Integrand size = 293, antiderivative size = 33 \[ \int \frac {-18 x^3+12 x^4-47 x^5+30 x^6-5 x^7+e^x \left (-9 x^5+6 x^6-x^7\right )+\left (-72 x^3+48 x^4-98 x^5+60 x^6-10 x^7+e^x \left (-18 x^5+21 x^6-8 x^7+x^8\right )\right ) \log (x)+\left (30 x^5-6 x^6-6 x^7+x^8\right ) \log ^2(x)}{36-24 x+184 x^2-120 x^3+245 x^4-150 x^5+25 x^6+e^{2 x} \left (9 x^4-6 x^5+x^6\right )+e^x \left (36 x^2-24 x^3+94 x^4-60 x^5+10 x^6\right )+\left (-60 x^2-16 x^3-126 x^4-44 x^5+60 x^6-10 x^7+e^x \left (-30 x^4-8 x^5+12 x^6-2 x^7\right )\right ) \log (x)+\left (25 x^4+30 x^5-x^6-6 x^7+x^8\right ) \log ^2(x)} \, dx=\frac {x^2}{\frac {5}{3-x}+x-\frac {5+e^x+\frac {2}{x^2}}{\log (x)}} \]
[Out]
\[ \int \frac {-18 x^3+12 x^4-47 x^5+30 x^6-5 x^7+e^x \left (-9 x^5+6 x^6-x^7\right )+\left (-72 x^3+48 x^4-98 x^5+60 x^6-10 x^7+e^x \left (-18 x^5+21 x^6-8 x^7+x^8\right )\right ) \log (x)+\left (30 x^5-6 x^6-6 x^7+x^8\right ) \log ^2(x)}{36-24 x+184 x^2-120 x^3+245 x^4-150 x^5+25 x^6+e^{2 x} \left (9 x^4-6 x^5+x^6\right )+e^x \left (36 x^2-24 x^3+94 x^4-60 x^5+10 x^6\right )+\left (-60 x^2-16 x^3-126 x^4-44 x^5+60 x^6-10 x^7+e^x \left (-30 x^4-8 x^5+12 x^6-2 x^7\right )\right ) \log (x)+\left (25 x^4+30 x^5-x^6-6 x^7+x^8\right ) \log ^2(x)} \, dx=\int \frac {-18 x^3+12 x^4-47 x^5+30 x^6-5 x^7+e^x \left (-9 x^5+6 x^6-x^7\right )+\left (-72 x^3+48 x^4-98 x^5+60 x^6-10 x^7+e^x \left (-18 x^5+21 x^6-8 x^7+x^8\right )\right ) \log (x)+\left (30 x^5-6 x^6-6 x^7+x^8\right ) \log ^2(x)}{36-24 x+184 x^2-120 x^3+245 x^4-150 x^5+25 x^6+e^{2 x} \left (9 x^4-6 x^5+x^6\right )+e^x \left (36 x^2-24 x^3+94 x^4-60 x^5+10 x^6\right )+\left (-60 x^2-16 x^3-126 x^4-44 x^5+60 x^6-10 x^7+e^x \left (-30 x^4-8 x^5+12 x^6-2 x^7\right )\right ) \log (x)+\left (25 x^4+30 x^5-x^6-6 x^7+x^8\right ) \log ^2(x)} \, dx \]
[In]
[Out]
Rubi steps \begin{align*} \text {integral}& = \int \frac {x^3 \left (-(-3+x)^2 \left (2+\left (5+e^x\right ) x^2\right )+(-3+x)^2 \left (-8-2 \left (5+e^x\right ) x^2+e^x x^3\right ) \log (x)+x^2 \left (30-6 x-6 x^2+x^3\right ) \log ^2(x)\right )}{\left ((-3+x) \left (2+\left (5+e^x\right ) x^2\right )+x^2 \left (5+3 x-x^2\right ) \log (x)\right )^2} \, dx \\ & = \int \left (-\frac {(-3+x) x^3 (-1-2 \log (x)+x \log (x))}{6-2 x+15 x^2+3 e^x x^2-5 x^3-e^x x^3-5 x^2 \log (x)-3 x^3 \log (x)+x^4 \log (x)}+\frac {x^3 \log (x) \left (-36+6 x-7 x^2-51 x^3+36 x^4-6 x^5+x^3 \log (x)+10 x^4 \log (x)-7 x^5 \log (x)+x^6 \log (x)\right )}{\left (6-2 x+15 x^2+3 e^x x^2-5 x^3-e^x x^3-5 x^2 \log (x)-3 x^3 \log (x)+x^4 \log (x)\right )^2}\right ) \, dx \\ & = -\int \frac {(-3+x) x^3 (-1-2 \log (x)+x \log (x))}{6-2 x+15 x^2+3 e^x x^2-5 x^3-e^x x^3-5 x^2 \log (x)-3 x^3 \log (x)+x^4 \log (x)} \, dx+\int \frac {x^3 \log (x) \left (-36+6 x-7 x^2-51 x^3+36 x^4-6 x^5+x^3 \log (x)+10 x^4 \log (x)-7 x^5 \log (x)+x^6 \log (x)\right )}{\left (6-2 x+15 x^2+3 e^x x^2-5 x^3-e^x x^3-5 x^2 \log (x)-3 x^3 \log (x)+x^4 \log (x)\right )^2} \, dx \\ & = -\int \frac {(3-x) x^3 (-1+(-2+x) \log (x))}{(-3+x) \left (2+\left (5+e^x\right ) x^2\right )-x^2 \left (-5-3 x+x^2\right ) \log (x)} \, dx+\int \left (-\frac {36 x^3 \log (x)}{\left (6-2 x+15 x^2+3 e^x x^2-5 x^3-e^x x^3-5 x^2 \log (x)-3 x^3 \log (x)+x^4 \log (x)\right )^2}+\frac {6 x^4 \log (x)}{\left (6-2 x+15 x^2+3 e^x x^2-5 x^3-e^x x^3-5 x^2 \log (x)-3 x^3 \log (x)+x^4 \log (x)\right )^2}-\frac {7 x^5 \log (x)}{\left (6-2 x+15 x^2+3 e^x x^2-5 x^3-e^x x^3-5 x^2 \log (x)-3 x^3 \log (x)+x^4 \log (x)\right )^2}-\frac {51 x^6 \log (x)}{\left (6-2 x+15 x^2+3 e^x x^2-5 x^3-e^x x^3-5 x^2 \log (x)-3 x^3 \log (x)+x^4 \log (x)\right )^2}+\frac {36 x^7 \log (x)}{\left (6-2 x+15 x^2+3 e^x x^2-5 x^3-e^x x^3-5 x^2 \log (x)-3 x^3 \log (x)+x^4 \log (x)\right )^2}-\frac {6 x^8 \log (x)}{\left (6-2 x+15 x^2+3 e^x x^2-5 x^3-e^x x^3-5 x^2 \log (x)-3 x^3 \log (x)+x^4 \log (x)\right )^2}+\frac {x^6 \log ^2(x)}{\left (6-2 x+15 x^2+3 e^x x^2-5 x^3-e^x x^3-5 x^2 \log (x)-3 x^3 \log (x)+x^4 \log (x)\right )^2}+\frac {10 x^7 \log ^2(x)}{\left (6-2 x+15 x^2+3 e^x x^2-5 x^3-e^x x^3-5 x^2 \log (x)-3 x^3 \log (x)+x^4 \log (x)\right )^2}-\frac {7 x^8 \log ^2(x)}{\left (6-2 x+15 x^2+3 e^x x^2-5 x^3-e^x x^3-5 x^2 \log (x)-3 x^3 \log (x)+x^4 \log (x)\right )^2}+\frac {x^9 \log ^2(x)}{\left (6-2 x+15 x^2+3 e^x x^2-5 x^3-e^x x^3-5 x^2 \log (x)-3 x^3 \log (x)+x^4 \log (x)\right )^2}\right ) \, dx \\ & = 6 \int \frac {x^4 \log (x)}{\left (6-2 x+15 x^2+3 e^x x^2-5 x^3-e^x x^3-5 x^2 \log (x)-3 x^3 \log (x)+x^4 \log (x)\right )^2} \, dx-6 \int \frac {x^8 \log (x)}{\left (6-2 x+15 x^2+3 e^x x^2-5 x^3-e^x x^3-5 x^2 \log (x)-3 x^3 \log (x)+x^4 \log (x)\right )^2} \, dx-7 \int \frac {x^5 \log (x)}{\left (6-2 x+15 x^2+3 e^x x^2-5 x^3-e^x x^3-5 x^2 \log (x)-3 x^3 \log (x)+x^4 \log (x)\right )^2} \, dx-7 \int \frac {x^8 \log ^2(x)}{\left (6-2 x+15 x^2+3 e^x x^2-5 x^3-e^x x^3-5 x^2 \log (x)-3 x^3 \log (x)+x^4 \log (x)\right )^2} \, dx+10 \int \frac {x^7 \log ^2(x)}{\left (6-2 x+15 x^2+3 e^x x^2-5 x^3-e^x x^3-5 x^2 \log (x)-3 x^3 \log (x)+x^4 \log (x)\right )^2} \, dx-36 \int \frac {x^3 \log (x)}{\left (6-2 x+15 x^2+3 e^x x^2-5 x^3-e^x x^3-5 x^2 \log (x)-3 x^3 \log (x)+x^4 \log (x)\right )^2} \, dx+36 \int \frac {x^7 \log (x)}{\left (6-2 x+15 x^2+3 e^x x^2-5 x^3-e^x x^3-5 x^2 \log (x)-3 x^3 \log (x)+x^4 \log (x)\right )^2} \, dx-51 \int \frac {x^6 \log (x)}{\left (6-2 x+15 x^2+3 e^x x^2-5 x^3-e^x x^3-5 x^2 \log (x)-3 x^3 \log (x)+x^4 \log (x)\right )^2} \, dx+\int \frac {x^6 \log ^2(x)}{\left (6-2 x+15 x^2+3 e^x x^2-5 x^3-e^x x^3-5 x^2 \log (x)-3 x^3 \log (x)+x^4 \log (x)\right )^2} \, dx+\int \frac {x^9 \log ^2(x)}{\left (6-2 x+15 x^2+3 e^x x^2-5 x^3-e^x x^3-5 x^2 \log (x)-3 x^3 \log (x)+x^4 \log (x)\right )^2} \, dx-\int \left (-\frac {3 x^3 (-1-2 \log (x)+x \log (x))}{6-2 x+15 x^2+3 e^x x^2-5 x^3-e^x x^3-5 x^2 \log (x)-3 x^3 \log (x)+x^4 \log (x)}+\frac {x^4 (-1-2 \log (x)+x \log (x))}{6-2 x+15 x^2+3 e^x x^2-5 x^3-e^x x^3-5 x^2 \log (x)-3 x^3 \log (x)+x^4 \log (x)}\right ) \, dx \\ & = 3 \int \frac {x^3 (-1-2 \log (x)+x \log (x))}{6-2 x+15 x^2+3 e^x x^2-5 x^3-e^x x^3-5 x^2 \log (x)-3 x^3 \log (x)+x^4 \log (x)} \, dx+6 \int \frac {x^4 \log (x)}{\left ((-3+x) \left (2+\left (5+e^x\right ) x^2\right )+x^2 \left (5+3 x-x^2\right ) \log (x)\right )^2} \, dx-6 \int \frac {x^8 \log (x)}{\left ((-3+x) \left (2+\left (5+e^x\right ) x^2\right )+x^2 \left (5+3 x-x^2\right ) \log (x)\right )^2} \, dx-7 \int \frac {x^5 \log (x)}{\left ((-3+x) \left (2+\left (5+e^x\right ) x^2\right )+x^2 \left (5+3 x-x^2\right ) \log (x)\right )^2} \, dx-7 \int \frac {x^8 \log ^2(x)}{\left ((-3+x) \left (2+\left (5+e^x\right ) x^2\right )+x^2 \left (5+3 x-x^2\right ) \log (x)\right )^2} \, dx+10 \int \frac {x^7 \log ^2(x)}{\left ((-3+x) \left (2+\left (5+e^x\right ) x^2\right )+x^2 \left (5+3 x-x^2\right ) \log (x)\right )^2} \, dx-36 \int \frac {x^3 \log (x)}{\left ((-3+x) \left (2+\left (5+e^x\right ) x^2\right )+x^2 \left (5+3 x-x^2\right ) \log (x)\right )^2} \, dx+36 \int \frac {x^7 \log (x)}{\left ((-3+x) \left (2+\left (5+e^x\right ) x^2\right )+x^2 \left (5+3 x-x^2\right ) \log (x)\right )^2} \, dx-51 \int \frac {x^6 \log (x)}{\left ((-3+x) \left (2+\left (5+e^x\right ) x^2\right )+x^2 \left (5+3 x-x^2\right ) \log (x)\right )^2} \, dx-\int \frac {x^4 (-1-2 \log (x)+x \log (x))}{6-2 x+15 x^2+3 e^x x^2-5 x^3-e^x x^3-5 x^2 \log (x)-3 x^3 \log (x)+x^4 \log (x)} \, dx+\int \frac {x^6 \log ^2(x)}{\left ((-3+x) \left (2+\left (5+e^x\right ) x^2\right )+x^2 \left (5+3 x-x^2\right ) \log (x)\right )^2} \, dx+\int \frac {x^9 \log ^2(x)}{\left ((-3+x) \left (2+\left (5+e^x\right ) x^2\right )+x^2 \left (5+3 x-x^2\right ) \log (x)\right )^2} \, dx \\ & = 3 \int \frac {x^3 (1-(-2+x) \log (x))}{(-3+x) \left (2+\left (5+e^x\right ) x^2\right )-x^2 \left (-5-3 x+x^2\right ) \log (x)} \, dx+6 \int \frac {x^4 \log (x)}{\left ((-3+x) \left (2+\left (5+e^x\right ) x^2\right )+x^2 \left (5+3 x-x^2\right ) \log (x)\right )^2} \, dx-6 \int \frac {x^8 \log (x)}{\left ((-3+x) \left (2+\left (5+e^x\right ) x^2\right )+x^2 \left (5+3 x-x^2\right ) \log (x)\right )^2} \, dx-7 \int \frac {x^5 \log (x)}{\left ((-3+x) \left (2+\left (5+e^x\right ) x^2\right )+x^2 \left (5+3 x-x^2\right ) \log (x)\right )^2} \, dx-7 \int \frac {x^8 \log ^2(x)}{\left ((-3+x) \left (2+\left (5+e^x\right ) x^2\right )+x^2 \left (5+3 x-x^2\right ) \log (x)\right )^2} \, dx+10 \int \frac {x^7 \log ^2(x)}{\left ((-3+x) \left (2+\left (5+e^x\right ) x^2\right )+x^2 \left (5+3 x-x^2\right ) \log (x)\right )^2} \, dx-36 \int \frac {x^3 \log (x)}{\left ((-3+x) \left (2+\left (5+e^x\right ) x^2\right )+x^2 \left (5+3 x-x^2\right ) \log (x)\right )^2} \, dx+36 \int \frac {x^7 \log (x)}{\left ((-3+x) \left (2+\left (5+e^x\right ) x^2\right )+x^2 \left (5+3 x-x^2\right ) \log (x)\right )^2} \, dx-51 \int \frac {x^6 \log (x)}{\left ((-3+x) \left (2+\left (5+e^x\right ) x^2\right )+x^2 \left (5+3 x-x^2\right ) \log (x)\right )^2} \, dx+\int \frac {x^6 \log ^2(x)}{\left ((-3+x) \left (2+\left (5+e^x\right ) x^2\right )+x^2 \left (5+3 x-x^2\right ) \log (x)\right )^2} \, dx+\int \frac {x^9 \log ^2(x)}{\left ((-3+x) \left (2+\left (5+e^x\right ) x^2\right )+x^2 \left (5+3 x-x^2\right ) \log (x)\right )^2} \, dx-\int \frac {x^4 (1-(-2+x) \log (x))}{(-3+x) \left (2+\left (5+e^x\right ) x^2\right )-x^2 \left (-5-3 x+x^2\right ) \log (x)} \, dx \\ & = 3 \int \left (-\frac {x^3}{6-2 x+15 x^2+3 e^x x^2-5 x^3-e^x x^3-5 x^2 \log (x)-3 x^3 \log (x)+x^4 \log (x)}-\frac {2 x^3 \log (x)}{6-2 x+15 x^2+3 e^x x^2-5 x^3-e^x x^3-5 x^2 \log (x)-3 x^3 \log (x)+x^4 \log (x)}+\frac {x^4 \log (x)}{6-2 x+15 x^2+3 e^x x^2-5 x^3-e^x x^3-5 x^2 \log (x)-3 x^3 \log (x)+x^4 \log (x)}\right ) \, dx+6 \int \frac {x^4 \log (x)}{\left ((-3+x) \left (2+\left (5+e^x\right ) x^2\right )+x^2 \left (5+3 x-x^2\right ) \log (x)\right )^2} \, dx-6 \int \frac {x^8 \log (x)}{\left ((-3+x) \left (2+\left (5+e^x\right ) x^2\right )+x^2 \left (5+3 x-x^2\right ) \log (x)\right )^2} \, dx-7 \int \frac {x^5 \log (x)}{\left ((-3+x) \left (2+\left (5+e^x\right ) x^2\right )+x^2 \left (5+3 x-x^2\right ) \log (x)\right )^2} \, dx-7 \int \frac {x^8 \log ^2(x)}{\left ((-3+x) \left (2+\left (5+e^x\right ) x^2\right )+x^2 \left (5+3 x-x^2\right ) \log (x)\right )^2} \, dx+10 \int \frac {x^7 \log ^2(x)}{\left ((-3+x) \left (2+\left (5+e^x\right ) x^2\right )+x^2 \left (5+3 x-x^2\right ) \log (x)\right )^2} \, dx-36 \int \frac {x^3 \log (x)}{\left ((-3+x) \left (2+\left (5+e^x\right ) x^2\right )+x^2 \left (5+3 x-x^2\right ) \log (x)\right )^2} \, dx+36 \int \frac {x^7 \log (x)}{\left ((-3+x) \left (2+\left (5+e^x\right ) x^2\right )+x^2 \left (5+3 x-x^2\right ) \log (x)\right )^2} \, dx-51 \int \frac {x^6 \log (x)}{\left ((-3+x) \left (2+\left (5+e^x\right ) x^2\right )+x^2 \left (5+3 x-x^2\right ) \log (x)\right )^2} \, dx+\int \frac {x^6 \log ^2(x)}{\left ((-3+x) \left (2+\left (5+e^x\right ) x^2\right )+x^2 \left (5+3 x-x^2\right ) \log (x)\right )^2} \, dx+\int \frac {x^9 \log ^2(x)}{\left ((-3+x) \left (2+\left (5+e^x\right ) x^2\right )+x^2 \left (5+3 x-x^2\right ) \log (x)\right )^2} \, dx-\int \left (-\frac {x^4}{6-2 x+15 x^2+3 