Optimal. Leaf size=31 \[ x-\log (3)+\left (\left (2+e^3\right )^2-(5-x)^2+\frac {x}{5}\right ) \log (4) \]
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Rubi [A] time = 0.01, antiderivative size = 15, normalized size of antiderivative = 0.48, number of steps used = 2, number of rules used = 1, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.071, Rules used = {12} \begin {gather*} x-\frac {1}{100} (51-10 x)^2 \log (4) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{5} \int (5+(51-10 x) \log (4)) \, dx\\ &=x-\frac {1}{100} (51-10 x)^2 \log (4)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 16, normalized size = 0.52 \begin {gather*} x+\frac {51}{5} x \log (4)-x^2 \log (4) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.64, size = 15, normalized size = 0.48 \begin {gather*} -\frac {2}{5} \, {\left (5 \, x^{2} - 51 \, x\right )} \log \relax (2) + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.31, size = 15, normalized size = 0.48 \begin {gather*} -\frac {2}{5} \, {\left (5 \, x^{2} - 51 \, x\right )} \log \relax (2) + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 15, normalized size = 0.48
method | result | size |
gosper | \(-\frac {x \left (10 x \ln \relax (2)-102 \ln \relax (2)-5\right )}{5}\) | \(15\) |
risch | \(-2 x^{2} \ln \relax (2)+\frac {102 x \ln \relax (2)}{5}+x\) | \(15\) |
default | \(\frac {2 \ln \relax (2) \left (-5 x^{2}+51 x \right )}{5}+x\) | \(16\) |
norman | \(\left (\frac {102 \ln \relax (2)}{5}+1\right ) x -2 x^{2} \ln \relax (2)\) | \(17\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.62, size = 15, normalized size = 0.48 \begin {gather*} -\frac {2}{5} \, {\left (5 \, x^{2} - 51 \, x\right )} \log \relax (2) + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.56, size = 13, normalized size = 0.42 \begin {gather*} x-\frac {\ln \relax (2)\,{\left (10\,x-51\right )}^2}{50} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.05, size = 17, normalized size = 0.55 \begin {gather*} - 2 x^{2} \log {\relax (2 )} + x \left (1 + \frac {102 \log {\relax (2 )}}{5}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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