Optimal. Leaf size=17 \[ 4 \left (-e^x+\frac {e^{10} x}{\log (5)}\right ) \]
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Rubi [A] time = 0.01, antiderivative size = 16, normalized size of antiderivative = 0.94, number of steps used = 3, number of rules used = 2, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {12, 2194} \begin {gather*} \frac {4 e^{10} x}{\log (5)}-4 e^x \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2194
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \left (4 e^{10}-4 e^x \log (5)\right ) \, dx}{\log (5)}\\ &=\frac {4 e^{10} x}{\log (5)}-4 \int e^x \, dx\\ &=-4 e^x+\frac {4 e^{10} x}{\log (5)}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 16, normalized size = 0.94 \begin {gather*} -4 e^x+\frac {4 e^{10} x}{\log (5)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.57, size = 17, normalized size = 1.00 \begin {gather*} \frac {4 \, {\left (x e^{10} - e^{x} \log \relax (5)\right )}}{\log \relax (5)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.12, size = 17, normalized size = 1.00 \begin {gather*} \frac {4 \, {\left (x e^{10} - e^{x} \log \relax (5)\right )}}{\log \relax (5)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.08, size = 15, normalized size = 0.88
method | result | size |
norman | \(\frac {4 \,{\mathrm e}^{10} x}{\ln \relax (5)}-4 \,{\mathrm e}^{x}\) | \(15\) |
risch | \(\frac {4 \,{\mathrm e}^{10} x}{\ln \relax (5)}-4 \,{\mathrm e}^{x}\) | \(15\) |
default | \(\frac {-4 \,{\mathrm e}^{x} \ln \relax (5)+4 x \,{\mathrm e}^{10}}{\ln \relax (5)}\) | \(18\) |
derivativedivides | \(\frac {-4 \,{\mathrm e}^{x} \ln \relax (5)+4 \,{\mathrm e}^{10} \ln \left ({\mathrm e}^{x}\right )}{\ln \relax (5)}\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.34, size = 17, normalized size = 1.00 \begin {gather*} \frac {4 \, {\left (x e^{10} - e^{x} \log \relax (5)\right )}}{\log \relax (5)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 6.31, size = 14, normalized size = 0.82 \begin {gather*} \frac {4\,x\,{\mathrm {e}}^{10}}{\ln \relax (5)}-4\,{\mathrm {e}}^x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 14, normalized size = 0.82 \begin {gather*} \frac {4 x e^{10}}{\log {\relax (5 )}} - 4 e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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