized size = 0.71 \begin {gather*} \frac {625}{256} \, x^{3} - \frac {3125}{256} \, x^{2} - \frac {625}{256} \, {\left (x^{2} - 5 \, x\right )} e^{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 21, normalized size = 0.68
method | result | size |
gosper | \(-\frac {625 x \left (x \,{\mathrm e}^{5}-x^{2}-5 \,{\mathrm e}^{5}+5 x \right )}{256}\) | \(21\) |
norman | \(\left (-\frac {625 \,{\mathrm e}^{5}}{256}-\frac {3125}{256}\right ) x^{2}+\frac {625 x^{3}}{256}+\frac {3125 x \,{\mathrm e}^{5}}{256}\) | \(22\) |
risch | \(-\frac {625 x^{2} {\mathrm e}^{5}}{256}+\frac {3125 x \,{\mathrm e}^{5}}{256}+\frac {625 x^{3}}{256}-\frac {3125 x^{2}}{256}\) | \(24\) |
default | \(\frac {{\mathrm e}^{5} \left (-625 x^{2}+3125 x \right )}{256}+\frac {625 x^{3}}{256}-\frac {3125 x^{2}}{256}\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.37, size = 22, normalized size = 0.71 \begin {gather*} \frac {625}{256} \, x^{3} - \frac {3125}{256} \, x^{2} - \frac {625}{256} \, {\left (x^{2} - 5 \, x\right )} e^{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 12, normalized size = 0.39 \begin {gather*} \frac {625\,x\,\left (x-{\mathrm {e}}^5\right )\,\left (x-5\right )}{256} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 29, normalized size = 0.94 \begin {gather*} \frac {625 x^{3}}{256} + x^{2} \left (- \frac {625 e^{5}}{256} - \frac {3125}{256}\right ) + \frac {3125 x e^{5}}{256} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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