e^x x^2-5 x^3-e^x x^3-5 x^2 \log (x)-3 x^3 \log (x)+x^4 \log (x)}-\frac {2 x^4 \log (x)}{6-2 x+15 x^2+3 e^x x^2-5 x^3-e^x x^3-5 x^2 \log (x)-3 x^3 \log (x)+x^4 \log (x)}+\frac {x^5 \log (x)}{6-2 x+15 x^2+3 e^x x^2-5 x^3-e^x x^3-5 x^2 \log (x)-3 x^3 \log (x)+x^4 \log (x)}\right ) \, dx \\ & = 2 \int \frac {x^4 \log (x)}{6-2 x+15 x^2+3 e^x x^2-5 x^3-e^x x^3-5 x^2 \log (x)-3 x^3 \log (x)+x^4 \log (x)} \, dx-3 \int \frac {x^3}{6-2 x+15 x^2+3 e^x x^2-5 x^3-e^x x^3-5 x^2 \log (x)-3 x^3 \log (x)+x^4 \log (x)} \, dx+3 \int \frac {x^4 \log (x)}{6-2 x+15 x^2+3 e^x x^2-5 x^3-e^x x^3-5 x^2 \log (x)-3 x^3 \log (x)+x^4 \log (x)} \, dx-6 \int \frac {x^3 \log (x)}{6-2 x+15 x^2+3 e^x x^2-5 x^3-e^x x^3-5 x^2 \log (x)-3 x^3 \log (x)+x^4 \log (x)} \, dx+6 \int \frac {x^4 \log (x)}{\left ((-3+x) \left (2+\left (5+e^x\right ) x^2\right )+x^2 \left (5+3 x-x^2\right ) \log (x)\right )^2} \, dx-6 \int \frac {x^8 \log (x)}{\left ((-3+x) \left (2+\left (5+e^x\right ) x^2\right )+x^2 \left (5+3 x-x^2\right ) \log (x)\right )^2} \, dx-7 \int \frac {x^5 \log (x)}{\left ((-3+x) \left (2+\left (5+e^x\right ) x^2\right )+x^2 \left (5+3 x-x^2\right ) \log (x)\right )^2} \, dx-7 \int \frac {x^8 \log ^2(x)}{\left ((-3+x) \left (2+\left (5+e^x\right ) x^2\right )+x^2 \left (5+3 x-x^2\right ) \log (x)\right )^2} \, dx+10 \int \frac {x^7 \log ^2(x)}{\left ((-3+x) \left (2+\left (5+e^x\right ) x^2\right )+x^2 \left (5+3 x-x^2\right ) \log (x)\right )^2} \, dx-36 \int \frac {x^3 \log (x)}{\left ((-3+x) \left (2+\left (5+e^x\right ) x^2\right )+x^2 \left (5+3 x-x^2\right ) \log (x)\right )^2} \, dx+36 \int \frac {x^7 \log (x)}{\left ((-3+x) \left (2+\left (5+e^x\right ) x^2\right )+x^2 \left (5+3 x-x^2\right ) \log (x)\right )^2} \, dx-51 \int \frac {x^6 \log (x)}{\left ((-3+x) \left (2+\left (5+e^x\right ) x^2\right )+x^2 \left (5+3 x-x^2\right ) \log (x)\right )^2} \, dx+\int \frac {x^4}{6-2 x+15 x^2+3 e^x x^2-5 x^3-e^x x^3-5 x^2 \log (x)-3 x^3 \log (x)+x^4 \log (x)} \, dx-\int \frac {x^5 \log (x)}{6-2 x+15 x^2+3 e^x x^2-5 x^3-e^x x^3-5 x^2 \log (x)-3 x^3 \log (x)+x^4 \log (x)} \, dx+\int \frac {x^6 \log ^2(x)}{\left ((-3+x) \left (2+\left (5+e^x\right ) x^2\right )+x^2 \left (5+3 x-x^2\right ) \log (x)\right )^2} \, dx+\int \frac {x^9 \log ^2(x)}{\left ((-3+x) \left (2+\left (5+e^x\right ) x^2\right )+x^2 \left (5+3 x-x^2\right ) \log (x)\right )^2} \, dx \\ & = 2 \int \frac {x^4 \log (x)}{-\left ((-3+x) \left (2+\left (5+e^x\right ) x^2\right )\right )+x^2 \left (-5-3 x+x^2\right ) \log (x)} \, dx-3 \int \frac {x^3}{-\left ((-3+x) \left (2+\left (5+e^x\right ) x^2\right )\right )+x^2 \left (-5-3 x+x^2\right ) \log (x)} \, dx+3 \int \frac {x^4 \log (x)}{-\left ((-3+x) \left (2+\left (5+e^x\right ) x^2\right )\right )+x^2 \left (-5-3 x+x^2\right ) \log (x)} \, dx+6 \int \frac {x^4 \log (x)}{\left ((-3+x) \left (2+\left (5+e^x\right ) x^2\right )+x^2 \left (5+3 x-x^2\right ) \log (x)\right )^2} \, dx-6 \int \frac {x^8 \log (x)}{\left ((-3+x) \left (2+\left (5+e^x\right ) x^2\right )+x^2 \left (5+3 x-x^2\right ) \log (x)\right )^2} \, dx-6 \int \frac {x^3 \log (x)}{-\left ((-3+x) \left (2+\left (5+e^x\right ) x^2\right )\right )+x^2 \left (-5-3 x+x^2\right ) \log (x)} \, dx-7 \int \frac {x^5 \log (x)}{\left ((-3+x) \left (2+\left (5+e^x\right ) x^2\right )+x^2 \left (5+3 x-x^2\right ) \log (x)\right )^2} \, dx-7 \int \frac {x^8 \log ^2(x)}{\left ((-3+x) \left (2+\left (5+e^x\right ) x^2\right )+x^2 \left (5+3 x-x^2\right ) \log (x)\right )^2} \, dx+10 \int \frac {x^7 \log ^2(x)}{\left ((-3+x) \left (2+\left (5+e^x\right ) x^2\right )+x^2 \left (5+3 x-x^2\right ) \log (x)\right )^2} \, dx-36 \int \frac {x^3 \log (x)}{\left ((-3+x) \left (2+\left (5+e^x\right ) x^2\right )+x^2 \left (5+3 x-x^2\right ) \log (x)\right )^2} \, dx+36 \int \frac {x^7 \log (x)}{\left ((-3+x) \left (2+\left (5+e^x\right ) x^2\right )+x^2 \left (5+3 x-x^2\right ) \log (x)\right )^2} \, dx-51 \int \frac {x^6 \log (x)}{\left ((-3+x) \left (2+\left (5+e^x\right ) x^2\right )+x^2 \left (5+3 x-x^2\right ) \log (x)\right )^2} \, dx+\int \frac {x^6 \log ^2(x)}{\left ((-3+x) \left (2+\left (5+e^x\right ) x^2\right )+x^2 \left (5+3 x-x^2\right ) \log (x)\right )^2} \, dx+\int \frac {x^9 \log ^2(x)}{\left ((-3+x) \left (2+\left (5+e^x\right ) x^2\right )+x^2 \left (5+3 x-x^2\right ) \log (x)\right )^2} \, dx+\int \frac {x^4}{-\left ((-3+x) \left (2+\left (5+e^x\right ) x^2\right )\right )+x^2 \left (-5-3 x+x^2\right ) \log (x)} \, dx-\int \frac {x^5 \log (x)}{-\left ((-3+x) \left (2+\left (5+e^x\right ) x^2\right )\right )+x^2 \left (-5-3 x+x^2\right ) \log (x)} \, dx \\ \end{align*}
Time = 0.15 (sec) , antiderivative size = 42, normalized size of antiderivative = 1.27 \[ \int \frac {-18 x^3+12 x^4-47 x^5+30 x^6-5 x^7+e^x \left (-9 x^5+6 x^6-x^7\right )+\left (-72 x^3+48 x^4-98 x^5+60 x^6-10 x^7+e^x \left (-18 x^5+21 x^6-8 x^7+x^8\right )\right ) \log (x)+\left (30 x^5-6 x^6-6 x^7+x^8\right ) \log ^2(x)}{36-24 x+184 x^2-120 x^3+245 x^4-150 x^5+25 x^6+e^{2 x} \left (9 x^4-6 x^5+x^6\right )+e^x \left (36 x^2-24 x^3+94 x^4-60 x^5+10 x^6\right )+\left (-60 x^2-16 x^3-126 x^4-44 x^5+60 x^6-10 x^7+e^x \left (-30 x^4-8 x^5+12 x^6-2 x^7\right )\right ) \log (x)+\left (25 x^4+30 x^5-x^6-6 x^7+x^8\right ) \log ^2(x)} \, dx=\frac {(-3+x) x^4 \log (x)}{-\left ((-3+x) \left (2+\left (5+e^x\right ) x^2\right )\right )+x^2 \left (-5-3 x+x^2\right ) \log (x)} \]
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Leaf count of result is larger than twice the leaf count of optimal. \(101\) vs. \(2(32)=64\).
