Optimal. Leaf size=27 \[ 3-\frac {3}{25} \left (-1+e^{2 x}\right )^2+x-x^2-\log ^2(2) \]
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Rubi [A] time = 0.01, antiderivative size = 25, normalized size of antiderivative = 0.93, number of steps used = 4, number of rules used = 2, integrand size = 23, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.087, Rules used = {12, 2194} \begin {gather*} -x^2+x+\frac {6 e^{2 x}}{25}-\frac {3 e^{4 x}}{25} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2194
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{25} \int \left (25+12 e^{2 x}-12 e^{4 x}-50 x\right ) \, dx\\ &=x-x^2+\frac {12}{25} \int e^{2 x} \, dx-\frac {12}{25} \int e^{4 x} \, dx\\ &=\frac {6 e^{2 x}}{25}-\frac {3 e^{4 x}}{25}+x-x^2\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 25, normalized size = 0.93 \begin {gather*} \frac {6 e^{2 x}}{25}-\frac {3 e^{4 x}}{25}+x-x^2 \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.56, size = 19, normalized size = 0.70 \begin {gather*} -x^{2} + x - \frac {3}{25} \, e^{\left (4 \, x\right )} + \frac {6}{25} \, e^{\left (2 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.13, size = 19, normalized size = 0.70 \begin {gather*} -x^{2} + x - \frac {3}{25} \, e^{\left (4 \, x\right )} + \frac {6}{25} \, e^{\left (2 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 20, normalized size = 0.74
method | result | size |
risch | \(x -x^{2}-\frac {3 \,{\mathrm e}^{4 x}}{25}+\frac {6 \,{\mathrm e}^{2 x}}{25}\) | \(20\) |
derivativedivides | \(x -x^{2}-\frac {3 \,{\mathrm e}^{4 x}}{25}+\frac {6 \,{\mathrm e}^{2 x}}{25}\) | \(22\) |
default | \(x -x^{2}-\frac {3 \,{\mathrm e}^{4 x}}{25}+\frac {6 \,{\mathrm e}^{2 x}}{25}\) | \(22\) |
norman | \(x -x^{2}-\frac {3 \,{\mathrm e}^{4 x}}{25}+\frac {6 \,{\mathrm e}^{2 x}}{25}\) | \(22\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.37, size = 19, normalized size = 0.70 \begin {gather*} -x^{2} + x - \frac {3}{25} \, e^{\left (4 \, x\right )} + \frac {6}{25} \, e^{\left (2 \, x\right )} \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 = 0.70 \begin {gather*} x+\frac {6\,{\mathrm {e}}^{2\,x}}{25}-\frac {3\,{\mathrm {e}}^{4\,x}}{25}-x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 20, normalized size = 0.74 \begin {gather*} - x^{2} + x - \frac {3 e^{4 x}}{25} + \frac {6 e^{2 x}}{25} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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