Optimal. Leaf size=18 \[ -6+x-\frac {e^{2 (4+x)}}{3 \log (5)} \]
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Rubi [A]
time = 0.01, antiderivative size = 17, normalized size of antiderivative = 0.94, number of steps
used = 3, number of rules used = 2, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {12, 2225}
\begin {gather*} x-\frac {e^{2 x+8}}{3 \log (5)} \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 (-2 e^{8+2 x}+3 \log (5)\right ) \, dx}{3 \log (5)}\\ &=x-\frac {2 \int e^{8+2 x} \, dx}{3 \log (5)}\\ &=x-\frac {e^{8+2 x}}{3 \log (5)}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.03, size = 15, normalized size = 0.83 \begin {gather*} x-\frac {e^{8+2 x}}{\log (125)} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.33, size = 21, normalized size = 1.17
method | result | size |
norman | \(x -\frac {{\mathrm e}^{2 x +8}}{3 \ln \left (5\right )}\) | \(15\) |
risch | \(x -\frac {{\mathrm e}^{2 x +8}}{3 \ln \left (5\right )}\) | \(15\) |
default | \(\frac {-{\mathrm e}^{2 x +8}+3 x \ln \left (5\right )}{3 \ln \left (5\right )}\) | \(21\) |
derivativedivides | \(\frac {-2 \,{\mathrm e}^{2 x +8}+3 \ln \left (5\right ) \ln \left ({\mathrm e}^{2 x +8}\right )}{6 \ln \left (5\right )}\) | \(27\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 20, normalized size = 1.11 \begin {gather*} \frac {3 \, x \log \left (5\right ) - e^{\left (2 \, x + 8\right )}}{3 \, \log \left (5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 20, normalized size = 1.11 \begin {gather*} \frac {3 \, x \log \left (5\right ) - e^{\left (2 \, x + 8\right )}}{3 \, \log \left (5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.05, size = 12, normalized size = 0.67 \begin {gather*} x - \frac {e^{2 x + 8}}{3 \log {\left (5 \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 20, normalized size = 1.11 \begin {gather*} \frac {3 \, x \log \left (5\right ) - e^{\left (2 \, x + 8\right )}}{3 \, \log \left (5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.08, size = 14, normalized size = 0.78 \begin {gather*} x-\frac {{\mathrm {e}}^{2\,x}\,{\mathrm {e}}^8}{3\,\ln \left (5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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