Integrand size = 325, antiderivative size = 28 \[ \int \frac {-36 x^4-162 e^4 x^4+81 x^4 \log (3)+e^{4 x} \left (-162 e^4+81 \log (3)\right )+e^{3 x} \left (648 e^4 x-324 x \log (3)\right )+e^{2 x} \left (-108 x^2-972 e^4 x^2+54 x^3+18 x^4+486 x^2 \log (3)\right )+e^x \left (144 x^3+648 e^4 x^3-54 x^4-18 x^5-324 x^3 \log (3)\right )}{324 e^8 x^4-36 e^4 x^5+x^6+\left (-324 e^4 x^4+18 x^5\right ) \log (3)+81 x^4 \log ^2(3)+e^{4 x} \left (324 e^8-324 e^4 \log (3)+81 \log ^2(3)\right )+e^{3 x} \left (-1296 e^8 x+1296 e^4 x \log (3)-324 x \log ^2(3)\right )+e^{2 x} \left (1944 e^8 x^2-36 e^4 x^3+\left (-1944 e^4 x^2+18 x^3\right ) \log (3)+486 x^2 \log ^2(3)\right )+e^x \left (-1296 e^8 x^3+72 e^4 x^4+\left (1296 e^4 x^3-36 x^4\right ) \log (3)-324 x^3 \log ^2(3)\right )} \, dx=\frac {4+x}{-2 e^4+\frac {x}{\left (3-\frac {3 e^x}{x}\right )^2}+\log (3)} \]
[Out]
\[ \int \frac {-36 x^4-162 e^4 x^4+81 x^4 \log (3)+e^{4 x} \left (-162 e^4+81 \log (3)\right )+e^{3 x} \left (648 e^4 x-324 x \log (3)\right )+e^{2 x} \left (-108 x^2-972 e^4 x^2+54 x^3+18 x^4+486 x^2 \log (3)\right )+e^x \left (144 x^3+648 e^4 x^3-54 x^4-18 x^5-324 x^3 \log (3)\right )}{324 e^8 x^4-36 e^4 x^5+x^6+\left (-324 e^4 x^4+18 x^5\right ) \log (3)+81 x^4 \log ^2(3)+e^{4 x} \left (324 e^8-324 e^4 \log (3)+81 \log ^2(3)\right )+e^{3 x} \left (-1296 e^8 x+1296 e^4 x \log (3)-324 x \log ^2(3)\right )+e^{2 x} \left (1944 e^8 x^2-36 e^4 x^3+\left (-1944 e^4 x^2+18 x^3\right ) \log (3)+486 x^2 \log ^2(3)\right )+e^x \left (-1296 e^8 x^3+72 e^4 x^4+\left (1296 e^4 x^3-36 x^4\right ) \log (3)-324 x^3 \log ^2(3)\right )} \, dx=\int \frac {-36 x^4-162 e^4 x^4+81 x^4 \log (3)+e^{4 x} \left (-162 e^4+81 \log (3)\right )+e^{3 x} \left (648 e^4 x-324 x \log (3)\right )+e^{2 x} \left (-108 x^2-972 e^4 x^2+54 x^3+18 x^4+486 x^2 \log (3)\right )+e^x \left (144 x^3+648 e^4 x^3-54 x^4-18 x^5-324 x^3 \log (3)\right )}{324 e^8 x^4-36 e^4 x^5+x^6+\left (-324 e^4 x^4+18 x^5\right ) \log (3)+81 x^4 \log ^2(3)+e^{4 x} \left (324 e^8-324 e^4 \log (3)+81 \log ^2(3)\right )+e^{3 x} \left (-1296 e^8 x+1296 e^4 x \log (3)-324 x \log ^2(3)\right )+e^{2 x} \left (1944 e^8 x^2-36 e^4 x^3+\left (-1944 e^4 x^2+18 x^3\right ) \log (3)+486 x^2 \log ^2(3)\right )+e^x \left (-1296 e^8 x^3+72 e^4 x^4+\left (1296 e^4 x^3-36 x^4\right ) \log (3)-324 x^3 \log ^2(3)\right )} \, dx \]
[In]
[Out]
Rubi steps \begin{align*} \text {integral}& = \int \frac {\left (-36-162 e^4\right ) x^4+81 x^4 \log (3)+e^{4 x} \left (-162 e^4+81 \log (3)\right )+e^{3 x} \left (648 e^4 x-324 x \log (3)\right )+e^{2 x} \left (-108 x^2-972 e^4 x^2+54 x^3+18 x^4+486 x^2 \log (3)\right )+e^x \left (144 x^3+648 e^4 x^3-54 x^4-18 x^5-324 x^3 \log (3)\right )}{324 e^8 x^4-36 e^4 x^5+x^6+\left (-324 e^4 x^4+18 x^5\right ) \log (3)+81 x^4 \log ^2(3)+e^{4 x} \left (324 e^8-324 e^4 \log (3)+81 \log ^2(3)\right )+e^{3 x} \left (-1296 e^8 x+1296 e^4 x \log (3)-324 x \log ^2(3)\right )+e^{2 x} \left (1944 e^8 x^2-36 e^4 x^3+\left (-1944 e^4 x^2+18 x^3\right ) \log (3)+486 x^2 \log ^2(3)\right )+e^x \left (-1296 e^8 x^3+72 e^4 x^4+\left (1296 e^4 x^3-36 x^4\right ) \log (3)-324 x^3 \log ^2(3)\right )} \, dx \\ & = \int \frac {x^4 \left (-36-162 e^4+81 \log (3)\right )+e^{4 x} \left (-162 e^4+81 \log (3)\right )+e^{3 x} \left (648 e^4 x-324 x \log (3)\right )+e^{2 x} \left (-108 x^2-972 e^4 x^2+54 x^3+18 x^4+486 x^2 \log (3)\right )+e^x \left (144 x^3+648 e^4 x^3-54 x^4-18 x^5-324 x^3 \log (3)\right )}{324 e^8 x^4-36 e^4 x^5+x^6+\left (-324 e^4 x^4+18 x^5\right ) \log (3)+81 x^4 \log ^2(3)+e^{4 x} \left (324 e^8-324 e^4 \log (3)+81 \log ^2(3)\right )+e^{3 x} \left (-1296 e^8 x+1296 e^4 x \log (3)-324 x \log ^2(3)\right )+e^{2 x} \left (1944 e^8 x^2-36 e^4 x^3+\left (-1944 e^4 x^2+18 x^3\right ) \log (3)+486 x^2 \log ^2(3)\right )+e^x \left (-1296 e^8 x^3+72 e^4 x^4+\left (1296 e^4 x^3-36 x^4\right ) \log (3)-324 x^3 \log ^2(3)\right )} \, dx \\ & = \int \frac {x^4 \left (-36-162 e^4+81 \log (3)\right )+e^{4 x} \left (-162 e^4+81 \log (3)\right )+e^{3 x} \left (648 e^4 x-324 x \log (3)\right )+e^{2 x} \left (-108 x^2-972 e^4 x^2+54 x^3+18 x^4+486 x^2 \log (3)\right )+e^x \left (144 x^3+648 e^4 x^3-54 x^4-18 x^5-324 x^3 \log (3)\right )}{-36 e^4 x^5+x^6+\left (-324 e^4 x^4+18 x^5\right ) \log (3)+x^4 \left (324 e^8+81 \log ^2(3)\right )+e^{4 x} \left (324 e^8-324 e^4 \log (3)+81 \log ^2(3)\right )+e^{3 x} \left (-1296 e^8 x+1296 e^4 x \log (3)-324 x \log ^2(3)\right )+e^{2 x} \left (1944 e^8 x^2-36 e^4 x^3+\left (-1944 e^4 x^2+18 x^3\right ) \log (3)+486 x^2 \log ^2(3)\right )+e^x \left (-1296 e^8 x^3+72 e^4 x^4+\left (1296 e^4 x^3-36 x^4\right ) \log (3)-324 x^3 \log ^2(3)\right )} \, dx \\ & = \int \frac {9 \left (e^x-x\right ) \left (-54 e^{4+x} x^2+18 e^4 x^3 \left (1+\frac {4-9 \log (3)}{18 e^4}\right )+e^x x^2 \left (-12+6 x+2 x^2+27 \log (3)\right )-18 e^{4+3 x} \left (1-\frac {\log (3)}{2 e^4}\right )+54 e^{4+2 x} x \left (1-\frac {\log (3)}{2 e^4}\right )\right )}{\left (18 e^4 x^2-x^2 (x+9 \log (3))+18 e^{4+2 x} \left (1-\frac {\log (3)}{2 e^4}\right )-36 e^{4+x} x \left (1-\frac {\log (3)}{2 e^4}\right )\right )^2} \, dx \\ & = 9 \int \frac {\left (e^x-x\right ) \left (-54 e^{4+x} x^2+18 e^4 x^3 \left (1+\frac {4-9 \log (3)}{18 e^4}\right )+e^x x^2 \left (-12+6 x+2 x^2+27 \log (3)\right )-18 e^{4+3 x} \left (1-\frac {\log (3)}{2 e^4}\right )+54 e^{4+2 x} x \left (1-\frac {\log (3)}{2 e^4}\right )\right )}{\left (18 e^4 x^2-x^2 (x+9 \log (3))+18 e^{4+2 x} \left (1-\frac {\log (3)}{2 e^4}\right )-36 e^{4+x} x \left (1-\frac {\log (3)}{2 e^4}\right )\right )^2} \, dx \\ & = 9 \int \left (-\frac {1}{9 \left (2 e^4-\log (3)\right )}+\frac {2 x^2 \left (6-2 x-x^2\right )}{9 \left (2 e^4-\log (3)\right ) \left (x^3-18 e^{4+2 x} \left (1-\frac {\log (3)}{2 e^4}\right )+36 e^{4+x} x \left (1-\frac {\log (3)}{2 e^4}\right )-18 e^4 x^2 \left (1-\frac {\log (3)}{2 e^4}\right )\right )}+\frac {x^3 (4+x) \left (2 x^3-36 e^{4+x} \left (1-\frac {\log (3)}{2 e^4}\right )+36 e^4 x \left (1-\frac {\log (3)}{2 e^4}\right )+36 e^{4+x} x \left (1-\frac {\log (3)}{2 e^4}\right )-3 x^2 \left (1+12 e^4-\log (729)\right )\right )}{9 \left (2 e^4-\log (3)\right ) \left (x^3-18 e^{4+2 x} \left (1-\frac {\log (3)}{2 e^4}\right )+36 e^{4+x} x \left (1-\frac {\log (3)}{2 e^4}\right )-18 e^4 x^2 \left (1-\frac {\log (3)}{2 e^4}\right )\right )^2}\right ) \, dx \\ & = -\frac {x}{2 e^4-\log (3)}+\frac {\int \frac {x^3 (4+x) \left (2 x^3-36 e^{4+x} \left (1-\frac {\log (3)}{2 e^4}\right )+36 e^4 x \left (1-\frac {\log (3)}{2 e^4}\right )+36 e^{4+x} x \left (1-\frac {\log (3)}{2 e^4}\right )-3 x^2 \left (1+12 e^4-\log (729)\right )\right )}{\left (x^3-18 e^{4+2 x} \left (1-\frac {\log (3)}{2 e^4}\right )+36 e^{4+x} x \left (1-\frac {\log (3)}{2 e^4}\right )-18 e^4 x^2 \left (1-\frac {\log (3)}{2 e^4}\right )\right )^2} \, dx}{2 e^4-\log (3)}+\frac {2 \int \frac {x^2 \left (6-2 x-x^2\right )}{x^3-18 e^{4+2 x} \left (1-\frac {\log (3)}{2 e^4}\right )+36 e^{4+x} x \left (1-\frac {\log (3)}{2 e^4}\right )-18 e^4 x^2 \left (1-\frac {\log (3)}{2 e^4}\right )} \, dx}{2 e^4-\log (3)} \\ & = -\frac {x}{2 e^4-\log (3)}+\frac {\int \left (\frac {4 x^3 \left (2 x^3-36 e^{4+x} \left (1-\frac {\log (3)}{2 e^4}\right )+36 e^4 x \left (1-\frac {\log (3)}{2 e^4}\right )+36 e^{4+x} x \left (1-\frac {\log (3)}{2 e^4}\right )-3 x^2 \left (1+12 e^4-\log (729)\right )\right )}{\left (x^3-18 e^{4+2 x} \left (1-\frac {\log (3)}{2 e^4}\right )+36 e^{4+x} x \left (1-\frac {\log (3)}{2 e^4}\right )-18 e^4 x^2 \left (1-\frac {\log (3)}{2 e^4}\right )\right )^2}+\frac {x^4 \left (2 x^3-36 e^{4+x} \left (1-\frac {\log (3)}{2 e^4}\right )+36 e^4 x \left (1-\frac {\log (3)}{2 e^4}\right )+36 e^{4+x} x \left (1-\frac {\log (3)}{2 e^4}\right )-3 x^2 \left (1+12 e^4-\log (729)\right )\right )}{\left (x^3-18 e^{4+2 x} \left (1-\frac {\log (3)}{2 e^4}\right )+36 e^{4+x} x \left (1-\frac {\log (3)}{2 e^4}\right )-18 e^4 x^2 \left (1-\frac {\log (3)}{2 e^4}\right )\right )^2}\right ) \, dx}{2 e^4-\log (3)}+\frac {2 \int \left (\frac {6 x^2}{x^3-18 e^{4+2 x} \left (1-\frac {\log (3)}{2 e^4}\right )+36 e^{4+x} x \left (1-\frac {\log (3)}{2 e^4}\right )-18 e^4 x^2 \left (1-\frac {\log (3)}{2 e^4}\right )}+\frac {2 x^3}{-x^3+18 e^{4+2 x} \left (1-\frac {\log (3)}{2 e^4}\right )-36 e^{4+x} x \left (1-\frac {\log (3)}{2 e^4}\right )+18 e^4 x^2 \left (1-\frac {\log (3)}{2 e^4}\right )}+\frac {x^4}{-x^3+18 e^{4+2 x} \left (1-\frac {\log (3)}{2 e^4}\right )-36 e^{4+x} x \left (1-\frac {\log (3)}{2 e^4}\right )+18 e^4 x^2 \left (1-\frac {\log (3)}{2 e^4}\right )}\right ) \, dx}{2 e^4-\log (3)} \\ & = -\frac {x}{2 e^4-\log (3)}+\frac {\int \frac {x^4 \left (2 x^3-36 e^{4+x} \left (1-\frac {\log (3)}{2 e^4}\right )+36 e^4 x \left (1-\frac {\log (3)}{2 e^4}\right )+36 e^{4+x} x \left (1-\frac {\log (3)}{2 e^4}\right )-3 x^2 \left (1+12 e^4-\log (729)\right )\right )}{\left (x^3-18 e^{4+2 x} \left (1-\frac {\log (3)}{2 e^4}\right )+36 e^{4+x} x \left (1-\frac {\log (3)}{2 e^4}\right )-18 e^4 x^2 \left (1-\frac {\log (3)}{2 e^4}\right )\right )^2} \, dx}{2 e^4-\log (3)}+\frac {2 \int \frac {x^4}{-x^3+18 e^{4+2 x} \left (1-\frac {\log (3)}{2 e^4}\right )-36 e^{4+x} x \left (1-\frac {\log (3)}{2 e^4}\right )+18 e^4 x^2 \left (1-\frac {\log (3)}{2 e^4}\right )} \, dx}{2 e^4-\log (3)}+\frac {4 \int \frac {x^3}{-x^3+18 e^{4+2 x} \left (1-\frac {\log (3)}{2 e^4}\right )-36 e^{4+x} x \left (1-\frac {\log (3)}{2 e^4}\right )+18 e^4 x^2 \left (1-\frac {\log (3)}{2 e^4}\right )} \, dx}{2 e^4-\log (3)}+\frac {4 \int \frac {x^3 \left (2 x^3-36 e^{4+x} \left (1-\frac {\log (3)}{2 e^4}\right )+36 e^4 x \left (1-\frac {\log (3)}{2 e^4}\right )+36 e^{4+x} x \left (1-\frac {\log (3)}{2 e^4}\right )-3 x^2 \left (1+12 e^4-\log (729)\right )\right )}{\left (x^3-18 