Integrand size = 114, antiderivative size = 23 \[ \int \frac {-e^9-2100 x-275 x^2+\left (-12250 x-1500 x^2\right ) \log (x)+\left (-8750 x-625 x^2\right ) \log ^2(x)}{e^{18}-50 e^9 x^2+625 x^4+\left (-500 e^9 x^2+12500 x^4\right ) \log (x)+\left (-1250 e^9 x^2+93750 x^4\right ) \log ^2(x)+312500 x^4 \log ^3(x)+390625 x^4 \log ^4(x)} \, dx=\frac {7+x}{-e^9+25 (x+5 x \log (x))^2} \]
[Out]
\[ \int \frac {-e^9-2100 x-275 x^2+\left (-12250 x-1500 x^2\right ) \log (x)+\left (-8750 x-625 x^2\right ) \log ^2(x)}{e^{18}-50 e^9 x^2+625 x^4+\left (-500 e^9 x^2+12500 x^4\right ) \log (x)+\left (-1250 e^9 x^2+93750 x^4\right ) \log ^2(x)+312500 x^4 \log ^3(x)+390625 x^4 \log ^4(x)} \, dx=\int \frac {-e^9-2100 x-275 x^2+\left (-12250 x-1500 x^2\right ) \log (x)+\left (-8750 x-625 x^2\right ) \log ^2(x)}{e^{18}-50 e^9 x^2+625 x^4+\left (-500 e^9 x^2+12500 x^4\right ) \log (x)+\left (-1250 e^9 x^2+93750 x^4\right ) \log ^2(x)+312500 x^4 \log ^3(x)+390625 x^4 \log ^4(x)} \, dx \]
[In]
[Out]
Rubi steps \begin{align*} \text {integral}& = \int \frac {-e^9-25 x (84+11 x)-250 x (49+6 x) \log (x)-625 x (14+x) \log ^2(x)}{\left (e^9-25 x^2-250 x^2 \log (x)-625 x^2 \log ^2(x)\right )^2} \, dx \\ & = \int \left (\frac {14+x}{x \left (e^9-25 x^2-250 x^2 \log (x)-625 x^2 \log ^2(x)\right )}-\frac {2 (7+x) \left (e^9+125 x^2+625 x^2 \log (x)\right )}{x \left (-e^9+25 x^2+250 x^2 \log (x)+625 x^2 \log ^2(x)\right )^2}\right ) \, dx \\ & = -\left (2 \int \frac {(7+x) \left (e^9+125 x^2+625 x^2 \log (x)\right )}{x \left (-e^9+25 x^2+250 x^2 \log (x)+625 x^2 \log ^2(x)\right )^2} \, dx\right )+\int \frac {14+x}{x \left (e^9-25 x^2-250 x^2 \log (x)-625 x^2 \log ^2(x)\right )} \, dx \\ & = -\left (2 \int \left (\frac {e^9+125 x^2+625 x^2 \log (x)}{\left (e^9-25 x^2-250 x^2 \log (x)-625 x^2 \log ^2(x)\right )^2}+\frac {7 \left (e^9+125 x^2+625 x^2 \log (x)\right )}{x \left (-e^9+25 x^2+250 x^2 \log (x)+625 x^2 \log ^2(x)\right )^2}\right ) \, dx\right )+\int \left (\frac {1}{e^9-25 x^2-250 x^2 \log (x)-625 x^2 \log ^2(x)}+\frac {14}{x \left (e^9-25 x^2-250 x^2 \log (x)-625 x^2 \log ^2(x)\right )}\right ) \, dx \\ & = -\left (2 \int \frac {e^9+125 x^2+625 x^2 \log (x)}{\left (e^9-25 x^2-250 x^2 \log (x)-625 x^2 \log ^2(x)\right )^2} \, dx\right )+14 \int \frac {1}{x \left (e^9-25 x^2-250 x^2 \log (x)-625 x^2 \log ^2(x)\right )} \, dx-14 \int \frac {e^9+125 x^2+625 x^2 \log (x)}{x \left (-e^9+25 x^2+250 x^2 \log (x)+625 x^2 \log ^2(x)\right )^2} \, dx+\int \frac {1}{e^9-25 x^2-250 x^2 \log (x)-625 x^2 \log ^2(x)} \, dx \\ & = -\left (2 \int \left (\frac {e^9}{\left (e^9-25 x^2-250 x^2 \log (x)-625 x^2 \log ^2(x)\right )^2}+\frac {125 x^2}{\left (e^9-25 x^2-250 x^2 \log (x)-625 x^2 \log ^2(x)\right )^2}+\frac {625 x^2 \log (x)}{\left (e^9-25 x^2-250 x^2 \log (x)-625 x^2 \log ^2(x)\right )^2}\right ) \, dx\right )+14 \int \frac {1}{x \left (e^9-25 x^2-250 x^2 \log (x)-625 x^2 \log ^2(x)\right )} \, dx-14 \int \left (\frac {125 x}{\left (e^9-25 x^2-250 x^2 \log (x)-625 x^2 \log ^2(x)\right )^2}+\frac {625 x \log (x)}{\left (e^9-25 x^2-250 x^2 \log (x)-625 x^2 \log ^2(x)\right )^2}+\frac {e^9}{x \left (-e^9+25 x^2+250 x^2 \log (x)+625 x^2 \log ^2(x)\right )^2}\right ) \, dx+\int \frac {1}{e^9-25 x^2-250 x^2 \log (x)-625 x^2 \log ^2(x)} \, dx \\ & = 14 \int \frac {1}{x \left (e^9-25 x^2-250 x^2 \log (x)-625 x^2 \log ^2(x)\right )} \, dx-250 \int \frac {x^2}{\left (e^9-25 x^2-250 x^2 \log (x)-625 x^2 \log ^2(x)\right )^2} \, dx-1250 \int \frac {x^2 \log (x)}{\left (e^9-25 x^2-250 x^2 \log (x)-625 x^2 \log ^2(x)\right )^2} \, dx-1750 \int \frac {x}{\left (e^9-25 x^2-250 x^2 \log (x)-625 x^2 \log ^2(x)\right )^2} \, dx-8750 \int \frac {x \log (x)}{\left (e^9-25 x^2-250 x^2 \log (x)-625 x^2 \log ^2(x)\right )^2} \, dx-\left (2 e^9\right ) \int \frac {1}{\left (e^9-25 x^2-250 x^2 \log (x)-625 x^2 \log ^2(x)\right )^2} \, dx-\left (14 e^9\right ) \int \frac {1}{x \left (-e^9+25 x^2+250 x^2 \log (x)+625 x^2 \log ^2(x)\right )^2} \, dx+\int \frac {1}{e^9-25 x^2-250 x^2 \log (x)-625 x^2 \log ^2(x)} \, dx \\ \end{align*}
Time = 0.56 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.39 \[ \int \frac {-e^9-2100 x-275 x^2+\left (-12250 x-1500 x^2\right ) \log (x)+\left (-8750 x-625 x^2\right ) \log ^2(x)}{e^{18}-50 e^9 x^2+625 x^4+\left (-500 e^9 x^2+12500 x^4\right ) \log (x)+\left (-1250 e^9 x^2+93750 x^4\right ) \log ^2(x)+312500 x^4 \log ^3(x)+390625 x^4 \log ^4(x)} \, dx=-\frac {7+x}{e^9-25 x^2-250 x^2 \log (x)-625 x^2 \log ^2(x)} \]
[In]
[Out]
Time = 0.91 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.39
method | result | size |
default | \(-\frac {x +7}{-625 x^{2} \ln \left (x \right )^{2}-250 x^{2} \ln \left (x \right )-25 x^{2}+{\mathrm e}^{9}}\) | \(32\) |
risch | \(-\frac {x +7}{-625 x^{2} \ln \left (x \right )^{2}-250 x^{2} \ln \left (x \right )-25 x^{2}+{\mathrm e}^{9}}\) | \(32\) |
norman | \(\frac {-x -7}{-625 x^{2} \ln \left (x \right )^{2}-250 x^{2} \ln \left (x \right )-25 x^{2}+{\mathrm e}^{9}}\) | \(33\) |
parallelrisch | \(\frac {-175-25 x}{-15625 x^{2} \ln \left (x \right )^{2}-6250 x^{2} \ln \left (x \right )-625 x^{2}+25 \,{\mathrm e}^{9}}\) | \(34\) |
[In]
[Out]
none
