Optimal. Leaf size=27 \[ 5 \left (-4+x-2 \left (5-x+\log \left (\left (-\frac {9 x}{2}+\frac {\log (x)}{4}\right )^2\right )\right )\right ) \]
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Rubi [A]
time = 0.23, antiderivative size = 15, normalized size of antiderivative = 0.56, number of steps
used = 6, number of rules used = 5, integrand size = 28, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.179, Rules used = {2641, 6873, 12,
6874, 6816} \begin {gather*} 15 x-20 \log (18 x-\log (x)) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2641
Rule 6816
Rule 6873
Rule 6874
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-20+360 x-270 x^2+15 x \log (x)}{x (-18 x+\log (x))} \, dx\\ &=\int \frac {5 \left (4-72 x+54 x^2-3 x \log (x)\right )}{x (18 x-\log (x))} \, dx\\ &=5 \int \frac {4-72 x+54 x^2-3 x \log (x)}{x (18 x-\log (x))} \, dx\\ &=5 \int \left (3-\frac {4 (-1+18 x)}{x (18 x-\log (x))}\right ) \, dx\\ &=15 x-20 \int \frac {-1+18 x}{x (18 x-\log (x))} \, dx\\ &=15 x-20 \log (18 x-\log (x))\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.03, size = 17, normalized size = 0.63 \begin {gather*} 5 (3 x-4 \log (18 x-\log (x))) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.24, size = 14, normalized size = 0.52
method | result | size |
default | \(15 x -20 \ln \left (\ln \left (x \right )-18 x \right )\) | \(14\) |
risch | \(15 x -20 \ln \left (\ln \left (x \right )-18 x \right )\) | \(14\) |
norman | \(15 x -20 \ln \left (18 x -\ln \left (x \right )\right )\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 13, normalized size = 0.48 \begin {gather*} 15 \, x - 20 \, \log \left (-18 \, x + \log \left (x\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.33, size = 13, normalized size = 0.48 \begin {gather*} 15 \, x - 20 \, \log \left (-18 \, x + \log \left (x\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.05, size = 12, normalized size = 0.44 \begin {gather*} 15 x - 20 \log {\left (- 18 x + \log {\left (x \right )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.38, size = 15, normalized size = 0.56 \begin {gather*} 15 \, x - 20 \, \log \left (18 \, x - \log \left (x\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.97, size = 15, normalized size = 0.56 \begin {gather*} 15\,x-20\,\ln \left (18\,x-\ln \left (x\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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