Integrand size = 16, antiderivative size = 15 \[ \int \frac {1}{144} \left (225+1000 \log (x)+400 \log ^2(x)\right ) \, dx=\frac {25}{81} x \left (\frac {3}{4}+3 \log (x)\right )^2 \]
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Time = 0.01 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.47, number of steps used = 5, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.188, Rules used = {12, 2332, 2333} \[ \int \frac {1}{144} \left (225+1000 \log (x)+400 \log ^2(x)\right ) \, dx=\frac {25 x}{144}+\frac {25}{9} x \log ^2(x)+\frac {25}{18} x \log (x) \]
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Rule 12
Rule 2332
Rule 2333
Rubi steps \begin{align*} \text {integral}& = \frac {1}{144} \int \left (225+1000 \log (x)+400 \log ^2(x)\right ) \, dx \\ & = \frac {25 x}{16}+\frac {25}{9} \int \log ^2(x) \, dx+\frac {125}{18} \int \log (x) \, dx \\ & = -\frac {775 x}{144}+\frac {125}{18} x \log (x)+\frac {25}{9} x \log ^2(x)-\frac {50}{9} \int \log (x) \, dx \\ & = \frac {25 x}{144}+\frac {25}{18} x \log (x)+\frac {25}{9} x \log ^2(x) \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.47 \[ \int \frac {1}{144} \left (225+1000 \log (x)+400 \log ^2(x)\right ) \, dx=\frac {25 x}{144}+\frac {25}{18} x \log (x)+\frac {25}{9} x \log ^2(x) \]
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Time = 0.03 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.13
method | result | size |
default | \(\frac {25 x}{144}+\frac {25 x \ln \left (x \right )^{2}}{9}+\frac {25 x \ln \left (x \right )}{18}\) | \(17\) |
norman | \(\frac {25 x}{144}+\frac {25 x \ln \left (x \right )^{2}}{9}+\frac {25 x \ln \left (x \right )}{18}\) | \(17\) |
risch | \(\frac {25 x}{144}+\frac {25 x \ln \left (x \right )^{2}}{9}+\frac {25 x \ln \left (x \right )}{18}\) | \(17\) |
parallelrisch | \(\frac {25 x}{144}+\frac {25 x \ln \left (x \right )^{2}}{9}+\frac {25 x \ln \left (x \right )}{18}\) | \(17\) |
parts | \(\frac {25 x}{144}+\frac {25 x \ln \left (x \right )^{2}}{9}+\frac {25 x \ln \left (x \right )}{18}\) | \(17\) |
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Time = 0.27 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.07 \[ \int \frac {1}{144} \left (225+1000 \log (x)+400 \log ^2(x)\right ) \, dx=\frac {25}{9} \, x \log \left (x\right )^{2} + \frac {25}{18} \, x \log \left (x\right ) + \frac {25}{144} \, x \]
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Time = 0.04 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.47 \[ \int \frac {1}{144} \left (225+1000 \log (x)+400 \log ^2(x)\right ) \, dx=\frac {25 x \log {\left (x \right )}^{2}}{9} + \frac {25 x \log {\left (x \right )}}{18} + \frac {25 x}{144} \]
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Time = 0.17 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.47 \[ \int \frac {1}{144} \left (225+1000 \log (x)+400 \log ^2(x)\right ) \, dx=\frac {25}{9} \, {\left (\log \left (x\right )^{2} - 2 \, \log \left (x\right ) + 2\right )} x + \frac {125}{18} \, x \log \left (x\right ) - \frac {775}{144} \, x \]
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Time = 0.26 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.07 \[ \int \frac {1}{144} \left (225+1000 \log (x)+400 \log ^2(x)\right ) \, dx=\frac {25}{9} \, x \log \left (x\right )^{2} + \frac {25}{18} \, x \log \left (x\right ) + \frac {25}{144} \, x \]
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Time = 7.98 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.73 \[ \int \frac {1}{144} \left (225+1000 \log (x)+400 \log ^2(x)\right ) \, dx=\frac {25\,x\,{\left (4\,\ln \left (x\right )+1\right )}^2}{144} \]
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