e^{4+2 x} \left (1-\frac {\log (3)}{2 e^4}\right )+36 e^{4+x} x \left (1-\frac {\log (3)}{2 e^4}\right )-18 e^4 x^2 \left (1-\frac {\log (3)}{2 e^4}\right )\right )^2} \, dx}{2 e^4-\log (3)}+\frac {12 \int \frac {x^2}{x^3-18 e^{4+2 x} \left (1-\frac {\log (3)}{2 e^4}\right )+36 e^{4+x} x \left (1-\frac {\log (3)}{2 e^4}\right )-18 e^4 x^2 \left (1-\frac {\log (3)}{2 e^4}\right )} \, dx}{2 e^4-\log (3)} \\ & = -\frac {x}{2 e^4-\log (3)}+\frac {\int \left (\frac {2 x^7}{\left (x^3-18 e^{4+2 x} \left (1-\frac {\log (3)}{2 e^4}\right )+36 e^{4+x} x \left (1-\frac {\log (3)}{2 e^4}\right )-18 e^4 x^2 \left (1-\frac {\log (3)}{2 e^4}\right )\right )^2}+\frac {18 x^5 \left (2 e^4-\log (3)\right )}{\left (x^3-18 e^{4+2 x} \left (1-\frac {\log (3)}{2 e^4}\right )+36 e^{4+x} x \left (1-\frac {\log (3)}{2 e^4}\right )-18 e^4 x^2 \left (1-\frac {\log (3)}{2 e^4}\right )\right )^2}+\frac {18 e^x x^5 \left (2 e^4-\log (3)\right )}{\left (x^3-18 e^{4+2 x} \left (1-\frac {\log (3)}{2 e^4}\right )+36 e^{4+x} x \left (1-\frac {\log (3)}{2 e^4}\right )-18 e^4 x^2 \left (1-\frac {\log (3)}{2 e^4}\right )\right )^2}+\frac {18 e^x x^4 \left (-2 e^4+\log (3)\right )}{\left (x^3-18 e^{4+2 x} \left (1-\frac {\log (3)}{2 e^4}\right )+36 e^{4+x} x \left (1-\frac {\log (3)}{2 e^4}\right )-18 e^4 x^2 \left (1-\frac {\log (3)}{2 e^4}\right )\right )^2}+\frac {3 x^6 \left (-1-12 e^4+\log (729)\right )}{\left (x^3-18 e^{4+2 x} \left (1-\frac {\log (3)}{2 e^4}\right )+36 e^{4+x} x \left (1-\frac {\log (3)}{2 e^4}\right )-18 e^4 x^2 \left (1-\frac {\log (3)}{2 e^4}\right )\right )^2}\right ) \, dx}{2 e^4-\log (3)}+\frac {2 \int \frac {x^4}{-x^3+18 e^{4+2 x} \left (1-\frac {\log (3)}{2 e^4}\right )-36 e^{4+x} x \left (1-\frac {\log (3)}{2 e^4}\right )+18 e^4 x^2 \left (1-\frac {\log (3)}{2 e^4}\right )} \, dx}{2 e^4-\log (3)}+\frac {4 \int \frac {x^3}{-x^3+18 e^{4+2 x} \left (1-\frac {\log (3)}{2 e^4}\right )-36 e^{4+x} x \left (1-\frac {\log (3)}{2 e^4}\right )+18 e^4 x^2 \left (1-\frac {\log (3)}{2 e^4}\right )} \, dx}{2 e^4-\log (3)}+\frac {4 \int \left (\frac {2 x^6}{\left (x^3-18 e^{4+2 x} \left (1-\frac {\log (3)}{2 e^4}\right )+36 e^{4+x} x \left (1-\frac {\log (3)}{2 e^4}\right )-18 e^4 x^2 \left (1-\frac {\log (3)}{2 e^4}\right )\right )^2}+\frac {18 x^4 \left (2 e^4-\log (3)\right )}{\left (x^3-18 e^{4+2 x} \left (1-\frac {\log (3)}{2 e^4}\right )+36 e^{4+x} x \left (1-\frac {\log (3)}{2 e^4}\right )-18 e^4 x^2 \left (1-\frac {\log (3)}{2 e^4}\right )\right )^2}+\frac {18 e^x x^4 \left (2 e^4-\log (3)\right )}{\left (x^3-18 e^{4+2 x} \left (1-\frac {\log (3)}{2 e^4}\right )+36 e^{4+x} x \left (1-\frac {\log (3)}{2 e^4}\right )-18 e^4 x^2 \left (1-\frac {\log (3)}{2 e^4}\right )\right )^2}+\frac {18 e^x x^3 \left (-2 e^4+\log (3)\right )}{\left (x^3-18 e^{4+2 x} \left (1-\frac {\log (3)}{2 e^4}\right )+36 e^{4+x} x \left (1-\frac {\log (3)}{2 e^4}\right )-18 e^4 x^2 \left (1-\frac {\log (3)}{2 e^4}\right )\right )^2}+\frac {3 x^5 \left (-1-12 e^4+\log (729)\right )}{\left (x^3-18 e^{4+2 x} \left (1-\frac {\log (3)}{2 e^4}\right )+36 e^{4+x} x \left (1-\frac {\log (3)}{2 e^4}\right )-18 e^4 x^2 \left (1-\frac {\log (3)}{2 e^4}\right )\right )^2}\right ) \, dx}{2 e^4-\log (3)}+\frac {12 \int \frac {x^2}{x^3-18 e^{4+2 