Optimal. Leaf size=18 \[ -\frac {\text {Ei}(1+t)}{e}+e^t \log (1+t) \]
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Rubi [A]
time = 0.01, 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 = {2225, 2634,
2209} \begin {gather*} e^t \log (t+1)-\frac {\text {ExpIntegralEi}(t+1)}{e} \end {gather*}
Antiderivative was successfully verified.
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Rule 2209
Rule 2225
Rule 2634
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 \begin {gather*} -\frac {\text {Ei}(1+t)}{e}+e^t \log (1+t) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.02, size = 19, normalized size = 1.06
method | result | size |
risch | \({\mathrm e}^{t} \ln \left (1+t \right )+{\mathrm e}^{-1} \expIntegral \left (1, -1-t \right )\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 3.45, size = 18, normalized size = 1.00 \begin {gather*} e^{\left (-1\right )} E_{1}\left (-t - 1\right ) + e^{t} \log \left (t + 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.83, size = 19, normalized size = 1.06 \begin {gather*} {\left (e^{\left (t + 1\right )} \log \left (t + 1\right ) - {\rm Ei}\left (t + 1\right )\right )} e^{\left (-1\right )} \end {gather*}
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 \begin {gather*} \int e^{t} \log {\left (t + 1 \right )}\, dt \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.46, size = 16, normalized size = 0.89 \begin {gather*} -{\rm Ei}\left (t + 1\right ) e^{\left (-1\right )} + e^{t} \log \left (t + 1\right ) \end {gather*}
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 \begin {gather*} \int \ln \left (t+1\right )\,{\mathrm {e}}^t \,d t \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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