Optimal. Leaf size=23 \[ e^{x+\frac {1+x}{3}}+\frac {e^2}{5-2 x} \]
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Rubi [A]
time = 0.15, antiderivative size = 23, normalized size of antiderivative = 1.00, number of steps
used = 5, number of rules used = 4, integrand size = 41, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.098, Rules used = {27, 12, 6874,
2225} \begin {gather*} e^{\frac {4 x}{3}+\frac {1}{3}}+\frac {e^2}{5-2 x} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 27
Rule 2225
Rule 6874
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {6 e^2+e^{\frac {1}{3} (1+4 x)} \left (100-80 x+16 x^2\right )}{3 (-5+2 x)^2} \, dx\\ &=\frac {1}{3} \int \frac {6 e^2+e^{\frac {1}{3} (1+4 x)} \left (100-80 x+16 x^2\right )}{(-5+2 x)^2} \, dx\\ &=\frac {1}{3} \int \left (4 e^{\frac {1}{3}+\frac {4 x}{3}}+\frac {6 e^2}{(-5+2 x)^2}\right ) \, dx\\ &=\frac {e^2}{5-2 x}+\frac {4}{3} \int e^{\frac {1}{3}+\frac {4 x}{3}} \, dx\\ &=e^{\frac {1}{3}+\frac {4 x}{3}}+\frac {e^2}{5-2 x}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.11, size = 32, normalized size = 1.39 \begin {gather*} \frac {2}{3} \left (\frac {3}{2} e^{\frac {1}{3}+\frac {4 x}{3}}+\frac {3 e^2}{10-4 x}\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 7.76, size = 19, normalized size = 0.83
method | result | size |
risch | \(-\frac {{\mathrm e}^{2}}{2 \left (x -\frac {5}{2}\right )}+{\mathrm e}^{\frac {4 x}{3}+\frac {1}{3}}\) | \(17\) |
derivativedivides | \(-\frac {2 \,{\mathrm e}^{2}}{4 x -10}+{\mathrm e}^{\frac {4 x}{3}+\frac {1}{3}}\) | \(19\) |
default | \(-\frac {2 \,{\mathrm e}^{2}}{4 x -10}+{\mathrm e}^{\frac {4 x}{3}+\frac {1}{3}}\) | \(19\) |
norman | \(\frac {2 \,{\mathrm e}^{\frac {4 x}{3}+\frac {1}{3}} x -5 \,{\mathrm e}^{\frac {4 x}{3}+\frac {1}{3}}-{\mathrm e}^{2}}{2 x -5}\) | \(31\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 25, normalized size = 1.09 \begin {gather*} \frac {{\left (2 \, x - 5\right )} e^{\left (\frac {4}{3} \, x + \frac {1}{3}\right )} - e^{2}}{2 \, x - 5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.07, size = 19, normalized size = 0.83 \begin {gather*} e^{\frac {4 x}{3} + \frac {1}{3}} - \frac {2 e^{2}}{4 x - 10} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 30, normalized size = 1.30 \begin {gather*} \frac {2 \, x e^{\left (\frac {4}{3} \, x + \frac {1}{3}\right )} - e^{2} - 5 \, e^{\left (\frac {4}{3} \, x + \frac {1}{3}\right )}}{2 \, x - 5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 3.40, size = 18, normalized size = 0.78 \begin {gather*} {\mathrm {e}}^{\frac {4\,x}{3}+\frac {1}{3}}-\frac {{\mathrm {e}}^2}{2\,x-5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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