x} \left (1-\frac {\log (3)}{2 e^4}\right )+36 e^{4+x} x \left (1-\frac {\log (3)}{2 e^4}\right )-18 e^4 x^2 \left (1-\frac {\log (3)}{2 e^4}\right )} \, dx}{2 e^4-\log (3)} \\ & = -\frac {x}{2 e^4-\log (3)}-18 \int \frac {e^x x^4}{\left (x^3-18 e^{4+2 x} \left (1-\frac {\log (3)}{2 e^4}\right )+36 e^{4+x} x \left (1-\frac {\log (3)}{2 e^4}\right )-18 e^4 x^2 \left (1-\frac {\log (3)}{2 e^4}\right )\right )^2} \, dx+18 \int \frac {x^5}{\left (x^3-18 e^{4+2 x} \left (1-\frac {\log (3)}{2 e^4}\right )+36 e^{4+x} x \left (1-\frac {\log (3)}{2 e^4}\right )-18 e^4 x^2 \left (1-\frac {\log (3)}{2 e^4}\right )\right )^2} \, dx+18 \int \frac {e^x x^5}{\left (x^3-18 e^{4+2 x} \left (1-\frac {\log (3)}{2 e^4}\right )+36 e^{4+x} x \left (1-\frac {\log (3)}{2 e^4}\right )-18 e^4 x^2 \left (1-\frac {\log (3)}{2 e^4}\right )\right )^2} \, dx-72 \int \frac {e^x x^3}{\left (x^3-18 e^{4+2 x} \left (1-\frac {\log (3)}{2 e^4}\right )+36 e^{4+x} x \left (1-\frac {\log (3)}{2 e^4}\right )-18 e^4 x^2 \left (1-\frac {\log (3)}{2 e^4}\right )\right )^2} \, dx+72 \int \frac {x^4}{\left (x^3-18 e^{4+2 x} \left (1-\frac {\log (3)}{2 e^4}\right )+36 e^{4+x} x \left (1-\frac {\log (3)}{2 e^4}\right )-18 e^4 x^2 \left (1-\frac {\log (3)}{2 e^4}\right )\right )^2} \, dx+72 \int \frac {e^x x^4}{\left (x^3-18 e^{4+2 x} \left (1-\frac {\log (3)}{2 e^4}\right )+36 e^{4+x} x \left (1-\frac {\log (3)}{2 e^4}\right )-18 e^4 x^2 \left (1-\frac {\log (3)}{2 e^4}\right )\right )^2} \, dx+\frac {2 \int \frac {x^7}{\left (x^3-18 e^{4+2 x} \left (1-\frac {\log (3)}{2 e^4}\right )+36 e^{4+x} x \left (1-\frac {\log (3)}{2 e^4}\right )-18 e^4 x^2 \left (1-\frac {\log (3)}{2 e^4}\right )\right )^2} \, dx}{2 e^4-\log (3)}+\frac {2 \int \frac {x^4}{-x^3+18 e^{4+2 x} \left (1-\frac {\log (3)}{2 e^4}\right )-36 e^{4+x} x \left (1-\frac {\log (3)}{2 e^4}\right )+18 e^4 x^2 \left (1-\frac {\log (3)}{2 e^4}\right )} \, dx}{2 e^4-\log (3)}+\frac {4 \int \frac {x^3}{-x^3+18 e^{4+2 x} \left (1-\frac {\log (3)}{2 e^4}\right )-36 e^{4+x} x \left (1-\frac {\log (3)}{2 e^4}\right )+18 e^4 x^2 \left (1-\frac {\log (3)}{2 e^4}\right )} \, dx}{2 e^4-\log (3)}+\frac {8 \int \frac {x^6}{\left (x^3-18 e^{4+2 x} \left (1-\frac {\log (3)}{2 e^4}\right )+36 e^{4+x} x \left (1-\frac {\log (3)}{2 e^4}\right )-18 e^4 x^2 \left (1-\frac {\log (3)}{2 e^4}\right )\right )^2} \, dx}{2 e^4-\log (3)}+\frac {12 \int \frac {x^2}{x^3-18 e^{4+2 x} \left (1-\frac {\log (3)}{2 e^4}\right )+36 e^{4+x} x \left (1-\frac {\log (3)}{2 e^4}\right )-18 e^4 x^2 \left (1-\frac {\log (3)}{2 e^4}\right )} \, dx}{2 e^4-\log (3)}-\frac {\left (3 \left (1+12 e^4-\log (729)\right )\right ) \int \frac {x^6}{\left (x^3-18 e^{4+2 x} \left (1-\frac {\log (3)}{2 e^4}\right )+36 e^{4+x} x \left (1-\frac {\log (3)}{2 e^4}\right )-18 e^4 x^2 \left (1-\frac {\log (3)}{2 e^4}\right )\right )^2} \, dx}{2 e^4-\log (3)}-\frac {\left (12 \left (1+12 e^4-\log (729)\right )\right ) \int \frac {x^5}{\left (x^3-18 e^{4+2 x} \left (1-\frac {\log (3)}{2 e^4}\right )+36 e^{4+x} x \left (1-\frac {\log (3)}{2 e^4}\right )-18 e^4 x^2 \left (1-\frac {\log (3)}{2 e^4}\right )\right )^2} \, dx}{2 e^4-\log (3)} \\ \end{align*}
Leaf count is larger than twice the leaf count of optimal. \(79\) vs. \(2(28)=56\).
