Optimal. Leaf size=17 \[ 4+2 x-\frac {10 x}{3 e^4 \log (5)} \]
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Rubi [A]
time = 0.00, antiderivative size = 16, normalized size of antiderivative = 0.94, number of steps
used = 1, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {8}
\begin {gather*} \frac {2}{3} x \left (3-\frac {5}{e^4 \log (5)}\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 8
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {2}{3} x \left (3-\frac {5}{e^4 \log (5)}\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 16, normalized size = 0.94 \begin {gather*} 2 x-\frac {10 x}{3 e^4 \log (5)} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.14, size = 20, normalized size = 1.18
method | result | size |
risch | \(2 x \,{\mathrm e}^{-4} {\mathrm e}^{4}-\frac {10 x \,{\mathrm e}^{-4}}{3 \ln \left (5\right )}\) | \(18\) |
default | \(\frac {x \left (6 \,{\mathrm e}^{4} \ln \left (5\right )-10\right ) {\mathrm e}^{-4}}{3 \ln \left (5\right )}\) | \(20\) |
norman | \(\frac {2 \left (3 \,{\mathrm e}^{4} \ln \left (5\right )-5\right ) {\mathrm e}^{-4} x}{3 \ln \left (5\right )}\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 17, normalized size = 1.00 \begin {gather*} \frac {2 \, {\left (3 \, e^{4} \log \left (5\right ) - 5\right )} x e^{\left (-4\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 = 0.40, size = 19, normalized size = 1.12 \begin {gather*} \frac {2 \, {\left (3 \, x e^{4} \log \left (5\right ) - 5 \, x\right )} e^{\left (-4\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 = 0.00, size = 19, normalized size = 1.12 \begin {gather*} \frac {x \left (- \frac {10}{3} + 2 e^{4} \log {\left (5 \right )}\right )}{e^{4} \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 = 17, normalized size = 1.00 \begin {gather*} \frac {2 \, {\left (3 \, e^{4} \log \left (5\right ) - 5\right )} x e^{\left (-4\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 = 0.00, size = 16, normalized size = 0.94 \begin {gather*} \frac {x\,{\mathrm {e}}^{-4}\,\left (2\,{\mathrm {e}}^4\,\ln \left (5\right )-\frac {10}{3}\right )}{\ln \left (5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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