Optimal. Leaf size=21 \[ 2+9 x^2 \left (1-4 \log \left (-x+4 x^2\right )\right ) \]
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Rubi [A] time = 0.19, antiderivative size = 20, normalized size of antiderivative = 0.95, number of steps used = 10, number of rules used = 7, integrand size = 37, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.189, Rules used = {6741, 12, 6742, 77, 2495, 30, 43} \begin {gather*} 9 x^2-36 x^2 \log (-((1-4 x) x)) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 30
Rule 43
Rule 77
Rule 2495
Rule 6741
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {18 x (-1+12 x-4 \log (x (-1+4 x))+16 x \log (x (-1+4 x)))}{1-4 x} \, dx\\ &=18 \int \frac {x (-1+12 x-4 \log (x (-1+4 x))+16 x \log (x (-1+4 x)))}{1-4 x} \, dx\\ &=18 \int \left (\frac {x (-1+12 x)}{1-4 x}-4 x \log (x (-1+4 x))\right ) \, dx\\ &=18 \int \frac {x (-1+12 x)}{1-4 x} \, dx-72 \int x \log (x (-1+4 x)) \, dx\\ &=-36 x^2 \log (-((1-4 x) x))+18 \int \left (-\frac {1}{2}-3 x-\frac {1}{2 (-1+4 x)}\right ) \, dx+36 \int x \, dx+144 \int \frac {x^2}{-1+4 x} \, dx\\ &=-9 x-9 x^2-\frac {9}{4} \log (1-4 x)-36 x^2 \log (-((1-4 x) x))+144 \int \left (\frac {1}{16}+\frac {x}{4}+\frac {1}{16 (-1+4 x)}\right ) \, dx\\ &=9 x^2-36 x^2 \log (-((1-4 x) x))\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.03, size = 23, normalized size = 1.10 \begin {gather*} -18 \left (-\frac {x^2}{2}+2 x^2 \log (x (-1+4 x))\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.77, size = 21, normalized size = 1.00 \begin {gather*} -36 \, x^{2} \log \left (4 \, x^{2} - x\right ) + 9 \, x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 21, normalized size = 1.00 \begin {gather*} -36 \, x^{2} \log \left (4 \, x^{2} - x\right ) + 9 \, x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.46, size = 22, normalized size = 1.05
method | result | size |
default | \(-36 \ln \left (4 x^{2}-x \right ) x^{2}+9 x^{2}\) | \(22\) |
norman | \(-36 \ln \left (4 x^{2}-x \right ) x^{2}+9 x^{2}\) | \(22\) |
risch | \(-36 \ln \left (4 x^{2}-x \right ) x^{2}+9 x^{2}\) | \(22\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.66, size = 36, normalized size = 1.71 \begin {gather*} -36 \, x^{2} \log \relax (x) + 9 \, x^{2} - \frac {9}{4} \, {\left (16 \, x^{2} - 1\right )} \log \left (4 \, x - 1\right ) - \frac {9}{4} \, \log \left (4 \, x - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.79, size = 19, normalized size = 0.90 \begin {gather*} -9\,x^2\,\left (4\,\ln \left (4\,x^2-x\right )-1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.14, size = 17, normalized size = 0.81 \begin {gather*} - 36 x^{2} \log {\left (4 x^{2} - x \right )} + 9 x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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