Integrand size = 38, antiderivative size = 14 \[ \int \frac {50-2 x^2-2 \log (5)}{625+50 x^2+x^4+\left (-50-2 x^2\right ) \log (5)+\log ^2(5)} \, dx=\frac {2 x}{25+x^2-\log (5)} \]
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Time = 0.03 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.079, Rules used = {2015, 28, 391} \[ \int \frac {50-2 x^2-2 \log (5)}{625+50 x^2+x^4+\left (-50-2 x^2\right ) \log (5)+\log ^2(5)} \, dx=\frac {2 x}{x^2+25-\log (5)} \]
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Rule 28
Rule 391
Rule 2015
Rubi steps \begin{align*} \text {integral}& = \int \frac {-2 x^2+2 (25-\log (5))}{x^4+2 x^2 (25-\log (5))+(-25+\log (5))^2} \, dx \\ & = \int \frac {-2 x^2+2 (25-\log (5))}{\left (25+x^2-\log (5)\right )^2} \, dx \\ & = \frac {2 x}{25+x^2-\log (5)} \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.00 \[ \int \frac {50-2 x^2-2 \log (5)}{625+50 x^2+x^4+\left (-50-2 x^2\right ) \log (5)+\log ^2(5)} \, dx=\frac {2 x}{25+x^2-\log (5)} \]
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Time = 0.16 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.07
method | result | size |
gosper | \(-\frac {2 x}{-x^{2}+\ln \left (5\right )-25}\) | \(15\) |
default | \(-\frac {2 x}{-x^{2}+\ln \left (5\right )-25}\) | \(15\) |
norman | \(-\frac {2 x}{-x^{2}+\ln \left (5\right )-25}\) | \(15\) |
risch | \(-\frac {2 x}{-x^{2}+\ln \left (5\right )-25}\) | \(15\) |
parallelrisch | \(-\frac {2 x}{-x^{2}+\ln \left (5\right )-25}\) | \(15\) |
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none
Time = 0.24 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.00 \[ \int \frac {50-2 x^2-2 \log (5)}{625+50 x^2+x^4+\left (-50-2 x^2\right ) \log (5)+\log ^2(5)} \, dx=\frac {2 \, x}{x^{2} - \log \left (5\right ) + 25} \]
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Time = 0.14 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.71 \[ \int \frac {50-2 x^2-2 \log (5)}{625+50 x^2+x^4+\left (-50-2 x^2\right ) \log (5)+\log ^2(5)} \, dx=\frac {2 x}{x^{2} - \log {\left (5 \right )} + 25} \]
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none
Time = 0.22 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.00 \[ \int \frac {50-2 x^2-2 \log (5)}{625+50 x^2+x^4+\left (-50-2 x^2\right ) \log (5)+\log ^2(5)} \, dx=\frac {2 \, x}{x^{2} - \log \left (5\right ) + 25} \]
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none
Time = 0.26 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.00 \[ \int \frac {50-2 x^2-2 \log (5)}{625+50 x^2+x^4+\left (-50-2 x^2\right ) \log (5)+\log ^2(5)} \, dx=\frac {2 \, x}{x^{2} - \log \left (5\right ) + 25} \]
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Time = 17.70 (sec) , antiderivative size = 1, normalized size of antiderivative = 0.07 \[ \int \frac {50-2 x^2-2 \log (5)}{625+50 x^2+x^4+\left (-50-2 x^2\right ) \log (5)+\log ^2(5)} \, dx=0 \]
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