Time = 0.22 (sec) , antiderivative size = 79, normalized size of antiderivative = 2.82 \[ \int \frac {-36 x^4-162 e^4 x^4+81 x^4 \log (3)+e^{4 x} \left (-162 e^4+81 \log (3)\right )+e^{3 x} \left (648 e^4 x-324 x \log (3)\right )+e^{2 x} \left (-108 x^2-972 e^4 x^2+54 x^3+18 x^4+486 x^2 \log (3)\right )+e^x \left (144 x^3+648 e^4 x^3-54 x^4-18 x^5-324 x^3 \log (3)\right )}{324 e^8 x^4-36 e^4 x^5+x^6+\left (-324 e^4 x^4+18 x^5\right ) \log (3)+81 x^4 \log ^2(3)+e^{4 x} \left (324 e^8-324 e^4 \log (3)+81 \log ^2(3)\right )+e^{3 x} \left (-1296 e^8 x+1296 e^4 x \log (3)-324 x \log ^2(3)\right )+e^{2 x} \left (1944 e^8 x^2-36 e^4 x^3+\left (-1944 e^4 x^2+18 x^3\right ) \log (3)+486 x^2 \log ^2(3)\right )+e^x \left (-1296 e^8 x^3+72 e^4 x^4+\left (1296 e^4 x^3-36 x^4\right ) \log (3)-324 x^3 \log ^2(3)\right )} \, dx=-\frac {x-\frac {x^3 (4+x)}{-18 e^{4+2 x}+36 e^{4+x} x-18 e^4 x^2+9 e^{2 x} \log (3)-18 e^x x \log (3)+x^2 (x+9 \log (3))}}{2 e^4-\log (3)} \]
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Leaf count of result is larger than twice the leaf count of optimal. \(86\) vs. \(2(26)=52\).
Time = 0.38 (sec) , antiderivative size = 87, normalized size of antiderivative = 3.11
method | result | size |
risch | \(-\frac {x}{-\ln \left (3\right )+2 \,{\mathrm e}^{4}}-\frac {x^{3} \left (4+x \right )}{\left (-\ln \left (3\right )+2 \,{\mathrm e}^{4}\right ) \left (18 \,{\mathrm e}^{4+2 x}-36 x \,{\mathrm e}^{4+x}+18 x^{2} {\mathrm e}^{4}-9 \ln \left (3\right ) {\mathrm e}^{2 x}+18 x \ln \left (3\right ) {\mathrm e}^{x}-9 x^{2} \ln \left (3\right )-x^{3}\right )}\) | \(87\) |
parallelrisch | \(-\frac {162 x^{2} {\mathrm e}^{4}-324 x \,{\mathrm e}^{4} {\mathrm e}^{x}+162 \,{\mathrm e}^{4} {\mathrm e}^{2 x}-81 x^{2} \ln \left (3\right )+162 x \ln \left (3\right ) {\mathrm e}^{x}-81 \ln \left (3\right ) {\mathrm e}^{2 x}-18 \,{\mathrm e}^{x} x^{2}+9 x \,{\mathrm e}^{2 x}+36 x^{2}-72 \,{\mathrm e}^{x} x +36 \,{\mathrm e}^{2 x}}{18 \,{\mathrm e}^{4} {\mathrm e}^{2 x}-36 x \,{\mathrm e}^{4} {\mathrm e}^{x}+18 x^{2} {\mathrm e}^{4}-9 \ln \left (3\right ) {\mathrm e}^{2 x}+18 x \ln \left (3\right ) {\mathrm e}^{x}-9 x^{2} \ln \left (3\right )-x^{3}}\) | \(130\) |
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Leaf count of result is larger than twice the leaf count of optimal. 145 vs. \(2 (28) = 56\).
Time = 0.27 (sec) , antiderivative size = 145, normalized size of antiderivative = 5.18 \[ \int \frac {-36 x^4-162 e^4 x^4+81 x^4 \log (3)+e^{4 x} \left (-162 e^4+81 \log (3)\right )+e^{3 x} \left (648 e^4 x-324 x \log (3)\right )+e^{2 x} \left (-108 x^2-972 e^4 x^2+54 x^3+18 x^4+486 x^2 \log (3)\right )+e^x \left (144 x^3+648 e^4 x^3-54 x^4-18 x^5-324 x^3 \log (3)\right )}{324 e^8 x^4-36 e^4 x^5+x^6+\left (-324 e^4 x^4+18 x^5\right ) \log (3)+81 x^4 \log ^2(3)+e^{4 x} \left (324 e^8-324 e^4 \log (3)+81 \log ^2(3)\right )+e^{3 x} \left (-1296 e^8 x+1296 e^4 x \log (3)-324 x \log ^2(3)\right )+e^{2 x} \left (1944 e^8 x^2-36 e^4 x^3+\left (-1944 e^4 x^2+18 x^3\right ) \log (3)+486 x^2 \log ^2(3)\right )+e^x \left (-1296 e^8 x^3+72 e^4 x^4+\left (1296 e^4 x^3-36 x^4\right ) \log (3)-324 x^3 \log ^2(3)\right )} \, dx=\frac {18 \, x^{3} e^{4} - 9 \, x^{3} \log \left (3\right ) + 4 \, x^{3} + 9 \, {\left (2 \, x e^{4} - x \log \left (3\right )\right )} e^{\left (2 \, x\right )} - 18 \, {\left (2 \, x^{2} e^{4} - x^{2} \log \left (3\right )\right )} e^{x}}{2 \, x^{3} e^{4} - 9 \, x^{2} \log \left (3\right )^{2} - 36 \, x^{2} e^{8} + 9 \, {\left (4 \, e^{4} \log \left (3\right ) - \log \left (3\right )^{2} - 4 \, e^{8}\right )} e^{\left (2 \, x\right )} - 18 \, {\left (4 \, x e^{4} \log \left (3\right ) - x \log \left (3\right )^{2} - 4 \, x e^{8}\right )} e^{x} - {\left (x^{3} - 36 \, x^{2} e^{4}\right )} \log \left (3\right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. 119 vs. \(2 (22) = 44\).
