Optimal. Leaf size=15 \[ 1+x+\frac {(-5+x) x}{5 \log (4)} \]
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Rubi [A]
time = 0.00, antiderivative size = 22, normalized size of antiderivative = 1.47, number of steps
used = 1, number of rules used = 1, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.059, Rules used = {9}
\begin {gather*} \frac {(2 x-5 (1-\log (4)))^2}{20 \log (4)} \end {gather*}
Antiderivative was successfully verified.
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Rule 9
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {(2 x-5 (1-\log (4)))^2}{20 \log (4)}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 20, normalized size = 1.33 \begin {gather*} \frac {-5 x+x^2+5 x \log (4)}{5 \log (4)} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.02, size = 19, normalized size = 1.27
method | result | size |
gosper | \(\frac {x \left (x +10 \ln \left (2\right )-5\right )}{10 \ln \left (2\right )}\) | \(15\) |
default | \(\frac {10 x \ln \left (2\right )+x^{2}-5 x}{10 \ln \left (2\right )}\) | \(19\) |
risch | \(x +\frac {x^{2}}{10 \ln \left (2\right )}-\frac {x}{2 \ln \left (2\right )}\) | \(19\) |
norman | \(\frac {x^{2}}{10 \ln \left (2\right )}+\frac {\left (2 \ln \left (2\right )-1\right ) x}{2 \ln \left (2\right )}\) | \(24\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.25, size = 18, normalized size = 1.20 \begin {gather*} \frac {x^{2} + 10 \, x \log \left (2\right ) - 5 \, x}{10 \, \log \left (2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 18, normalized size = 1.20 \begin {gather*} \frac {x^{2} + 10 \, x \log \left (2\right ) - 5 \, x}{10 \, \log \left (2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 20, normalized size = 1.33 \begin {gather*} \frac {x^{2}}{10 \log {\left (2 \right )}} + \frac {x \left (-1 + 2 \log {\left (2 \right )}\right )}{2 \log {\left (2 \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.43, size = 18, normalized size = 1.20 \begin {gather*} \frac {x^{2} + 10 \, x \log \left (2\right ) - 5 \, x}{10 \, \log \left (2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 6.17, size = 15, normalized size = 1.00 \begin {gather*} \frac {5\,{\left (\frac {x}{5}+\ln \left (2\right )-\frac {1}{2}\right )}^2}{2\,\ln \left (2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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