Optimal. Leaf size=23 \[ \frac {1-e^4+e^{-1-4 (-6+x)+x}+x}{\log (16)} \]
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Rubi [A]
time = 0.01, antiderivative size = 19, normalized size of antiderivative = 0.83, number of steps
used = 3, number of rules used = 2, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {12, 2225}
\begin {gather*} \frac {x}{\log (16)}+\frac {e^{23-3 x}}{\log (16)} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2225
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \left (1-3 e^{23-3 x}\right ) \, dx}{\log (16)}\\ &=\frac {x}{\log (16)}-\frac {3 \int e^{23-3 x} \, dx}{\log (16)}\\ &=\frac {e^{23-3 x}}{\log (16)}+\frac {x}{\log (16)}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 14, normalized size = 0.61 \begin {gather*} \frac {e^{23-3 x}+x}{\log (16)} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.29, size = 15, normalized size = 0.65
method | result | size |
default | \(\frac {x +{\mathrm e}^{-3 x +23}}{4 \ln \left (2\right )}\) | \(15\) |
norman | \(\frac {x}{4 \ln \left (2\right )}+\frac {{\mathrm e}^{-3 x +23}}{4 \ln \left (2\right )}\) | \(21\) |
risch | \(\frac {x}{4 \ln \left (2\right )}+\frac {{\mathrm e}^{-3 x +23}}{4 \ln \left (2\right )}\) | \(21\) |
derivativedivides | \(-\frac {-3 \,{\mathrm e}^{-3 x +23}+\ln \left ({\mathrm e}^{-3 x +23}\right )}{12 \ln \left (2\right )}\) | \(23\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 14, normalized size = 0.61 \begin {gather*} \frac {x + e^{\left (-3 \, x + 23\right )}}{4 \, \log \left (2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 14, normalized size = 0.61 \begin {gather*} \frac {x + e^{\left (-3 \, x + 23\right )}}{4 \, \log \left (2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 17, normalized size = 0.74 \begin {gather*} \frac {x}{4 \log {\left (2 \right )}} + \frac {e^{23 - 3 x}}{4 \log {\left (2 \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 14, normalized size = 0.61 \begin {gather*} \frac {x + e^{\left (-3 \, x + 23\right )}}{4 \, \log \left (2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.07, size = 18, normalized size = 0.78 \begin {gather*} \frac {3\,x+3\,{\mathrm {e}}^{23-3\,x}}{12\,\ln \left (2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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