Time = 5.65 (sec) , antiderivative size = 102, normalized size of antiderivative = 3.09
method | result | size |
parallelrisch | \(\frac {18-6 x +x^{5} \ln \left (x \right )+9 \,{\mathrm e}^{x} x^{2}-3 \,{\mathrm e}^{x} x^{3}-15 x^{3}+45 x^{2}-9 x^{3} \ln \left (x \right )-15 x^{2} \ln \left (x \right )}{x^{4} \ln \left (x \right )-3 x^{3} \ln \left (x \right )-{\mathrm e}^{x} x^{3}-5 x^{2} \ln \left (x \right )+3 \,{\mathrm e}^{x} x^{2}-5 x^{3}+15 x^{2}-2 x +6}\) | \(102\) |
risch | \(\frac {x^{2} \left (-3+x \right )}{x^{2}-3 x -5}+\frac {x^{2} \left ({\mathrm e}^{x} x^{4}+5 x^{4}-6 \,{\mathrm e}^{x} x^{3}-30 x^{3}+9 \,{\mathrm e}^{x} x^{2}+47 x^{2}-12 x +18\right )}{\left (x^{2}-3 x -5\right ) \left (x^{4} \ln \left (x \right )-3 x^{3} \ln \left (x \right )-{\mathrm e}^{x} x^{3}-5 x^{2} \ln \left (x \right )+3 \,{\mathrm e}^{x} x^{2}-5 x^{3}+15 x^{2}-2 x +6\right )}\) | \(124\) |
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Time = 0.24 (sec) , antiderivative size = 60, normalized size of antiderivative = 1.82 \[ \int \frac {-18 x^3+12 x^4-47 x^5+30 x^6-5 x^7+e^x \left (-9 x^5+6 x^6-x^7\right )+\left (-72 x^3+48 x^4-98 x^5+60 x^6-10 x^7+e^x \left (-18 x^5+21 x^6-8 x^7+x^8\right )\right ) \log (x)+\left (30 x^5-6 x^6-6 x^7+x^8\right ) \log ^2(x)}{36-24 x+184 x^2-120 x^3+245 x^4-150 x^5+25 x^6+e^{2 x} \left (9 x^4-6 x^5+x^6\right )+e^x \left (36 x^2-24 x^3+94 x^4-60 x^5+10 x^6\right )+\left (-60 x^2-16 x^3-126 x^4-44 x^5+60 x^6-10 x^7+e^x \left (-30 x^4-8 x^5+12 x^6-2 x^7\right )\right ) \log (x)+\left (25 x^4+30 x^5-x^6-6 x^7+x^8\right ) \log ^2(x)} \, dx=-\frac {{\left (x^{5} - 3 \, x^{4}\right )} \log \left (x\right )}{5 \, x^{3} - 15 \, x^{2} + {\left (x^{3} - 3 \, x^{2}\right )} e^{x} - {\left (x^{4} - 3 \, x^{3} - 5 \, x^{2}\right )} \log \left (x\right ) + 2 \, x - 6} \]
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Leaf count of result is larger than twice the leaf count of optimal. 65 vs. \(2 (22) = 44\).
Time = 0.42 (sec) , antiderivative size = 65, normalized size of antiderivative = 1.97 \[ \int \frac {-18 x^3+12 x^4-47 x^5+30 x^6-5 x^7+e^x \left (-9 x^5+6 x^6-x^7\right )+\left (-72 x^3+48 x^4-98 x^5+60 x^6-10 x^7+e^x \left (-18 x^5+21 x^6-8 x^7+x^8\right )\right ) \log (x)+\left (30 x^5-6 x^6-6 x^7+x^8\right ) \log ^2(x)}{36-24 x+184 x^2-120 x^3+245 x^4-150 x^5+25 x^6+e^{2 x} \left (9 x^4-6 x^5+x^6\right )+e^x \left (36 x^2-24 x^3+94 x^4-60 x^5+10 x^6\right )+\left (-60 x^2-16 x^3-126 x^4-44 x^5+60 x^6-10 x^7+e^x \left (-30 x^4-8 x^5+12 x^6-2 x^7\right )\right ) \log (x)+\left (25 x^4+30 x^5-x^6-6 x^7+x^8\right ) \log ^2(x)} \, dx=\frac {- x^{5} \log {\left (x \right )} + 3 x^{4} \log {\left (x \right )}}{- x^{4} \log {\left (x \right )} + 3 x^{3} \log {\left (x \right )} + 5 x^{3} + 5 x^{2} \log {\left (x \right )} - 15 x^{2} + 2 x + \left (x^{3} - 3 x^{2}\right ) e^{x} - 6} \]
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Time = 0.34 (sec) , antiderivative size = 60, normalized size of antiderivative = 1.82 \[ \int \frac {-18 x^3+12 x^4-47 x^5+30 x^6-5 x^7+e^x \left (-9 x^5+6 x^6-x^7\right )+\left (-72 x^3+48 x^4-98 x^5+60 x^6-10 x^7+e^x \left (-18 x^5+21 x^6-8 x^7+x^8\right )\right ) \log (x)+\left (30 x^5-6 x^6-6 x^7+x^8\right ) \log ^2(x)}{36-24 x+184 x^2-120 x^3+245 x^4-150 x^5+25 x^6+e^{2 x} \left (9 x^4-6 x^5+x^6\right )+e^x \left (36 x^2-24 x^3+94 x^4-60 x^5+10 x^6\right )+\left (-60 x^2-16 x^3-126 x^4-44 x^5+60 x^6-10 x^7+e^x \left (-30 x^4-8 x^5+12 x^6-2 x^7\right )\right ) \log (x)+\left (25 x^4+30 x^5-x^6-6 x^7+x^8\right ) \log ^2(x)} \, dx=-\frac {{\left (x^{5} - 3 \, x^{4}\right )} \log \left (x\right )}{5 \, x^{3} - 15 \, x^{2} + {\left (x^{3} - 3 \, x^{2}\right )} e^{x} - {\left (x^{4} - 3 \, x^{3} - 5 \, x^{2}\right )} \log \left (x\right ) + 2 \, x - 6} \]
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Leaf count of result is larger than twice the leaf count of optimal. 108 vs. \(2 (30) = 60\).
