Integrand size = 45, antiderivative size = 21 \[ \int -\frac {84 x}{\left (20 e^6+21 x^2\right ) \log \left (20 e^6+21 x^2\right ) \log ^3\left (\log \left (20 e^6+21 x^2\right )\right )} \, dx=\frac {1}{\log ^2\left (\log \left (x^2-20 \left (-e^6-x^2\right )\right )\right )} \]
[Out]
Time = 0.06 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.71, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.044, Rules used = {12, 6818} \[ \int -\frac {84 x}{\left (20 e^6+21 x^2\right ) \log \left (20 e^6+21 x^2\right ) \log ^3\left (\log \left (20 e^6+21 x^2\right )\right )} \, dx=\frac {1}{\log ^2\left (\log \left (21 x^2+20 e^6\right )\right )} \]
[In]
[Out]
Rule 12
Rule 6818
Rubi steps \begin{align*} \text {integral}& = -\left (84 \int \frac {x}{\left (20 e^6+21 x^2\right ) \log \left (20 e^6+21 x^2\right ) \log ^3\left (\log \left (20 e^6+21 x^2\right )\right )} \, dx\right ) \\ & = \frac {1}{\log ^2\left (\log \left (20 e^6+21 x^2\right )\right )} \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.71 \[ \int -\frac {84 x}{\left (20 e^6+21 x^2\right ) \log \left (20 e^6+21 x^2\right ) \log ^3\left (\log \left (20 e^6+21 x^2\right )\right )} \, dx=\frac {1}{\log ^2\left (\log \left (20 e^6+21 x^2\right )\right )} \]
[In]
[Out]
Time = 1.10 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.71
method | result | size |
risch | \(\frac {1}{{\ln \left (\ln \left (20 \,{\mathrm e}^{6}+21 x^{2}\right )\right )}^{2}}\) | \(15\) |
derivativedivides | \(\frac {1}{{\ln \left (\ln \left (20 \,{\mathrm e}^{2} {\mathrm e}^{4}+21 x^{2}\right )\right )}^{2}}\) | \(17\) |
default | \(\frac {1}{{\ln \left (\ln \left (20 \,{\mathrm e}^{2} {\mathrm e}^{4}+21 x^{2}\right )\right )}^{2}}\) | \(17\) |
parallelrisch | \(\frac {1}{{\ln \left (\ln \left (20 \,{\mathrm e}^{2} {\mathrm e}^{4}+21 x^{2}\right )\right )}^{2}}\) | \(17\) |
[In]
[Out]
none
Time = 0.25 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.67 \[ \int -\frac {84 x}{\left (20 e^6+21 x^2\right ) \log \left (20 e^6+21 x^2\right ) \log ^3\left (\log \left (20 e^6+21 x^2\right )\right )} \, dx=\frac {1}{\log \left (\log \left (21 \, x^{2} + 20 \, e^{6}\right )\right )^{2}} \]
[In]
[Out]
Time = 0.06 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.71 \[ \int -\frac {84 x}{\left (20 e^6+21 x^2\right ) \log \left (20 e^6+21 x^2\right ) \log ^3\left (\log \left (20 e^6+21 x^2\right )\right )} \, dx=\frac {1}{\log {\left (\log {\left (21 x^{2} + 20 e^{6} \right )} \right )}^{2}} \]
[In]
[Out]
none
Time = 0.18 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.67 \[ \int -\frac {84 x}{\left (20 e^6+21 x^2\right ) \log \left (20 e^6+21 x^2\right ) \log ^3\left (\log \left (20 e^6+21 x^2\right )\right )} \, dx=\frac {1}{\log \left (\log \left (21 \, x^{2} + 20 \, e^{6}\right )\right )^{2}} \]
[In]
[Out]
none
Time = 0.26 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.67 \[ \int -\frac {84 x}{\left (20 e^6+21 x^2\right ) \log \left (20 e^6+21 x^2\right ) \log ^3\left (\log \left (20 e^6+21 x^2\right )\right )} \, dx=\frac {1}{\log \left (\log \left (21 \, x^{2} + 20 \, e^{6}\right )\right )^{2}} \]
[In]
[Out]
Time = 9.97 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.67 \[ \int -\frac {84 x}{\left (20 e^6+21 x^2\right ) \log \left (20 e^6+21 x^2\right ) \log ^3\left (\log \left (20 e^6+21 x^2\right )\right )} \, dx=\frac {1}{{\ln \left (\ln \left (21\,x^2+20\,{\mathrm {e}}^6\right )\right )}^2} \]
[In]
[Out]