Integrand size = 25, antiderivative size = 20 \[ \int \frac {5-10 x^2+\left (10 x^2+10 x^3\right ) \log (3)}{x^2} \, dx=5 \left (4-\frac {1}{x}-2 x+(1+x)^2 \log (3)\right ) \]
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Time = 0.01 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.040, Rules used = {14} \[ \int \frac {5-10 x^2+\left (10 x^2+10 x^3\right ) \log (3)}{x^2} \, dx=5 x^2 \log (3)-\frac {5}{x}-10 x (1-\log (3)) \]
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Rule 14
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {5}{x^2}+10 (-1+\log (3))+10 x \log (3)\right ) \, dx \\ & = -\frac {5}{x}-10 x (1-\log (3))+5 x^2 \log (3) \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.20 \[ \int \frac {5-10 x^2+\left (10 x^2+10 x^3\right ) \log (3)}{x^2} \, dx=5 \left (-\frac {1}{x}-2 x+x \log (9)+\frac {1}{2} x^2 \log (9)\right ) \]
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Time = 0.07 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10
method | result | size |
default | \(5 x^{2} \ln \left (3\right )+10 x \ln \left (3\right )-10 x -\frac {5}{x}\) | \(22\) |
risch | \(5 x^{2} \ln \left (3\right )+10 x \ln \left (3\right )-10 x -\frac {5}{x}\) | \(22\) |
norman | \(\frac {-5+\left (10 \ln \left (3\right )-10\right ) x^{2}+5 x^{3} \ln \left (3\right )}{x}\) | \(24\) |
gosper | \(\frac {5 x^{3} \ln \left (3\right )+10 x^{2} \ln \left (3\right )-10 x^{2}-5}{x}\) | \(26\) |
parallelrisch | \(\frac {5 x^{3} \ln \left (3\right )+10 x^{2} \ln \left (3\right )-10 x^{2}-5}{x}\) | \(26\) |
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none
Time = 0.23 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.25 \[ \int \frac {5-10 x^2+\left (10 x^2+10 x^3\right ) \log (3)}{x^2} \, dx=-\frac {5 \, {\left (2 \, x^{2} - {\left (x^{3} + 2 \, x^{2}\right )} \log \left (3\right ) + 1\right )}}{x} \]
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Time = 0.05 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.95 \[ \int \frac {5-10 x^2+\left (10 x^2+10 x^3\right ) \log (3)}{x^2} \, dx=5 x^{2} \log {\left (3 \right )} + x \left (-10 + 10 \log {\left (3 \right )}\right ) - \frac {5}{x} \]
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none
Time = 0.19 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.00 \[ \int \frac {5-10 x^2+\left (10 x^2+10 x^3\right ) \log (3)}{x^2} \, dx=5 \, x^{2} \log \left (3\right ) + 10 \, x {\left (\log \left (3\right ) - 1\right )} - \frac {5}{x} \]
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Time = 0.27 (sec) , antiderivative size = 21, normalized size of antiderivative = 1.05 \[ \int \frac {5-10 x^2+\left (10 x^2+10 x^3\right ) \log (3)}{x^2} \, dx=5 \, x^{2} \log \left (3\right ) + 10 \, x \log \left (3\right ) - 10 \, x - \frac {5}{x} \]
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Time = 10.85 (sec) , antiderivative size = 21, normalized size of antiderivative = 1.05 \[ \int \frac {5-10 x^2+\left (10 x^2+10 x^3\right ) \log (3)}{x^2} \, dx=x\,\left (10\,\ln \left (3\right )-10\right )+5\,x^2\,\ln \left (3\right )-\frac {5}{x} \]
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