Integrand size = 17, antiderivative size = 18 \[ \int \frac {-2 x+(-11+2 x) \log (3)}{\log (3)} \, dx=(-5+x)^2-x-\frac {x^2}{\log (3)} \]
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Time = 0.00 (sec) , antiderivative size = 21, normalized size of antiderivative = 1.17, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.059, Rules used = {12} \[ \int \frac {-2 x+(-11+2 x) \log (3)}{\log (3)} \, dx=\frac {1}{4} (11-2 x)^2-\frac {x^2}{\log (3)} \]
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Rule 12
Rubi steps \begin{align*} \text {integral}& = \frac {\int (-2 x+(-11+2 x) \log (3)) \, dx}{\log (3)} \\ & = \frac {1}{4} (11-2 x)^2-\frac {x^2}{\log (3)} \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.06 \[ \int \frac {-2 x+(-11+2 x) \log (3)}{\log (3)} \, dx=-11 x+\frac {x^2 (-2+\log (9))}{2 \log (3)} \]
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Time = 0.08 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.94
method | result | size |
norman | \(\frac {\left (\ln \left (3\right )-1\right ) x^{2}}{\ln \left (3\right )}-11 x\) | \(17\) |
risch | \(x^{2}-11 x -\frac {x^{2}}{\ln \left (3\right )}\) | \(17\) |
gosper | \(\frac {x \left (x \ln \left (3\right )-11 \ln \left (3\right )-x \right )}{\ln \left (3\right )}\) | \(19\) |
default | \(\frac {x^{2} \ln \left (3\right )-11 x \ln \left (3\right )-x^{2}}{\ln \left (3\right )}\) | \(23\) |
parallelrisch | \(\frac {x^{2} \ln \left (3\right )-11 x \ln \left (3\right )-x^{2}}{\ln \left (3\right )}\) | \(23\) |
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Time = 0.23 (sec) , antiderivative size = 21, normalized size of antiderivative = 1.17 \[ \int \frac {-2 x+(-11+2 x) \log (3)}{\log (3)} \, dx=-\frac {x^{2} - {\left (x^{2} - 11 \, x\right )} \log \left (3\right )}{\log \left (3\right )} \]
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Time = 0.02 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.78 \[ \int \frac {-2 x+(-11+2 x) \log (3)}{\log (3)} \, dx=\frac {x^{2} \left (-1 + \log {\left (3 \right )}\right )}{\log {\left (3 \right )}} - 11 x \]
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Time = 0.23 (sec) , antiderivative size = 21, normalized size of antiderivative = 1.17 \[ \int \frac {-2 x+(-11+2 x) \log (3)}{\log (3)} \, dx=-\frac {x^{2} - {\left (x^{2} - 11 \, x\right )} \log \left (3\right )}{\log \left (3\right )} \]
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none
Time = 0.25 (sec) , antiderivative size = 21, normalized size of antiderivative = 1.17 \[ \int \frac {-2 x+(-11+2 x) \log (3)}{\log (3)} \, dx=-\frac {x^{2} - {\left (x^{2} - 11 \, x\right )} \log \left (3\right )}{\log \left (3\right )} \]
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Time = 0.07 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.89 \[ \int \frac {-2 x+(-11+2 x) \log (3)}{\log (3)} \, dx=\frac {x^2\,\left (\ln \left (3\right )-1\right )}{\ln \left (3\right )}-11\,x \]
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