Optimal. Leaf size=13 \[ \frac {\log \left (12 \left (x+x^2\right )\right )}{\log ^2(4)} \]
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Rubi [A] time = 0.01, antiderivative size = 11, normalized size of antiderivative = 0.85, number of steps used = 2, number of rules used = 2, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.118, Rules used = {12, 628} \begin {gather*} \frac {\log \left (x^2+x\right )}{\log ^2(4)} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 628
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \frac {1+2 x}{x+x^2} \, dx}{\log ^2(4)}\\ &=\frac {\log \left (x+x^2\right )}{\log ^2(4)}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 12, normalized size = 0.92 \begin {gather*} \frac {\log (x)+\log (1+x)}{\log ^2(4)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.85, size = 12, normalized size = 0.92 \begin {gather*} \frac {\log \left (x^{2} + x\right )}{4 \, \log \relax (2)^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.21, size = 13, normalized size = 1.00 \begin {gather*} \frac {\log \left ({\left | x^{2} + x \right |}\right )}{4 \, \log \relax (2)^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.56, size = 13, normalized size = 1.00
method | result | size |
derivativedivides | \(\frac {\ln \left (x^{2}+x \right )}{4 \ln \relax (2)^{2}}\) | \(13\) |
default | \(\frac {\ln \left (\left (x +1\right ) x \right )}{4 \ln \relax (2)^{2}}\) | \(13\) |
risch | \(\frac {\ln \left (x^{2}+x \right )}{4 \ln \relax (2)^{2}}\) | \(13\) |
norman | \(\frac {\ln \relax (x )}{4 \ln \relax (2)^{2}}+\frac {\ln \left (x +1\right )}{4 \ln \relax (2)^{2}}\) | \(20\) |
meijerg | \(\frac {\ln \relax (x )-\ln \left (x +1\right )}{4 \ln \relax (2)^{2}}+\frac {\ln \left (x +1\right )}{2 \ln \relax (2)^{2}}\) | \(27\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.35, size = 12, normalized size = 0.92 \begin {gather*} \frac {\log \left (x^{2} + x\right )}{4 \, \log \relax (2)^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.11, size = 12, normalized size = 0.92 \begin {gather*} \frac {\ln \left (x\,\left (x+1\right )\right )}{4\,{\ln \relax (2)}^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.17, size = 12, normalized size = 0.92 \begin {gather*} \frac {\log {\left (x^{2} + x \right )}}{4 \log {\relax (2 )}^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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