Optimal. Leaf size=31 \[ \frac {5 x \log (2) \left (x-\frac {(2+x)^2-\log (5)}{x}\right )}{-5+2 x^2} \]
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Rubi [A]
time = 0.02, antiderivative size = 22, normalized size of antiderivative = 0.71, number of steps
used = 3, number of rules used = 3, integrand size = 36, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.083, Rules used = {28, 1828, 8}
\begin {gather*} \frac {5 \log (2) (4 x+4-\log (5))}{5-2 x^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 8
Rule 28
Rule 1828
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=4 \int \frac {\left (100+80 x+40 x^2\right ) \log (2)-20 x \log (2) \log (5)}{\left (-10+4 x^2\right )^2} \, dx\\ &=\frac {5 \log (2) (4+4 x-\log (5))}{5-2 x^2}+\frac {\int 0 \, dx}{5}\\ &=\frac {5 \log (2) (4+4 x-\log (5))}{5-2 x^2}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 20, normalized size = 0.65 \begin {gather*} \frac {20 \log (2) (-4-4 x+\log (5))}{-20+8 x^2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.03, size = 21, normalized size = 0.68
method | result | size |
gosper | \(\frac {5 \ln \left (2\right ) \left (\ln \left (5\right )-4 x -4\right )}{2 x^{2}-5}\) | \(21\) |
default | \(-\frac {20 \ln \left (2\right ) \left (\frac {x}{2}-\frac {\ln \left (5\right )}{8}+\frac {1}{2}\right )}{x^{2}-\frac {5}{2}}\) | \(21\) |
risch | \(\frac {-10 x \ln \left (2\right )+\frac {5 \ln \left (2\right ) \ln \left (5\right )}{2}-10 \ln \left (2\right )}{x^{2}-\frac {5}{2}}\) | \(25\) |
norman | \(\frac {-20 x \ln \left (2\right )+5 \ln \left (2\right ) \ln \left (5\right )-20 \ln \left (2\right )}{2 x^{2}-5}\) | \(27\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.25, size = 27, normalized size = 0.87 \begin {gather*} -\frac {5 \, {\left (4 \, x \log \left (2\right ) - \log \left (5\right ) \log \left (2\right ) + 4 \, \log \left (2\right )\right )}}{2 \, x^{2} - 5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 25, normalized size = 0.81 \begin {gather*} -\frac {5 \, {\left (4 \, {\left (x + 1\right )} \log \left (2\right ) - \log \left (5\right ) \log \left (2\right )\right )}}{2 \, x^{2} - 5} \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 = 0.84 \begin {gather*} \frac {- 20 x \log {\left (2 \right )} - 20 \log {\left (2 \right )} + 5 \log {\left (2 \right )} \log {\left (5 \right )}}{2 x^{2} - 5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 27, normalized size = 0.87 \begin {gather*} -\frac {5 \, {\left (4 \, x \log \left (2\right ) - \log \left (5\right ) \log \left (2\right ) + 4 \, \log \left (2\right )\right )}}{2 \, x^{2} - 5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.13, size = 22, normalized size = 0.71 \begin {gather*} -\frac {5\,\ln \left (2\right )\,\left (4\,x-\ln \left (5\right )+4\right )}{2\,x^2-5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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