Integrand size = 20, antiderivative size = 22 \[ \int \frac {-1+\left (6+2 x-3 x^2\right ) \log (5)}{\log (5)} \, dx=-1+2 x-x^3+(2+x)^2-\frac {x}{\log (5)} \]
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Time = 0.01 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.86, number of steps used = 3, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {12} \[ \int \frac {-1+\left (6+2 x-3 x^2\right ) \log (5)}{\log (5)} \, dx=-x^3+x^2+6 x-\frac {x}{\log (5)} \]
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Rule 12
Rubi steps \begin{align*} \text {integral}& = \frac {\int \left (-1+\left (6+2 x-3 x^2\right ) \log (5)\right ) \, dx}{\log (5)} \\ & = -\frac {x}{\log (5)}+\int \left (6+2 x-3 x^2\right ) \, dx \\ & = 6 x+x^2-x^3-\frac {x}{\log (5)} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.86 \[ \int \frac {-1+\left (6+2 x-3 x^2\right ) \log (5)}{\log (5)} \, dx=6 x+x^2-x^3-\frac {x}{\log (5)} \]
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Time = 0.03 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.91
method | result | size |
risch | \(-x^{3}+x^{2}+6 x -\frac {x}{\ln \left (5\right )}\) | \(20\) |
norman | \(x^{2}+\frac {\left (6 \ln \left (5\right )-1\right ) x}{\ln \left (5\right )}-x^{3}\) | \(22\) |
gosper | \(-\frac {x \left (x^{2} \ln \left (5\right )-x \ln \left (5\right )-6 \ln \left (5\right )+1\right )}{\ln \left (5\right )}\) | \(25\) |
parallelrisch | \(\frac {\ln \left (5\right ) \left (-x^{3}+x^{2}+6 x \right )-x}{\ln \left (5\right )}\) | \(25\) |
default | \(\frac {-x^{3} \ln \left (5\right )+x^{2} \ln \left (5\right )+6 x \ln \left (5\right )-x}{\ln \left (5\right )}\) | \(28\) |
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none
Time = 0.29 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.05 \[ \int \frac {-1+\left (6+2 x-3 x^2\right ) \log (5)}{\log (5)} \, dx=-\frac {{\left (x^{3} - x^{2} - 6 \, x\right )} \log \left (5\right ) + x}{\log \left (5\right )} \]
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Time = 0.03 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.77 \[ \int \frac {-1+\left (6+2 x-3 x^2\right ) \log (5)}{\log (5)} \, dx=- x^{3} + x^{2} + \frac {x \left (-1 + 6 \log {\left (5 \right )}\right )}{\log {\left (5 \right )}} \]
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none
Time = 0.19 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.05 \[ \int \frac {-1+\left (6+2 x-3 x^2\right ) \log (5)}{\log (5)} \, dx=-\frac {{\left (x^{3} - x^{2} - 6 \, x\right )} \log \left (5\right ) + x}{\log \left (5\right )} \]
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none
Time = 0.26 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.05 \[ \int \frac {-1+\left (6+2 x-3 x^2\right ) \log (5)}{\log (5)} \, dx=-\frac {{\left (x^{3} - x^{2} - 6 \, x\right )} \log \left (5\right ) + x}{\log \left (5\right )} \]
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Time = 0.05 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.95 \[ \int \frac {-1+\left (6+2 x-3 x^2\right ) \log (5)}{\log (5)} \, dx=-x^3+x^2+\frac {\left (6\,\ln \left (5\right )-1\right )\,x}{\ln \left (5\right )} \]
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