Time = 0.39 (sec) , antiderivative size = 108, normalized size of antiderivative = 3.27 \[ \int \frac {-18 x^3+12 x^4-47 x^5+30 x^6-5 x^7+e^x \left (-9 x^5+6 x^6-x^7\right )+\left (-72 x^3+48 x^4-98 x^5+60 x^6-10 x^7+e^x \left (-18 x^5+21 x^6-8 x^7+x^8\right )\right ) \log (x)+\left (30 x^5-6 x^6-6 x^7+x^8\right ) \log ^2(x)}{36-24 x+184 x^2-120 x^3+245 x^4-150 x^5+25 x^6+e^{2 x} \left (9 x^4-6 x^5+x^6\right )+e^x \left (36 x^2-24 x^3+94 x^4-60 x^5+10 x^6\right )+\left (-60 x^2-16 x^3-126 x^4-44 x^5+60 x^6-10 x^7+e^x \left (-30 x^4-8 x^5+12 x^6-2 x^7\right )\right ) \log (x)+\left (25 x^4+30 x^5-x^6-6 x^7+x^8\right ) \log ^2(x)} \, dx=\frac {x^{5} \log \left (x\right ) - 2 \, x^{4} \log \left (x\right ) - x^{3} e^{x} - 3 \, x^{3} \log \left (x\right ) - 5 \, x^{3} + 3 \, x^{2} e^{x} - 5 \, x^{2} \log \left (x\right ) + 15 \, x^{2} - 2 \, x + 6}{x^{4} \log \left (x\right ) - x^{3} e^{x} - 3 \, x^{3} \log \left (x\right ) - 5 \, x^{3} + 3 \, x^{2} e^{x} - 5 \, x^{2} \log \left (x\right ) + 15 \, x^{2} - 2 \, x + 6} \]
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Timed out. \[ \int \frac {-18 x^3+12 x^4-47 x^5+30 x^6-5 x^7+e^x \left (-9 x^5+6 x^6-x^7\right )+\left (-72 x^3+48 x^4-98 x^5+60 x^6-10 x^7+e^x \left (-18 x^5+21 x^6-8 x^7+x^8\right )\right ) \log (x)+\left (30 x^5-6 x^6-6 x^7+x^8\right ) \log ^2(x)}{36-24 x+184 x^2-120 x^3+245 x^4-150 x^5+25 x^6+e^{2 x} \left (9 x^4-6 x^5+x^6\right )+e^x \left (36 x^2-24 x^3+94 x^4-60 x^5+10 x^6\right )+\left (-60 x^2-16 x^3-126 x^4-44 x^5+60 x^6-10 x^7+e^x \left (-30 x^4-8 x^5+12 x^6-2 x^7\right )\right ) \log (x)+\left (25 x^4+30 x^5-x^6-6 x^7+x^8\right ) \log ^2(x)} \, dx=-\int \frac {\ln \left (x\right )\,\left ({\mathrm {e}}^x\,\left (-x^8+8\,x^7-21\,x^6+18\,x^5\right )+72\,x^3-48\,x^4+98\,x^5-60\,x^6+10\,x^7\right )-{\ln \left (x\right )}^2\,\left (x^8-6\,x^7-6\,x^6+30\,x^5\right )+18\,x^3-12\,x^4+47\,x^5-30\,x^6+5\,x^7+{\mathrm {e}}^x\,\left (x^7-6\,x^6+9\,x^5\right )}{{\mathrm {e}}^{2\,x}\,\left (x^6-6\,x^5+9\,x^4\right )-24\,x-\ln \left (x\right )\,\left ({\mathrm {e}}^x\,\left (2\,x^7-12\,x^6+8\,x^5+30\,x^4\right )+60\,x^2+16\,x^3+126\,x^4+44\,x^5-60\,x^6+10\,x^7\right )+{\mathrm {e}}^x\,\left (10\,x^6-60\,x^5+94\,x^4-24\,x^3+36\,x^2\right )+{\ln \left (x\right )}^2\,\left (x^8-6\,x^7-x^6+30\,x^5+25\,x^4\right )+184\,x^2-120\,x^3+245\,x^4-150\,x^5+25\,x^6+36} \,d x \]
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