Time = 0.31 (sec) , antiderivative size = 119, normalized size of antiderivative = 4.25 \[ \int \frac {-36 x^4-162 e^4 x^4+81 x^4 \log (3)+e^{4 x} \left (-162 e^4+81 \log (3)\right )+e^{3 x} \left (648 e^4 x-324 x \log (3)\right )+e^{2 x} \left (-108 x^2-972 e^4 x^2+54 x^3+18 x^4+486 x^2 \log (3)\right )+e^x \left (144 x^3+648 e^4 x^3-54 x^4-18 x^5-324 x^3 \log (3)\right )}{324 e^8 x^4-36 e^4 x^5+x^6+\left (-324 e^4 x^4+18 x^5\right ) \log (3)+81 x^4 \log ^2(3)+e^{4 x} \left (324 e^8-324 e^4 \log (3)+81 \log ^2(3)\right )+e^{3 x} \left (-1296 e^8 x+1296 e^4 x \log (3)-324 x \log ^2(3)\right )+e^{2 x} \left (1944 e^8 x^2-36 e^4 x^3+\left (-1944 e^4 x^2+18 x^3\right ) \log (3)+486 x^2 \log ^2(3)\right )+e^x \left (-1296 e^8 x^3+72 e^4 x^4+\left (1296 e^4 x^3-36 x^4\right ) \log (3)-324 x^3 \log ^2(3)\right )} \, dx=- \frac {x}{- \log {\left (3 \right )} + 2 e^{4}} + \frac {- x^{4} - 4 x^{3}}{- 2 x^{3} e^{4} + x^{3} \log {\left (3 \right )} - 36 x^{2} e^{4} \log {\left (3 \right )} + 9 x^{2} \log {\left (3 \right )}^{2} + 36 x^{2} e^{8} + \left (- 72 x e^{8} - 18 x \log {\left (3 \right )}^{2} + 72 x e^{4} \log {\left (3 \right )}\right ) e^{x} + \left (- 36 e^{4} \log {\left (3 \right )} + 9 \log {\left (3 \right )}^{2} + 36 e^{8}\right ) e^{2 x}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 131 vs. \(2 (28) = 56\).
Time = 0.50 (sec) , antiderivative size = 131, normalized size of antiderivative = 4.68 \[ \int \frac {-36 x^4-162 e^4 x^4+81 x^4 \log (3)+e^{4 x} \left (-162 e^4+81 \log (3)\right )+e^{3 x} \left (648 e^4 x-324 x \log (3)\right )+e^{2 x} \left (-108 x^2-972 e^4 x^2+54 x^3+18 x^4+486 x^2 \log (3)\right )+e^x \left (144 x^3+648 e^4 x^3-54 x^4-18 x^5-324 x^3 \log (3)\right )}{324 e^8 x^4-36 e^4 x^5+x^6+\left (-324 e^4 x^4+18 x^5\right ) \log (3)+81 x^4 \log ^2(3)+e^{4 x} \left (324 e^8-324 e^4 \log (3)+81 \log ^2(3)\right )+e^{3 x} \left (-1296 e^8 x+1296 e^4 x \log (3)-324 x \log ^2(3)\right )+e^{2 x} \left (1944 e^8 x^2-36 e^4 x^3+\left (-1944 e^4 x^2+18 x^3\right ) \log (3)+486 x^2 \log ^2(3)\right )+e^x \left (-1296 e^8 x^3+72 e^4 x^4+\left (1296 e^4 x^3-36 x^4\right ) \log (3)-324 x^3 \log ^2(3)\right )} \, dx=\frac {x^{3} {\left (18 \, e^{4} - 9 \, \log \left (3\right ) + 4\right )} - 18 \, x^{2} {\left (2 \, e^{4} - \log \left (3\right )\right )} e^{x} + 9 \, x {\left (2 \, e^{4} - \log \left (3\right )\right )} e^{\left (2 \, x\right )}}{x^{3} {\left (2 \, e^{4} - \log \left (3\right )\right )} + 9 \, {\left (4 \, e^{4} \log \left (3\right ) - \log \left (3\right )^{2} - 4 \, e^{8}\right )} x^{2} - 18 \, {\left (4 \, e^{4} \log \left (3\right ) - \log \left (3\right )^{2} - 4 \, e^{8}\right )} x e^{x} + 9 \, {\left (4 \, e^{4} \log \left (3\right ) - \log \left (3\right )^{2} - 4 \, e^{8}\right )} e^{\left (2 \, x\right )}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 155 vs. \(2 (28) = 56\).
