Integrand size = 104, antiderivative size = 31 \[ \int \frac {e^{-\frac {e^x}{\log (2)}} \left (e^x \left (-33 x^2-8 x^3+x^4\right )+\left (88 x+17 x^2-x^3\right ) \log (2)+\left (e^x \left (-33 x-8 x^2+x^3\right )+(33+11 x) \log (2)\right ) \log \left (9+6 x+x^2\right )\right )}{\left (1452+220 x-76 x^2+4 x^3\right ) \log (2)} \, dx=\frac {e^{-\frac {e^x}{\log (2)}} x \left (x+\log \left ((3+x)^2\right )\right )}{4 (11-x)} \]
[Out]
\[ \int \frac {e^{-\frac {e^x}{\log (2)}} \left (e^x \left (-33 x^2-8 x^3+x^4\right )+\left (88 x+17 x^2-x^3\right ) \log (2)+\left (e^x \left (-33 x-8 x^2+x^3\right )+(33+11 x) \log (2)\right ) \log \left (9+6 x+x^2\right )\right )}{\left (1452+220 x-76 x^2+4 x^3\right ) \log (2)} \, dx=\int \frac {e^{-\frac {e^x}{\log (2)}} \left (e^x \left (-33 x^2-8 x^3+x^4\right )+\left (88 x+17 x^2-x^3\right ) \log (2)+\left (e^x \left (-33 x-8 x^2+x^3\right )+(33+11 x) \log (2)\right ) \log \left (9+6 x+x^2\right )\right )}{\left (1452+220 x-76 x^2+4 x^3\right ) \log (2)} \, dx \]
[In]
[Out]
Rubi steps \begin{align*} \text {integral}& = \frac {\int \frac {e^{-\frac {e^x}{\log (2)}} \left (e^x \left (-33 x^2-8 x^3+x^4\right )+\left (88 x+17 x^2-x^3\right ) \log (2)+\left (e^x \left (-33 x-8 x^2+x^3\right )+(33+11 x) \log (2)\right ) \log \left (9+6 x+x^2\right )\right )}{1452+220 x-76 x^2+4 x^3} \, dx}{\log (2)} \\ & = \frac {\int \left (\frac {e^{x-\frac {e^x}{\log (2)}} x \left (x+\log \left ((3+x)^2\right )\right )}{4 (-11+x)}-\frac {e^{-\frac {e^x}{\log (2)}} \log (2) \left (-88 x-17 x^2+x^3-33 \log \left ((3+x)^2\right )-11 x \log \left ((3+x)^2\right )\right )}{4 (-11+x)^2 (3+x)}\right ) \, dx}{\log (2)} \\ & = -\left (\frac {1}{4} \int \frac {e^{-\frac {e^x}{\log (2)}} \left (-88 x-17 x^2+x^3-33 \log \left ((3+x)^2\right )-11 x \log \left ((3+x)^2\right )\right )}{(-11+x)^2 (3+x)} \, dx\right )+\frac {\int \frac {e^{x-\frac {e^x}{\log (2)}} x \left (x+\log \left ((3+x)^2\right )\right )}{-11+x} \, dx}{4 \log (2)} \\ & = -\left (\frac {1}{4} \int \left (-\frac {88 e^{-\frac {e^x}{\log (2)}} x}{(-11+x)^2 (3+x)}-\frac {17 e^{-\frac {e^x}{\log (2)}} x^2}{(-11+x)^2 (3+x)}+\frac {e^{-\frac {e^x}{\log (2)}} x^3}{(-11+x)^2 (3+x)}-\frac {11 e^{-\frac {e^x}{\log (2)}} \log \left ((3+x)^2\right )}{(-11+x)^2}\right ) \, dx\right )+\frac {\int \left (\frac {e^{x-\frac {e^x}{\log (2)}} x^2}{-11+x}+\frac {e^{x-\frac {e^x}{\log (2)}} x \log \left ((3+x)^2\right )}{-11+x}\right ) \, dx}{4 \log (2)} \\ & = -\left (\frac {1}{4} \int \frac {e^{-\frac {e^x}{\log (2)}} x^3}{(-11+x)^2 (3+x)} \, dx\right )+\frac {11}{4} \int \frac {e^{-\frac {e^x}{\log (2)}} \log \left ((3+x)^2\right )}{(-11+x)^2} \, dx+\frac {17}{4} \int \frac {e^{-\frac {e^x}{\log (2)}} x^2}{(-11+x)^2 (3+x)} \, dx+22 \int \frac {e^{-\frac {e^x}{\log (2)}} x}{(-11+x)^2 (3+x)} \, dx+\frac {\int \frac {e^{x-\frac {e^x}{\log (2)}} x^2}{-11+x} \, dx}{4 \log (2)}+\frac {\int \frac {e^{x-\frac {e^x}{\log (2)}} x \log \left ((3+x)^2\right )}{-11+x} \, dx}{4 \log (2)} \\ & = -\frac {1}{4} e^{-\frac {e^x}{\log (2)}} \log \left ((3+x)^2\right )-\frac {1}{4} \int \left (e^{-\frac {e^x}{\log (2)}}+\frac {1331 e^{-\frac {e^x}{\log (2)}}}{14 (-11+x)^2}+\frac {3751 e^{-\frac {e^x}{\log (2)}}}{196 (-11+x)}-\frac {27 e^{-\frac {e^x}{\log (2)}}}{196 (3+x)}\right ) \, dx-\frac {11}{4} \int \frac {2 \int \frac {e^{-\frac {e^x}{\log (2)}}}{(-11+x)^2} \, dx}{3+x} \, dx+\frac {17}{4} \int \left (\frac {121 e^{-\frac {e^x}{\log (2)}}}{14 (-11+x)^2}+\frac {187 e^{-\frac {e^x}{\log (2)}}}{196 (-11+x)}+\frac {9 e^{-\frac {e^x}{\log (2)}}}{196 (3+x)}\right ) \, dx+22 \int \left (\frac {11 e^{-\frac {e^x}{\log (2)}}}{14 (-11+x)^2}+\frac {3 e^{-\frac {e^x}{\log (2)}}}{196 (-11+x)}-\frac {3 e^{-\frac {e^x}{\log (2)}}}{196 (3+x)}\right ) \, dx+\frac {\int \left (11 e^{x-\frac {e^x}{\log (2)}}+\frac {121 e^{x-\frac {e^x}{\log (2)}}}{-11+x}+e^{x-\frac {e^x}{\log (2)}} x\right ) \, dx}{4 \log (2)}-\frac {\int \frac {2 \left (-e^{-\frac {e^x}{\log (2)}} \log (2)+11 \int \frac {e^{x-\frac {e^x}{\log (2)}}}{-11+x} \, dx\right )}{3+x} \, dx}{4 \log (2)}+\frac {1}{4} \left (11 \log \left ((3+x)^2\right )\right ) \int \frac {e^{-\frac {e^x}{\log (2)}}}{(-11+x)^2} \, dx+\frac {\left (11 \log \left ((3+x)^2\right )\right ) \int \frac {e^{x-\frac {e^x}{\log (2)}}}{-11+x} \, dx}{4 \log (2)} \\ & = -\frac {1}{4} e^{-\frac {e^x}{\log (2)}} \log \left ((3+x)^2\right )+\frac {27}{784} \int \frac {e^{-\frac {e^x}{\log (2)}}}{3+x} \, dx+\frac {153}{784} \int \frac {e^{-\frac {e^x}{\log (2)}}}{3+x} \, dx-\frac {1}{4} \int e^{-\frac {e^x}{\log (2)}} \, dx+\frac {33}{98} \int \frac {e^{-\frac {e^x}{\log (2)}}}{-11+x} \, dx-\frac {33}{98} \int \frac {e^{-\frac {e^x}{\log (2)}}}{3+x} \, dx+\frac {3179}{784} \int \frac {e^{-\frac {e^x}{\log (2)}}}{-11+x} \, dx-\frac {3751}{784} \int \frac {e^{-\frac {e^x}{\log (2)}}}{-11+x} \, dx-\frac {11}{2} \int \frac {\int \frac {e^{-\frac {e^x}{\log (2)}}}{(-11+x)^2} \, dx}{3+x} \, dx+\frac {121}{7} \int \frac {e^{-\frac {e^x}{\log (2)}}}{(-11+x)^2} \, dx-\frac {1331}{56} \int \frac {e^{-\frac {e^x}{\log (2)}}}{(-11+x)^2} \, dx+\frac {2057}{56} \int \frac {e^{-\frac {e^x}{\log (2)}}}{(-11+x)^2} \, dx+\frac {\int e^{x-\frac {e^x}{\log (2)}} x \, dx}{4 \log (2)}-\frac {\int \frac {-e^{-\frac {e^x}{\log (2)}} \log (2)+11 \int \frac {e^{x-\frac {e^x}{\log (2)}}}{-11+x} \, dx}{3+x} \, dx}{2 \log (2)}+\frac {11 \int e^{x-\frac {e^x}{\log (2)}} \, dx}{4 \log (2)}+\frac {121 \int \frac {e^{x-\frac {e^x}{\log (2)}}}{-11+x} \, dx}{4 \log (2)}+\frac {1}{4} \left (11 \log \left ((3+x)^2\right )\right ) \int \frac {e^{-\frac {e^x}{\log (2)}}}{(-11+x)^2} \, dx+\frac {\left (11 \log \left ((3+x)^2\right )\right ) \int \frac {e^{x-\frac {e^x}{\log (2)}}}{-11+x} \, dx}{4 \log (2)} \\ & = -\frac {1}{4} e^{-\frac {e^x}{\log (2)}} \log \left ((3+x)^2\right )+\frac {27}{784} \int \frac {e^{-\frac {e^x}{\log (2)}}}{3+x} \, dx+\frac {153}{784} \int \frac {e^{-\frac {e^x}{\log (2)}}}{3+x} \, dx-\frac {1}{4} \text {Subst}\left (\int \frac {e^{-\frac {x}{\log (2)}}}{x} \, dx,x,e^x\right )+\frac {33}{98} \int \frac {e^{-\frac {e^x}{\log (2)}}}{-11+x} \, dx-\frac {33}{98} \int \frac {e^{-\frac {e^x}{\log (2)}}}{3+x} \, dx+\frac {3179}{784} \int \frac {e^{-\frac {e^x}{\log (2)}}}{-11+x} \, dx-\frac {3751}{784} \int \frac {e^{-\frac {e^x}{\log (2)}}}{-11+x} \, dx-\frac {11}{2} \int \frac {\int \frac {e^{-\frac {e^x}{\log (2)}}}{(-11+x)^2} \, dx}{3+x} \, dx+\frac {121}{7} \int \frac {e^{-\frac {e^x}{\log (2)}}}{(-11+x)^2} \, dx-\frac {1331}{56} \int \frac {e^{-\frac {e^x}{\log (2)}}}{(-11+x)^2} \, dx+\frac {2057}{56} \int \frac {e^{-\frac {e^x}{\log (2)}}}{(-11+x)^2} \, dx+\frac {\int e^{x-\frac {e^x}{\log (2)}} x \, dx}{4 \log (2)}-\frac {\int \left (-\frac {e^{-\frac {e^x}{\log (2)}} \log (2)}{3+x}+\frac {11 \int \frac {e^{x-\frac {e^x}{\log (2)}}}{-11+x} \, dx}{3+x}\right ) \, dx}{2 \log (2)}+\frac {11 \text {Subst}\left (\int e^{-\frac {x}{\log (2)}} \, dx,x,e^x\right )}{4 \log (2)}+\frac {121 \int \frac {e^{x-\frac {e^x}{\log (2)}}}{-11+x} \, dx}{4 \log (2)}+\frac {1}{4} \left (11 \log \left ((3+x)^2\right )\right ) \int \frac {e^{-\frac {e^x}{\log (2)}}}{(-11+x)^2} \, dx+\frac {\left (11 \log \left ((3+x)^2\right )\right ) \int \frac {e^{x-\frac {e^x}{\log (2)}}}{-11+x} \, dx}{4 \log (2)} \\ & = -\frac {11}{4} e^{-\frac {e^x}{\log (2)}}-\frac {1}{4} \operatorname {ExpIntegralEi}\left (-\frac {e^x}{\log (2)}\right )-\frac {1}{4} e^{-\frac {e^x}{\log (2)}} \log \left ((3+x)^2\right )+\frac {27}{784} \int \frac {e^{-\frac {e^x}{\log (2)}}}{3+x} \, dx+\frac {153}{784} \int \frac {e^{-\frac {e^x}{\log (2)}}}{3+x} \, dx+\frac {33}{98} \int \frac {e^{-\frac {e^x}{\log (2)}}}{-11+x} \, dx-\frac {33}{98} \int \frac {e^{-\frac {e^x}{\log (2)}}}{3+x} \, dx+\frac {1}{2} \int \frac {e^{-\frac {e^x}{\log (2)}}}{3+x} \, dx+\frac {3179}{784} \int \frac {e^{-\frac {e^x}{\log (2)}}}{-11+x} \, dx-\frac {3751}{784} \int \frac {e^{-\frac {e^x}{\log (2)}}}{-11+x} \, dx-\frac {11}{2} \int \frac {\int \frac {e^{-\frac {e^x}{\log (2)}}}{(-11+x)^2} \, dx}{3+x} \, dx+\frac {121}{7} \int \frac {e^{-\frac {e^x}{\log (2)}}}{(-11+x)^2} \, dx-\frac {1331}{56} \int \frac {e^{-\frac {e^x}{\log (2)}}}{(-11+x)^2} \, dx+\frac {2057}{56} \int \frac {e^{-\frac {e^x}{\log (2)}}}{(-11+x)^2} \, dx+\frac {\int e^{x-\frac {e^x}{\log (2)}} x \, dx}{4 \log (2)}-\frac {11 \int \frac {\int \frac {e^{x-\frac {e^x}{\log (2)}}}{-11+x} \, dx}{3+x} \, dx}{2 \log (2)}+\frac {121 \int \frac {e^{x-\frac {e^x}{\log (2)}}}{-11+x} \, dx}{4 \log (2)}+\frac {1}{4} \left (11 \log \left ((3+x)^2\right )\right ) \int \frac {e^{-\frac {e^x}{\log (2)}}}{(-11+x)^2} \, dx+\frac {\left (11 \log \left ((3+x)^2\right )\right ) \int \frac {e^{x-\frac {e^x}{\log (2)}}}{-11+x} \, dx}{4 \log (2)} \\ \end{align*}
\[ \int \frac {e^{-\frac {e^x}{\log (2)}} \left (e^x \left (-33 x^2-8 x^3+x^4\right )+\left (88 x+17 x^2-x^3\right ) \log (2)+\left (e^x \left (-33 x-8 x^2+x^3\right )+(33+11 x) \log (2)\right ) \log \left (9+6 x+x^2\right )\right )}{\left (1452+220 x-76 x^2+4 x^3\right ) \log (2)} \, dx=\int \frac {e^{-\frac {e^x}{\log (2)}} \left (e^x \left (-33 x^2-8 x^3+x^4\right )+\left (88 x+17 x^2-x^3\right ) \log (2)+\left (e^x \left (-33 x-8 x^2+x^3\right )+(33+11 x) \log (2)\right ) \log \left (9+6 x+x^2\right )\right )}{\left (1452+220 x-76 x^2+4 x^3\right ) \log (2)} \, dx \]
[In]
[Out]
Time = 2.17 (sec) , antiderivative size = 42, normalized size of antiderivative = 1.35
method | result | size |
parallelrisch | \(-\frac {\left (x^{2} \ln \left (2\right )+\ln \left (2\right ) \ln \left (x^{2}+6 x +9\right ) x \right ) {\mathrm e}^{-\frac {{\mathrm e}^{x}}{\ln \left (2\right )}}}{4 \ln \left (2\right ) \left (x -11\right )}\) | \(42\) |
risch | \(-\frac {x \left (-i \pi \operatorname {csgn}\left (i \left (3+x \right )\right )^{2} \operatorname {csgn}\left (i \left (3+x \right )^{2}\right )+2 i \pi \,\operatorname {csgn}\left (i \left (3+x \right )\right ) \operatorname {csgn}\left (i \left (3+x \right )^{2}\right )^{2}-i \pi \operatorname {csgn}\left (i \left (3+x \right )^{2}\right )^{3}+2 x +4 \ln \left (3+x \right )\right ) {\mathrm e}^{-\frac {{\mathrm e}^{x}}{\ln \left (2\right )}}}{8 \left (x -11\right )}\) | \(87\) |
[In]
[Out]
none
Time = 0.26 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.00 \[ \int \frac {e^{-\frac {e^x}{\log (2)}} \left (e^x \left (-33 x^2-8 x^3+x^4\right )+\left (88 x+17 x^2-x^3\right ) \log (2)+\left (e^x \left (-33 x-8 x^2+x^3\right )+(33+11 x) \log (2)\right ) \log \left (9+6 x+x^2\right )\right )}{\left (1452+220 x-76 x^2+4 x^3\right ) \log (2)} \, dx=-\frac {{\left (x^{2} + x \log \left (x^{2} + 6 \, x + 9\right )\right )} e^{\left (-\frac {e^{x}}{\log \left (2\right )}\right )}}{4 \, {\left (x - 11\right )}} \]
