Integrand size = 78, antiderivative size = 26 \[ \int \frac {-2880-1620 x-225 x^2+\left (-2880-1610 x-225 x^2\right ) \log \left (\frac {32 x+9 x^2}{36+10 x}\right )}{\left (576 x^2+322 x^3+45 x^4\right ) \log ^2\left (\frac {32 x+9 x^2}{36+10 x}\right )} \, dx=4+\frac {5}{x \log \left (x+\frac {x}{-9-\frac {x}{4+x}}\right )} \]
[Out]
\[ \int \frac {-2880-1620 x-225 x^2+\left (-2880-1610 x-225 x^2\right ) \log \left (\frac {32 x+9 x^2}{36+10 x}\right )}{\left (576 x^2+322 x^3+45 x^4\right ) \log ^2\left (\frac {32 x+9 x^2}{36+10 x}\right )} \, dx=\int \frac {-2880-1620 x-225 x^2+\left (-2880-1610 x-225 x^2\right ) \log \left (\frac {32 x+9 x^2}{36+10 x}\right )}{\left (576 x^2+322 x^3+45 x^4\right ) \log ^2\left (\frac {32 x+9 x^2}{36+10 x}\right )} \, dx \]
[In]
[Out]
Rubi steps \begin{align*} \text {integral}& = \int \frac {-2880-1620 x-225 x^2+\left (-2880-1610 x-225 x^2\right ) \log \left (\frac {32 x+9 x^2}{36+10 x}\right )}{x^2 \left (576+322 x+45 x^2\right ) \log ^2\left (\frac {32 x+9 x^2}{36+10 x}\right )} \, dx \\ & = \int \left (-\frac {45 \left (64+36 x+5 x^2\right )}{x^2 (18+5 x) (32+9 x) \log ^2\left (\frac {x (32+9 x)}{36+10 x}\right )}-\frac {5}{x^2 \log \left (\frac {x (32+9 x)}{36+10 x}\right )}\right ) \, dx \\ & = -\left (5 \int \frac {1}{x^2 \log \left (\frac {x (32+9 x)}{36+10 x}\right )} \, dx\right )-45 \int \frac {64+36 x+5 x^2}{x^2 (18+5 x) (32+9 x) \log ^2\left (\frac {x (32+9 x)}{36+10 x}\right )} \, dx \\ & = -\left (5 \int \frac {1}{x^2 \log \left (\frac {x (32+9 x)}{36+10 x}\right )} \, dx\right )-45 \int \left (\frac {1}{9 x^2 \log ^2\left (\frac {x (32+9 x)}{36+10 x}\right )}+\frac {1}{2592 x \log ^2\left (\frac {x (32+9 x)}{36+10 x}\right )}+\frac {25}{162 (18+5 x) \log ^2\left (\frac {x (32+9 x)}{36+10 x}\right )}-\frac {9}{32 (32+9 x) \log ^2\left (\frac {x (32+9 x)}{36+10 x}\right )}\right ) \, dx \\ & = -\left (\frac {5}{288} \int \frac {1}{x \log ^2\left (\frac {x (32+9 x)}{36+10 x}\right )} \, dx\right )-5 \int \frac {1}{x^2 \log ^2\left (\frac {x (32+9 x)}{36+10 x}\right )} \, dx-5 \int \frac {1}{x^2 \log \left (\frac {x (32+9 x)}{36+10 x}\right )} \, dx-\frac {125}{18} \int \frac {1}{(18+5 x) \log ^2\left (\frac {x (32+9 x)}{36+10 x}\right )} \, dx+\frac {405}{32} \int \frac {1}{(32+9 x) \log ^2\left (\frac {x (32+9 x)}{36+10 x}\right )} \, dx \\ \end{align*}
Time = 0.34 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.85 \[ \int \frac {-2880-1620 x-225 x^2+\left (-2880-1610 x-225 x^2\right ) \log \left (\frac {32 x+9 x^2}{36+10 x}\right )}{\left (576 x^2+322 x^3+45 x^4\right ) \log ^2\left (\frac {32 x+9 x^2}{36+10 x}\right )} \, dx=\frac {5}{x \log \left (\frac {x (32+9 x)}{36+10 x}\right )} \]
[In]
[Out]
Time = 0.77 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.00
method | result | size |
norman | \(\frac {5}{x \ln \left (\frac {9 x^{2}+32 x}{10 x +36}\right )}\) | \(26\) |
risch | \(\frac {5}{x \ln \left (\frac {9 x^{2}+32 x}{10 x +36}\right )}\) | \(26\) |
[In]
[Out]
none
Time = 0.24 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.00 \[ \int \frac {-2880-1620 x-225 x^2+\left (-2880-1610 x-225 x^2\right ) \log \left (\frac {32 x+9 x^2}{36+10 x}\right )}{\left (576 x^2+322 x^3+45 x^4\right ) \log ^2\left (\frac {32 x+9 x^2}{36+10 x}\right )} \, dx=\frac {5}{x \log \left (\frac {9 \, x^{2} + 32 \, x}{2 \, {\left (5 \, x + 18\right )}}\right )} \]
[In]
[Out]
Time = 0.07 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.65 \[ \int \frac {-2880-1620 x-225 x^2+\left (-2880-1610 x-225 x^2\right ) \log \left (\frac {32 x+9 x^2}{36+10 x}\right )}{\left (576 x^2+322 x^3+45 x^4\right ) \log ^2\left (\frac {32 x+9 x^2}{36+10 x}\right )} \, dx=\frac {5}{x \log {\left (\frac {9 x^{2} + 32 x}{10 x + 36} \right )}} \]
[In]
[Out]
none
Time = 0.32 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.19 \[ \int \frac {-2880-1620 x-225 x^2+\left (-2880-1610 x-225 x^2\right ) \log \left (\frac {32 x+9 x^2}{36+10 x}\right )}{\left (576 x^2+322 x^3+45 x^4\right ) \log ^2\left (\frac {32 x+9 x^2}{36+10 x}\right )} \, dx=-\frac {5}{x \log \left (2\right ) - x \log \left (9 \, x + 32\right ) + x \log \left (5 \, x + 18\right ) - x \log \left (x\right )} \]
[In]
[Out]
none
Time = 0.30 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.00 \[ \int \frac {-2880-1620 x-225 x^2+\left (-2880-1610 x-225 x^2\right ) \log \left (\frac {32 x+9 x^2}{36+10 x}\right )}{\left (576 x^2+322 x^3+45 x^4\right ) \log ^2\left (\frac {32 x+9 x^2}{36+10 x}\right )} \, dx=\frac {5}{x \log \left (\frac {9 \, x^{2} + 32 \, x}{2 \, {\left (5 \, x + 18\right )}}\right )} \]
[In]
[Out]
Time = 9.53 (sec) , antiderivative size = 25, normalized size of antiderivative = 0.96 \[ \int \frac {-2880-1620 x-225 x^2+\left (-2880-1610 x-225 x^2\right ) \log \left (\frac {32 x+9 x^2}{36+10 x}\right )}{\left (576 x^2+322 x^3+45 x^4\right ) \log ^2\left (\frac {32 x+9 x^2}{36+10 x}\right )} \, dx=\frac {5}{x\,\ln \left (\frac {9\,x^2+32\,x}{10\,x+36}\right )} \]
[In]
[Out]