Optimal. Leaf size=28 \[ \frac {1}{3} \left (2 x+\frac {1}{3} (2+\log (x)) (256-\log (x+10 (3+x)))\right ) \]
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Rubi [A]
time = 0.26, antiderivative size = 44, normalized size of antiderivative = 1.57, number of steps
used = 11, number of rules used = 6, integrand size = 39, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {1607, 6874,
907, 2354, 2438, 2439} \begin {gather*} \frac {2 x}{3}-\frac {1}{9} \log \left (\frac {11 x}{30}+1\right ) \log (x)-\frac {1}{9} \log (30) \log (x)+\frac {256 \log (x)}{9}-\frac {2}{9} \log (11 x+30) \end {gather*}
Antiderivative was successfully verified.
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Rule 907
Rule 1607
Rule 2354
Rule 2438
Rule 2439
Rule 6874
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {7680+2974 x+66 x^2-11 x \log (x)+(-30-11 x) \log (30+11 x)}{x (270+99 x)} \, dx\\ &=\int \left (\frac {7680+2974 x+66 x^2-11 x \log (x)}{9 x (30+11 x)}-\frac {\log (30+11 x)}{9 x}\right ) \, dx\\ &=\frac {1}{9} \int \frac {7680+2974 x+66 x^2-11 x \log (x)}{x (30+11 x)} \, dx-\frac {1}{9} \int \frac {\log (30+11 x)}{x} \, dx\\ &=-\frac {1}{9} \log (30) \log (x)-\frac {1}{9} \int \frac {\log \left (1+\frac {11 x}{30}\right )}{x} \, dx+\frac {1}{9} \int \left (\frac {2 \left (3840+1487 x+33 x^2\right )}{x (30+11 x)}-\frac {11 \log (x)}{30+11 x}\right ) \, dx\\ &=-\frac {1}{9} \log (30) \log (x)+\frac {1}{9} \text {Li}_2\left (-\frac {11 x}{30}\right )+\frac {2}{9} \int \frac {3840+1487 x+33 x^2}{x (30+11 x)} \, dx-\frac {11}{9} \int \frac {\log (x)}{30+11 x} \, dx\\ &=-\frac {1}{9} \log (30) \log (x)-\frac {1}{9} \log \left (1+\frac {11 x}{30}\right ) \log (x)+\frac {1}{9} \text {Li}_2\left (-\frac {11 x}{30}\right )+\frac {1}{9} \int \frac {\log \left (1+\frac {11 x}{30}\right )}{x} \, dx+\frac {2}{9} \int \left (3+\frac {128}{x}-\frac {11}{30+11 x}\right ) \, dx\\ &=\frac {2 x}{3}+\frac {256 \log (x)}{9}-\frac {1}{9} \log (30) \log (x)-\frac {1}{9} \log \left (1+\frac {11 x}{30}\right ) \log (x)-\frac {2}{9} \log (30+11 x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.04, size = 30, normalized size = 1.07 \begin {gather*} \frac {1}{9} \left (6 x-(-256+\log (30)) \log (x)-\log \left (1+\frac {11 x}{30}\right ) (2+\log (x))\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(47\) vs.
\(2(20)=40\).
time = 0.24, size = 48, normalized size = 1.71
method | result | size |
norman | \(-\frac {2 \ln \left (11 x +30\right )}{9}+\frac {256 \ln \left (x \right )}{9}+\frac {2 x}{3}-\frac {\ln \left (x \right ) \ln \left (11 x +30\right )}{9}\) | \(27\) |
risch | \(-\frac {2 \ln \left (11 x +30\right )}{9}+\frac {256 \ln \left (x \right )}{9}+\frac {2 x}{3}-\frac {\ln \left (x \right ) \ln \left (11 x +30\right )}{9}\) | \(27\) |
default | \(-\frac {\left (\ln \left (11 x +30\right )-\ln \left (\frac {11 x}{30}+1\right )\right ) \ln \left (-\frac {11 x}{30}\right )}{9}-\frac {\ln \left (x \right ) \ln \left (\frac {11 x}{30}+1\right )}{9}+\frac {2 x}{3}+\frac {256 \ln \left (x \right )}{9}-\frac {2 \ln \left (11 x +30\right )}{9}\) | \(48\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 26, normalized size = 0.93 \begin {gather*} -\frac {1}{9} \, \log \left (11 \, x + 30\right ) \log \left (x\right ) + \frac {2}{3} \, x - \frac {2}{9} \, \log \left (11 \, x + 30\right ) + \frac {256}{9} \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.31, size = 20, normalized size = 0.71 \begin {gather*} -\frac {1}{9} \, {\left (\log \left (x\right ) + 2\right )} \log \left (11 \, x + 30\right ) + \frac {2}{3} \, x + \frac {256}{9} \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.12, size = 32, normalized size = 1.14 \begin {gather*} \frac {2 x}{3} - \frac {\log {\left (x \right )} \log {\left (11 x + 30 \right )}}{9} + \frac {256 \log {\left (x \right )}}{9} - \frac {2 \log {\left (x + \frac {30}{11} \right )}}{9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 26, normalized size = 0.93 \begin {gather*} -\frac {1}{9} \, \log \left (11 \, x + 30\right ) \log \left (x\right ) + \frac {2}{3} \, x - \frac {2}{9} \, \log \left (11 \, x + 30\right ) + \frac {256}{9} \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.60, size = 24, normalized size = 0.86 \begin {gather*} \frac {2\,x}{3}-\frac {2\,\ln \left (x+\frac {30}{11}\right )}{9}+\frac {256\,\ln \left (x\right )}{9}-\frac {\ln \left (11\,x+30\right )\,\ln \left (x\right )}{9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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