Integrand size = 37, antiderivative size = 21 \[ \int \frac {6 x-32 x \log ^2(2)}{-15+3 x^2+\left (80-16 x^2\right ) \log ^2(2)+3 \log (9)} \, dx=\log \left (\frac {1}{3} \left (-5+x^2\right ) \left (3-16 \log ^2(2)\right )+\log (9)\right ) \]
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Time = 0.01 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.33, number of steps used = 3, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.081, Rules used = {6, 12, 1601} \[ \int \frac {6 x-32 x \log ^2(2)}{-15+3 x^2+\left (80-16 x^2\right ) \log ^2(2)+3 \log (9)} \, dx=\log \left (-3 x^2-16 \left (5-x^2\right ) \log ^2(2)+3 (5-\log (9))\right ) \]
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Rule 6
Rule 12
Rule 1601
Rubi steps \begin{align*} \text {integral}& = \int \frac {x \left (6-32 \log ^2(2)\right )}{-15+3 x^2+\left (80-16 x^2\right ) \log ^2(2)+3 \log (9)} \, dx \\ & = \left (2 \left (3-16 \log ^2(2)\right )\right ) \int \frac {x}{-15+3 x^2+\left (80-16 x^2\right ) \log ^2(2)+3 \log (9)} \, dx \\ & = \log \left (-3 x^2-16 \left (5-x^2\right ) \log ^2(2)+3 (5-\log (9))\right ) \\ \end{align*}
Time = 0.02 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.10 \[ \int \frac {6 x-32 x \log ^2(2)}{-15+3 x^2+\left (80-16 x^2\right ) \log ^2(2)+3 \log (9)} \, dx=\log \left (-15+80 \log ^2(2)+x^2 \left (3-16 \log ^2(2)\right )+\log (729)\right ) \]
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Time = 2.14 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.19
method | result | size |
derivativedivides | \(\ln \left (6 \ln \left (3\right )+\left (-16 x^{2}+80\right ) \ln \left (2\right )^{2}+3 x^{2}-15\right )\) | \(25\) |
risch | \(\ln \left (x^{2} \left (16 \ln \left (2\right )^{2}-3\right )-80 \ln \left (2\right )^{2}-6 \ln \left (3\right )+15\right )\) | \(26\) |
default | \(\ln \left (16 x^{2} \ln \left (2\right )^{2}-80 \ln \left (2\right )^{2}-3 x^{2}-6 \ln \left (3\right )+15\right )\) | \(28\) |
norman | \(\ln \left (16 x^{2} \ln \left (2\right )^{2}-80 \ln \left (2\right )^{2}-3 x^{2}-6 \ln \left (3\right )+15\right )\) | \(28\) |
parallelrisch | \(\ln \left (\frac {16 x^{2} \ln \left (2\right )^{2}-80 \ln \left (2\right )^{2}-3 x^{2}-6 \ln \left (3\right )+15}{16 \ln \left (2\right )^{2}-3}\right )\) | \(39\) |
meijerg | \(-\frac {\left (-32 \ln \left (2\right )^{2}+6\right ) \ln \left (1-\frac {x^{2} \left (16 \ln \left (2\right )^{2}-3\right )}{80 \ln \left (2\right )^{2}+6 \ln \left (3\right )-15}\right )}{2 \left (16 \ln \left (2\right )^{2}-3\right )}\) | \(51\) |
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Time = 0.25 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.10 \[ \int \frac {6 x-32 x \log ^2(2)}{-15+3 x^2+\left (80-16 x^2\right ) \log ^2(2)+3 \log (9)} \, dx=\log \left (16 \, {\left (x^{2} - 5\right )} \log \left (2\right )^{2} - 3 \, x^{2} - 6 \, \log \left (3\right ) + 15\right ) \]
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Time = 0.30 (sec) , antiderivative size = 42, normalized size of antiderivative = 2.00 \[ \int \frac {6 x-32 x \log ^2(2)}{-15+3 x^2+\left (80-16 x^2\right ) \log ^2(2)+3 \log (9)} \, dx=\frac {\left (-6 + 32 \log {\left (2 \right )}^{2}\right ) \log {\left (x^{2} \left (-3 + 16 \log {\left (2 \right )}^{2}\right ) - 80 \log {\left (2 \right )}^{2} - 6 \log {\left (3 \right )} + 15 \right )}}{2 \left (-3 + 16 \log {\left (2 \right )}^{2}\right )} \]
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Time = 0.21 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.10 \[ \int \frac {6 x-32 x \log ^2(2)}{-15+3 x^2+\left (80-16 x^2\right ) \log ^2(2)+3 \log (9)} \, dx=\log \left (16 \, {\left (x^{2} - 5\right )} \log \left (2\right )^{2} - 3 \, x^{2} - 6 \, \log \left (3\right ) + 15\right ) \]
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Time = 0.28 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.33 \[ \int \frac {6 x-32 x \log ^2(2)}{-15+3 x^2+\left (80-16 x^2\right ) \log ^2(2)+3 \log (9)} \, dx=\log \left ({\left | 16 \, x^{2} \log \left (2\right )^{2} - 3 \, x^{2} - 80 \, \log \left (2\right )^{2} - 6 \, \log \left (3\right ) + 15 \right |}\right ) \]
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Time = 0.21 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.19 \[ \int \frac {6 x-32 x \log ^2(2)}{-15+3 x^2+\left (80-16 x^2\right ) \log ^2(2)+3 \log (9)} \, dx=\ln \left (\left (16\,{\ln \left (2\right )}^2-3\right )\,x^2-\ln \left (729\right )-80\,{\ln \left (2\right )}^2+15\right ) \]
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