Optimal. Leaf size=25 \[ 5 \left (4 e^5+4 \left (4-e^{2 x}\right )\right )-\frac {x}{2} \]
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Rubi [A] time = 0.00, antiderivative size = 13, normalized size of antiderivative = 0.52, 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 {x}{2}-20 e^{2 x} \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 (-1-80 e^{2 x}\right ) \, dx\\ &=-\frac {x}{2}-40 \int e^{2 x} \, dx\\ &=-20 e^{2 x}-\frac {x}{2}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 13, normalized size = 0.52 \begin {gather*} -20 e^{2 x}-\frac {x}{2} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.99, size = 10, normalized size = 0.40 \begin {gather*} -\frac {1}{2} \, x - 20 \, e^{\left (2 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.97, size = 10, normalized size = 0.40 \begin {gather*} -\frac {1}{2} \, x - 20 \, 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 = 11, normalized size = 0.44
method | result | size |
default | \(-\frac {x}{2}-20 \,{\mathrm e}^{2 x}\) | \(11\) |
norman | \(-\frac {x}{2}-20 \,{\mathrm e}^{2 x}\) | \(11\) |
risch | \(-\frac {x}{2}-20 \,{\mathrm e}^{2 x}\) | \(11\) |
derivativedivides | \(-20 \,{\mathrm e}^{2 x}-\frac {\ln \left ({\mathrm e}^{x}\right )}{2}\) | \(13\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 10, normalized size = 0.40 \begin {gather*} -\frac {1}{2} \, x - 20 \, e^{\left (2 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 10, normalized size = 0.40 \begin {gather*} -\frac {x}{2}-20\,{\mathrm {e}}^{2\,x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 10, normalized size = 0.40 \begin {gather*} - \frac {x}{2} - 20 e^{2 x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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