Time = 0.32 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.39 \[ \int \frac {-e^9-2100 x-275 x^2+\left (-12250 x-1500 x^2\right ) \log (x)+\left (-8750 x-625 x^2\right ) \log ^2(x)}{e^{18}-50 e^9 x^2+625 x^4+\left (-500 e^9 x^2+12500 x^4\right ) \log (x)+\left (-1250 e^9 x^2+93750 x^4\right ) \log ^2(x)+312500 x^4 \log ^3(x)+390625 x^4 \log ^4(x)} \, dx=\frac {x + 7}{625 \, x^{2} \log \left (x\right )^{2} + 250 \, x^{2} \log \left (x\right ) + 25 \, x^{2} - e^{9}} \]
[In]
[Out]
Time = 0.11 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.26 \[ \int \frac {-e^9-2100 x-275 x^2+\left (-12250 x-1500 x^2\right ) \log (x)+\left (-8750 x-625 x^2\right ) \log ^2(x)}{e^{18}-50 e^9 x^2+625 x^4+\left (-500 e^9 x^2+12500 x^4\right ) \log (x)+\left (-1250 e^9 x^2+93750 x^4\right ) \log ^2(x)+312500 x^4 \log ^3(x)+390625 x^4 \log ^4(x)} \, dx=\frac {x + 7}{625 x^{2} \log {\left (x \right )}^{2} + 250 x^{2} \log {\left (x \right )} + 25 x^{2} - e^{9}} \]
[In]
[Out]
none
Time = 0.25 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.39 \[ \int \frac {-e^9-2100 x-275 x^2+\left (-12250 x-1500 x^2\right ) \log (x)+\left (-8750 x-625 x^2\right ) \log ^2(x)}{e^{18}-50 e^9 x^2+625 x^4+\left (-500 e^9 x^2+12500 x^4\right ) \log (x)+\left (-1250 e^9 x^2+93750 x^4\right ) \log ^2(x)+312500 x^4 \log ^3(x)+390625 x^4 \log ^4(x)} \, dx=\frac {x + 7}{625 \, x^{2} \log \left (x\right )^{2} + 250 \, x^{2} \log \left (x\right ) + 25 \, x^{2} - e^{9}} \]
[In]
[Out]
none
Time = 0.30 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.43 \[ \int \frac {-e^9-2100 x-275 x^2+\left (-12250 x-1500 x^2\right ) \log (x)+\left (-8750 x-625 x^2\right ) \log ^2(x)}{e^{18}-50 e^9 x^2+625 x^4+\left (-500 e^9 x^2+12500 x^4\right ) \log (x)+\left (-1250 e^9 x^2+93750 x^4\right ) \log ^2(x)+312500 x^4 \log ^3(x)+390625 x^4 \log ^4(x)} \, dx=\frac {2 \, {\left (x + 7\right )}}{625 \, x^{2} \log \left (x\right )^{2} + 250 \, x^{2} \log \left (x\right ) + 25 \, x^{2} - e^{9}} \]
[In]
[Out]
Timed out. \[ \int \frac {-e^9-2100 x-275 x^2+\left (-12250 x-1500 x^2\right ) \log (x)+\left (-8750 x-625 x^2\right ) \log ^2(x)}{e^{18}-50 e^9 x^2+625 x^4+\left (-500 e^9 x^2+12500 x^4\right ) \log (x)+\left (-1250 e^9 x^2+93750 x^4\right ) \log ^2(x)+312500 x^4 \log ^3(x)+390625 x^4 \log ^4(x)} \, dx=\int -\frac {2100\,x+{\mathrm {e}}^9+{\ln \left (x\right )}^2\,\left (625\,x^2+8750\,x\right )+\ln \left (x\right )\,\left (1500\,x^2+12250\,x\right )+275\,x^2}{{\mathrm {e}}^{18}-\ln \left (x\right )\,\left (500\,x^2\,{\mathrm {e}}^9-12500\,x^4\right )+312500\,x^4\,{\ln \left (x\right )}^3+390625\,x^4\,{\ln \left (x\right )}^4-50\,x^2\,{\mathrm {e}}^9-{\ln \left (x\right )}^2\,\left (1250\,x^2\,{\mathrm {e}}^9-93750\,x^4\right )+625\,x^4} \,d x \]
[In]
[Out]