Optimal. Leaf size=24 \[ -2+\frac {1+x+\frac {5}{-5+2 x}+5 (3+\log (4))}{x} \]
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Rubi [A]
time = 0.07, antiderivative size = 19, normalized size of antiderivative = 0.79, number of steps
used = 4, number of rules used = 3, integrand size = 42, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.071, Rules used = {1608, 27, 1834}
\begin {gather*} \frac {5 (3+\log (4))}{x}-\frac {2}{5-2 x} \end {gather*}
Antiderivative was successfully verified.
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Rule 27
Rule 1608
Rule 1834
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-375+300 x-64 x^2+\left (-125+100 x-20 x^2\right ) \log (4)}{x^2 \left (25-20 x+4 x^2\right )} \, dx\\ &=\int \frac {-375+300 x-64 x^2+\left (-125+100 x-20 x^2\right ) \log (4)}{x^2 (-5+2 x)^2} \, dx\\ &=\int \left (-\frac {4}{(-5+2 x)^2}-\frac {5 (3+\log (4))}{x^2}\right ) \, dx\\ &=-\frac {2}{5-2 x}+\frac {5 (3+\log (4))}{x}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.02, size = 19, normalized size = 0.79 \begin {gather*} \frac {2}{-5+2 x}+\frac {5 (3+\log (4))}{x} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.04, size = 22, normalized size = 0.92
method | result | size |
default | \(\frac {2}{2 x -5}-\frac {-10 \ln \left (2\right )-15}{x}\) | \(22\) |
gosper | \(\frac {20 x \ln \left (2\right )-50 \ln \left (2\right )+32 x -75}{x \left (2 x -5\right )}\) | \(26\) |
norman | \(\frac {\left (20 \ln \left (2\right )+32\right ) x -50 \ln \left (2\right )-75}{x \left (2 x -5\right )}\) | \(26\) |
risch | \(\frac {2 \left (10 \ln \left (2\right )+16\right ) x -50 \ln \left (2\right )-75}{x \left (2 x -5\right )}\) | \(27\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 27, normalized size = 1.12 \begin {gather*} \frac {4 \, x {\left (5 \, \log \left (2\right ) + 8\right )} - 50 \, \log \left (2\right ) - 75}{2 \, x^{2} - 5 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.40, size = 26, normalized size = 1.08 \begin {gather*} \frac {10 \, {\left (2 \, x - 5\right )} \log \left (2\right ) + 32 \, x - 75}{2 \, x^{2} - 5 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.19, size = 26, normalized size = 1.08 \begin {gather*} - \frac {x \left (-32 - 20 \log {\left (2 \right )}\right ) + 50 \log {\left (2 \right )} + 75}{2 x^{2} - 5 x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 26, normalized size = 1.08 \begin {gather*} \frac {20 \, x \log \left (2\right ) + 32 \, x - 50 \, \log \left (2\right ) - 75}{2 \, x^{2} - 5 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.09, size = 20, normalized size = 0.83 \begin {gather*} \frac {10\,\ln \left (2\right )+15}{x}+\frac {2}{2\,x-5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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