Optimal. Leaf size=8 \[ \frac{1}{2} \log (x+1) \]
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Rubi [A] time = 0.0008358, antiderivative size = 8, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 7, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.143, Rules used = {31} \[ \frac{1}{2} \log (x+1) \]
Antiderivative was successfully verified.
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Rule 31
Rubi steps
\begin{align*} \int \frac{1}{2+2 x} \, dx &=\frac{1}{2} \log (1+x)\\ \end{align*}
Mathematica [A] time = 0.0011513, size = 10, normalized size = 1.25 \[ \frac{1}{2} \log (2 x+2) \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 9, normalized size = 1.1 \begin{align*}{\frac{\ln \left ( 2+2\,x \right ) }{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.0238, size = 8, normalized size = 1. \begin{align*} \frac{1}{2} \, \log \left (x + 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.53517, size = 22, normalized size = 2.75 \begin{align*} \frac{1}{2} \, \log \left (x + 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.066004, size = 7, normalized size = 0.88 \begin{align*} \frac{\log{\left (2 x + 2 \right )}}{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.16433, size = 9, normalized size = 1.12 \begin{align*} \frac{1}{2} \, \log \left ({\left | x + 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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