[In]
[Out]
Time = 0.20 (sec) , antiderivative size = 29, normalized size of antiderivative = 0.94 \[ \int \frac {e^{-\frac {e^x}{\log (2)}} \left (e^x \left (-33 x^2-8 x^3+x^4\right )+\left (88 x+17 x^2-x^3\right ) \log (2)+\left (e^x \left (-33 x-8 x^2+x^3\right )+(33+11 x) \log (2)\right ) \log \left (9+6 x+x^2\right )\right )}{\left (1452+220 x-76 x^2+4 x^3\right ) \log (2)} \, dx=\frac {\left (- x^{2} - x \log {\left (x^{2} + 6 x + 9 \right )}\right ) e^{- \frac {e^{x}}{\log {\left (2 \right )}}}}{4 x - 44} \]
[In]
[Out]
none
Time = 0.35 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.16 \[ \int \frac {e^{-\frac {e^x}{\log (2)}} \left (e^x \left (-33 x^2-8 x^3+x^4\right )+\left (88 x+17 x^2-x^3\right ) \log (2)+\left (e^x \left (-33 x-8 x^2+x^3\right )+(33+11 x) \log (2)\right ) \log \left (9+6 x+x^2\right )\right )}{\left (1452+220 x-76 x^2+4 x^3\right ) \log (2)} \, dx=-\frac {{\left (x^{2} \log \left (2\right ) + 2 \, x \log \left (2\right ) \log \left (x + 3\right )\right )} e^{\left (-\frac {e^{x}}{\log \left (2\right )}\right )}}{4 \, {\left (x - 11\right )} \log \left (2\right )} \]
[In]
[Out]
\[ \int \frac {e^{-\frac {e^x}{\log (2)}} \left (e^x \left (-33 x^2-8 x^3+x^4\right )+\left (88 x+17 x^2-x^3\right ) \log (2)+\left (e^x \left (-33 x-8 x^2+x^3\right )+(33+11 x) \log (2)\right ) \log \left (9+6 x+x^2\right )\right )}{\left (1452+220 x-76 x^2+4 x^3\right ) \log (2)} \, dx=\int { \frac {{\left ({\left (x^{4} - 8 \, x^{3} - 33 \, x^{2}\right )} e^{x} - {\left (x^{3} - 17 \, x^{2} - 88 \, x\right )} \log \left (2\right ) + {\left ({\left (x^{3} - 8 \, x^{2} - 33 \, x\right )} e^{x} + 11 \, {\left (x + 3\right )} \log \left (2\right )\right )} \log \left (x^{2} + 6 \, x + 9\right )\right )} e^{\left (-\frac {e^{x}}{\log \left (2\right )}\right )}}{4 \, {\left (x^{3} - 19 \, x^{2} + 55 \, x + 363\right )} \log \left (2\right )} \,d x } \]
[In]
[Out]
Timed out. \[ \int \frac {e^{-\frac {e^x}{\log (2)}} \left (e^x \left (-33 x^2-8 x^3+x^4\right )+\left (88 x+17 x^2-x^3\right ) \log (2)+\left (e^x \left (-33 x-8 x^2+x^3\right )+(33+11 x) \log (2)\right ) \log \left (9+6 x+x^2\right )\right )}{\left (1452+220 x-76 x^2+4 x^3\right ) \log (2)} \, dx=-\int -\frac {{\mathrm {e}}^{-\frac {{\mathrm {e}}^x}{\ln \left (2\right )}}\,\left (\ln \left (x^2+6\,x+9\right )\,\left (\ln \left (2\right )\,\left (11\,x+33\right )-{\mathrm {e}}^x\,\left (-x^3+8\,x^2+33\,x\right )\right )-{\mathrm {e}}^x\,\left (-x^4+8\,x^3+33\,x^2\right )+\ln \left (2\right )\,\left (-x^3+17\,x^2+88\,x\right )\right )}{\ln \left (2\right )\,\left (4\,x^3-76\,x^2+220\,x+1452\right )} \,d x \]
[In]
[Out]