Optimal. Leaf size=26 \[ x+\frac {-x+\log \left (5+x+x (3+x)+\frac {\log (2)}{25}\right )}{\log (2)} \]
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Rubi [A] time = 0.08, antiderivative size = 32, normalized size of antiderivative = 1.23, number of steps used = 4, number of rules used = 3, integrand size = 48, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {1984, 1657, 628} \begin {gather*} \frac {\log \left (25 x^2+100 x+125+\log (2)\right )}{\log (2)}-\frac {x (1-\log (2))}{\log (2)} \end {gather*}
Antiderivative was successfully verified.
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Rule 628
Rule 1657
Rule 1984
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-25-25 x^2 (1-\log (2))+124 \log (2)+\log ^2(2)-50 x (1-\log (4))}{100 x \log (2)+25 x^2 \log (2)+\log (2) (125+\log (2))} \, dx\\ &=\int \left (1-\frac {1}{\log (2)}+\frac {50 (2+x)}{100 x \log (2)+25 x^2 \log (2)+\log (2) (125+\log (2))}\right ) \, dx\\ &=-\frac {x (1-\log (2))}{\log (2)}+50 \int \frac {2+x}{100 x \log (2)+25 x^2 \log (2)+\log (2) (125+\log (2))} \, dx\\ &=-\frac {x (1-\log (2))}{\log (2)}+\frac {\log \left (125+100 x+25 x^2+\log (2)\right )}{\log (2)}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.03, size = 25, normalized size = 0.96 \begin {gather*} \frac {x (-1+\log (2))+\log \left (125+100 x+25 x^2+\log (2)\right )}{\log (2)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.79, size = 26, normalized size = 1.00 \begin {gather*} \frac {x \log \relax (2) - x + \log \left (25 \, x^{2} + 100 \, x + \log \relax (2) + 125\right )}{\log \relax (2)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.24, size = 32, normalized size = 1.23 \begin {gather*} \frac {x \log \relax (2) - x}{\log \relax (2)} + \frac {\log \left (25 \, x^{2} + 100 \, x + \log \relax (2) + 125\right )}{\log \relax (2)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.76, size = 27, normalized size = 1.04
method | result | size |
default | \(\frac {x \ln \relax (2)-x +\ln \left (25 x^{2}+\ln \relax (2)+100 x +125\right )}{\ln \relax (2)}\) | \(27\) |
risch | \(x -\frac {x}{\ln \relax (2)}+\frac {\ln \left (25 x^{2}+\ln \relax (2)+100 x +125\right )}{\ln \relax (2)}\) | \(28\) |
norman | \(\frac {\left (\ln \relax (2)-1\right ) x}{\ln \relax (2)}+\frac {\ln \left (25 x^{2}+\ln \relax (2)+100 x +125\right )}{\ln \relax (2)}\) | \(30\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.59, size = 29, normalized size = 1.12 \begin {gather*} \frac {x {\left (\log \relax (2) - 1\right )}}{\log \relax (2)} + \frac {\log \left (25 \, x^{2} + 100 \, x + \log \relax (2) + 125\right )}{\log \relax (2)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.16, size = 32, normalized size = 1.23 \begin {gather*} \frac {\ln \left (x^2+4\,x+\frac {\ln \relax (2)}{25}+5\right )}{\ln \relax (2)}+\frac {x\,\left (25\,\ln \relax (2)-25\right )}{25\,\ln \relax (2)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.23, size = 26, normalized size = 1.00 \begin {gather*} - x \left (-1 + \frac {1}{\log {\relax (2 )}}\right ) + \frac {\log {\left (25 x^{2} + 100 x + \log {\relax (2 )} + 125 \right )}}{\log {\relax (2 )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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