Time = 3.54 (sec) , antiderivative size = 155, normalized size of antiderivative = 5.54 \[ \int \frac {-36 x^4-162 e^4 x^4+81 x^4 \log (3)+e^{4 x} \left (-162 e^4+81 \log (3)\right )+e^{3 x} \left (648 e^4 x-324 x \log (3)\right )+e^{2 x} \left (-108 x^2-972 e^4 x^2+54 x^3+18 x^4+486 x^2 \log (3)\right )+e^x \left (144 x^3+648 e^4 x^3-54 x^4-18 x^5-324 x^3 \log (3)\right )}{324 e^8 x^4-36 e^4 x^5+x^6+\left (-324 e^4 x^4+18 x^5\right ) \log (3)+81 x^4 \log ^2(3)+e^{4 x} \left (324 e^8-324 e^4 \log (3)+81 \log ^2(3)\right )+e^{3 x} \left (-1296 e^8 x+1296 e^4 x \log (3)-324 x \log ^2(3)\right )+e^{2 x} \left (1944 e^8 x^2-36 e^4 x^3+\left (-1944 e^4 x^2+18 x^3\right ) \log (3)+486 x^2 \log ^2(3)\right )+e^x \left (-1296 e^8 x^3+72 e^4 x^4+\left (1296 e^4 x^3-36 x^4\right ) \log (3)-324 x^3 \log ^2(3)\right )} \, dx=\frac {x^{4} + 18 \, x^{3} e^{4} - 9 \, x^{3} \log \left (3\right ) + 18 \, x^{2} e^{x} \log \left (3\right ) + 8 \, x^{3} - 36 \, x^{2} e^{\left (x + 4\right )} - 9 \, x e^{\left (2 \, x\right )} \log \left (3\right ) + 18 \, x e^{\left (2 \, x + 4\right )}}{2 \, x^{3} e^{4} - x^{3} \log \left (3\right ) + 36 \, x^{2} e^{4} \log \left (3\right ) - 9 \, x^{2} \log \left (3\right )^{2} + 18 \, x e^{x} \log \left (3\right )^{2} - 36 \, x^{2} e^{8} - 72 \, x e^{\left (x + 4\right )} \log \left (3\right ) - 9 \, e^{\left (2 \, x\right )} \log \left (3\right )^{2} + 72 \, x e^{\left (x + 8\right )} + 36 \, e^{\left (2 \, x + 4\right )} \log \left (3\right ) - 36 \, e^{\left (2 \, x + 8\right )}} \]
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Timed out. \[ \int \frac {-36 x^4-162 e^4 x^4+81 x^4 \log (3)+e^{4 x} \left (-162 e^4+81 \log (3)\right )+e^{3 x} \left (648 e^4 x-324 x \log (3)\right )+e^{2 x} \left (-108 x^2-972 e^4 x^2+54 x^3+18 x^4+486 x^2 \log (3)\right )+e^x \left (144 x^3+648 e^4 x^3-54 x^4-18 x^5-324 x^3 \log (3)\right )}{324 e^8 x^4-36 e^4 x^5+x^6+\left (-324 e^4 x^4+18 x^5\right ) \log (3)+81 x^4 \log ^2(3)+e^{4 x} \left (324 e^8-324 e^4 \log (3)+81 \log ^2(3)\right )+e^{3 x} \left (-1296 e^8 x+1296 e^4 x \log (3)-324 x \log ^2(3)\right )+e^{2 x} \left (1944 e^8 x^2-36 e^4 x^3+\left (-1944 e^4 x^2+18 x^3\right ) \log (3)+486 x^2 \log ^2(3)\right )+e^x \left (-1296 e^8 x^3+72 e^4 x^4+\left (1296 e^4 x^3-36 x^4\right ) \log (3)-324 x^3 \log ^2(3)\right )} \, dx=\int -\frac {{\mathrm {e}}^x\,\left (324\,x^3\,\ln \left (3\right )-648\,x^3\,{\mathrm {e}}^4-144\,x^3+54\,x^4+18\,x^5\right )-{\mathrm {e}}^{3\,x}\,\left (648\,x\,{\mathrm {e}}^4-324\,x\,\ln \left (3\right )\right )+{\mathrm {e}}^{4\,x}\,\left (162\,{\mathrm {e}}^4-81\,\ln \left (3\right )\right )+162\,x^4\,{\mathrm {e}}^4-81\,x^4\,\ln \left (3\right )+36\,x^4-{\mathrm {e}}^{2\,x}\,\left (486\,x^2\,\ln \left (3\right )-972\,x^2\,{\mathrm {e}}^4-108\,x^2+54\,x^3+18\,x^4\right )}{81\,x^4\,{\ln \left (3\right )}^2+{\mathrm {e}}^{4\,x}\,\left (324\,{\mathrm {e}}^8-324\,{\mathrm {e}}^4\,\ln \left (3\right )+81\,{\ln \left (3\right )}^2\right )+{\mathrm {e}}^{2\,x}\,\left (486\,x^2\,{\ln \left (3\right )}^2-36\,x^3\,{\mathrm {e}}^4+1944\,x^2\,{\mathrm {e}}^8-\ln \left (3\right )\,\left (1944\,x^2\,{\mathrm {e}}^4-18\,x^3\right )\right )-{\mathrm {e}}^{3\,x}\,\left (1296\,x\,{\mathrm {e}}^8+324\,x\,{\ln \left (3\right )}^2-1296\,x\,{\mathrm {e}}^4\,\ln \left (3\right )\right )-36\,x^5\,{\mathrm {e}}^4+324\,x^4\,{\mathrm {e}}^8-{\mathrm {e}}^x\,\left (324\,x^3\,{\ln \left (3\right )}^2-72\,x^4\,{\mathrm {e}}^4+1296\,x^3\,{\mathrm {e}}^8-\ln \left (3\right )\,\left (1296\,x^3\,{\mathrm {e}}^4-36\,x^4\right )\right )+x^6-\ln \left (3\right )\,\left (324\,x^4\,{\mathrm {e}}^4-18\,x^5\right )} \,d x \]
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