Optimal. Leaf size=12 \[ \frac {1}{2} \log \left (2 x+x^2\right ) \]
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Rubi [A]
time = 0.00, antiderivative size = 12, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {642}
\begin {gather*} \frac {1}{2} \log \left (x^2+2 x\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 642
Rubi steps
\begin {align*} \int \frac {1+x}{2 x+x^2} \, dx &=\frac {1}{2} \log \left (2 x+x^2\right )\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 15, normalized size = 1.25 \begin {gather*} \frac {\log (x)}{2}+\frac {1}{2} \log (2+x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.40, size = 9, normalized size = 0.75
method | result | size |
default | \(\frac {\ln \left (x \left (2+x \right )\right )}{2}\) | \(9\) |
risch | \(\frac {\ln \left (x^{2}+2 x \right )}{2}\) | \(11\) |
norman | \(\frac {\ln \left (x \right )}{2}+\frac {\ln \left (2+x \right )}{2}\) | \(12\) |
meijerg | \(\frac {\ln \left (\frac {x}{2}+1\right )}{2}+\frac {\ln \left (x \right )}{2}-\frac {\ln \left (2\right )}{2}\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 10, normalized size = 0.83 \begin {gather*} \frac {1}{2} \, \log \left (x^{2} + 2 \, x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 1.87, size = 10, normalized size = 0.83 \begin {gather*} \frac {1}{2} \, \log \left (x^{2} + 2 \, x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.02, size = 8, normalized size = 0.67 \begin {gather*} \frac {\log {\left (x^{2} + 2 x \right )}}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.02, size = 13, normalized size = 1.08 \begin {gather*} \frac {1}{2} \, \log \left (2 \, {\left | \frac {1}{2} \, x^{2} + x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.18, size = 8, normalized size = 0.67 \begin {gather*} \frac {\ln \left (x\,\left (x+2\right )\right )}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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