Optimal. Leaf size=18 \[ e^t \log (t+1)-\frac {\text {Ei}(t+1)}{e} \]
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Rubi [A] time = 0.02, antiderivative size = 18, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 3, integrand size = 8, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.375, Rules used = {2194, 2554, 2178} \[ e^t \log (t+1)-\frac {\text {ExpIntegralEi}(t+1)}{e} \]
Antiderivative was successfully verified.
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Rule 2178
Rule 2194
Rule 2554
Rubi steps
\begin {align*} \int e^t \log (1+t) \, dt &=e^t \log (1+t)-\int \frac {e^t}{1+t} \, dt\\ &=-\frac {\text {Ei}(1+t)}{e}+e^t \log (1+t)\\ \end {align*}
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Mathematica [A] time = 0.01, size = 18, normalized size = 1.00 \[ e^t \log (t+1)-\frac {\text {Ei}(t+1)}{e} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.41, size = 19, normalized size = 1.06 \[ {\left (e^{\left (t + 1\right )} \log \left (t + 1\right ) - {\rm Ei}\left (t + 1\right )\right )} e^{\left (-1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.01, size = 16, normalized size = 0.89 \[ -{\rm Ei}\left (t + 1\right ) e^{\left (-1\right )} + e^{t} \log \left (t + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 19, normalized size = 1.06 \[ {\mathrm e}^{t} \ln \left (t +1\right )+{\mathrm e}^{-1} \Ei \left (1, -t -1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.77, size = 18, normalized size = 1.00 \[ e^{\left (-1\right )} E_{1}\left (-t - 1\right ) + e^{t} \log \left (t + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.06 \[ \int \ln \left (t+1\right )\,{\mathrm {e}}^t \,d t \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int e^{t} \log {\left (t + 1 \right )}\, dt \]
Verification of antiderivative is not currently implemented for this CAS.
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