Optimal. Leaf size=21 \[ 6+\frac {1}{2} \left (-\frac {5}{4}+e^{2 x}-x\right )-x \]
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Rubi [A] time = 0.00, antiderivative size = 15, normalized size of antiderivative = 0.71, number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {12, 2194} \begin {gather*} \frac {e^{2 x}}{2}-\frac {3 x}{2} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2194
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{2} \int \left (-3+2 e^{2 x}\right ) \, dx\\ &=-\frac {3 x}{2}+\int e^{2 x} \, dx\\ &=\frac {e^{2 x}}{2}-\frac {3 x}{2}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 15, normalized size = 0.71 \begin {gather*} \frac {e^{2 x}}{2}-\frac {3 x}{2} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.51, size = 10, normalized size = 0.48 \begin {gather*} -\frac {3}{2} \, x + \frac {1}{2} \, e^{\left (2 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 10, normalized size = 0.48 \begin {gather*} -\frac {3}{2} \, x + \frac {1}{2} \, e^{\left (2 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 11, normalized size = 0.52
method | result | size |
default | \(-\frac {3 x}{2}+\frac {{\mathrm e}^{2 x}}{2}\) | \(11\) |
norman | \(-\frac {3 x}{2}+\frac {{\mathrm e}^{2 x}}{2}\) | \(11\) |
risch | \(-\frac {3 x}{2}+\frac {{\mathrm e}^{2 x}}{2}\) | \(11\) |
derivativedivides | \(\frac {{\mathrm e}^{2 x}}{2}-\frac {3 \ln \left ({\mathrm e}^{2 x}\right )}{4}\) | \(15\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 10, normalized size = 0.48 \begin {gather*} -\frac {3}{2} \, x + \frac {1}{2} \, e^{\left (2 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 10, normalized size = 0.48 \begin {gather*} \frac {{\mathrm {e}}^{2\,x}}{2}-\frac {3\,x}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 10, normalized size = 0.48 \begin {gather*} - \frac {3 x}{2} + \frac {e^{2 x}}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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