Optimal. Leaf size=13 \[ \log \left (-\frac {25}{2} e^x (1+x)^2\right ) \]
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Rubi [A]
time = 0.00, antiderivative size = 8, normalized size of antiderivative = 0.62, number of steps
used = 2, number of rules used = 1, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {45}
\begin {gather*} x+2 \log (x+1) \end {gather*}
Antiderivative was successfully verified.
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Rule 45
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (1+\frac {2}{1+x}\right ) \, dx\\ &=x+2 \log (1+x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 8, normalized size = 0.62 \begin {gather*} x+2 \log (1+x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.15, size = 9, normalized size = 0.69
method | result | size |
default | \(x +2 \ln \left (x +1\right )\) | \(9\) |
norman | \(x +2 \ln \left (x +1\right )\) | \(9\) |
meijerg | \(x +2 \ln \left (x +1\right )\) | \(9\) |
risch | \(x +2 \ln \left (x +1\right )\) | \(9\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 8, normalized size = 0.62 \begin {gather*} x + 2 \, \log \left (x + 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 8, normalized size = 0.62 \begin {gather*} x + 2 \, \log \left (x + 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.02, size = 7, normalized size = 0.54 \begin {gather*} x + 2 \log {\left (x + 1 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 9, normalized size = 0.69 \begin {gather*} x + 2 \, \log \left ({\left | x + 1 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 8, normalized size = 0.62 \begin {gather*} x+2\,\ln \left (x+1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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