Optimal. Leaf size=20 \[ 27+\left (-2+e^x\right )^2-x+x \log \left (\frac {5 x}{2}\right ) \]
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Rubi [A]
time = 0.01, antiderivative size = 22, normalized size of antiderivative = 1.10, number of steps
used = 4, number of rules used = 2, integrand size = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.105, Rules used = {2225, 2332}
\begin {gather*} -x-4 e^x+e^{2 x}+x \log \left (\frac {5 x}{2}\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 2225
Rule 2332
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=2 \int e^{2 x} \, dx-4 \int e^x \, dx+\int \log \left (\frac {5 x}{2}\right ) \, dx\\ &=-4 e^x+e^{2 x}-x+x \log \left (\frac {5 x}{2}\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 21, normalized size = 1.05 \begin {gather*} e^x \left (-4+e^x\right )-x+x \log \left (\frac {5 x}{2}\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.06, size = 19, normalized size = 0.95
method | result | size |
default | \({\mathrm e}^{2 x}-4 \,{\mathrm e}^{x}+\ln \left (\frac {5 x}{2}\right ) x -x\) | \(19\) |
norman | \({\mathrm e}^{2 x}-4 \,{\mathrm e}^{x}+\ln \left (\frac {5 x}{2}\right ) x -x\) | \(19\) |
risch | \({\mathrm e}^{2 x}-4 \,{\mathrm e}^{x}+\ln \left (\frac {5 x}{2}\right ) x -x\) | \(19\) |
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*} x \log \left (\frac {5}{2} \, x\right ) - x + e^{\left (2 \, x\right )} - 4 \, e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.33, size = 18, normalized size = 0.90 \begin {gather*} x \log \left (\frac {5}{2} \, x\right ) - x + e^{\left (2 \, x\right )} - 4 \, e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.05, size = 19, normalized size = 0.95 \begin {gather*} x \log {\left (\frac {5 x}{2} \right )} - x + e^{2 x} - 4 e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 18, normalized size = 0.90 \begin {gather*} x \log \left (\frac {5}{2} \, x\right ) - x + e^{\left (2 \, x\right )} - 4 \, e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.12, size = 17, normalized size = 0.85 \begin {gather*} {\mathrm {e}}^{2\,x}-4\,{\mathrm {e}}^x+x\,\left (\ln \left (\frac {5\,x}{2}\right )-1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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