Integrand size = 171, antiderivative size = 33 \[ \int \frac {e^{-\frac {e^x (-5-x)}{-3-x+\log ^2(2)}} \left (27+18 x+3 x^2+(-18-6 x) \log ^2(2)+3 \log ^4(2)+e^x \left (-78-87 x-30 x^2-3 x^3+\left (36+24 x+3 x^2\right ) \log ^2(2)\right )+e^{\frac {e^x (-5-x)}{-3-x+\log ^2(2)}} \left (9-12 x-11 x^2-2 x^3+\left (-6+10 x+4 x^2\right ) \log ^2(2)+(1-2 x) \log ^4(2)\right )\right )}{9+6 x+x^2+(-6-2 x) \log ^2(2)+\log ^4(2)} \, dx=x-x^2+3 e^{-\frac {e^x (5+x)}{3+x-\log ^2(2)}} (2+x) \] Output:
x-x^2+3/exp((5+x)*exp(x)/(x-ln(2)^2+3))*(2+x)
Time = 0.15 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.03 \[ \int \frac {e^{-\frac {e^x (-5-x)}{-3-x+\log ^2(2)}} \left (27+18 x+3 x^2+(-18-6 x) \log ^2(2)+3 \log ^4(2)+e^x \left (-78-87 x-30 x^2-3 x^3+\left (36+24 x+3 x^2\right ) \log ^2(2)\right )+e^{\frac {e^x (-5-x)}{-3-x+\log ^2(2)}} \left (9-12 x-11 x^2-2 x^3+\left (-6+10 x+4 x^2\right ) \log ^2(2)+(1-2 x) \log ^4(2)\right )\right )}{9+6 x+x^2+(-6-2 x) \log ^2(2)+\log ^4(2)} \, dx=x-x^2+e^{-\frac {e^x (5+x)}{3+x-\log ^2(2)}} (6+3 x) \] Input:
Integrate[(27 + 18*x + 3*x^2 + (-18 - 6*x)*Log[2]^2 + 3*Log[2]^4 + E^x*(-7 8 - 87*x - 30*x^2 - 3*x^3 + (36 + 24*x + 3*x^2)*Log[2]^2) + E^((E^x*(-5 - x))/(-3 - x + Log[2]^2))*(9 - 12*x - 11*x^2 - 2*x^3 + (-6 + 10*x + 4*x^2)* Log[2]^2 + (1 - 2*x)*Log[2]^4))/(E^((E^x*(-5 - x))/(-3 - x + Log[2]^2))*(9 + 6*x + x^2 + (-6 - 2*x)*Log[2]^2 + Log[2]^4)),x]
Output:
x - x^2 + (6 + 3*x)/E^((E^x*(5 + x))/(3 + x - Log[2]^2))
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
| \(\displaystyle \int \frac {e^{-\frac {e^x (-x-5)}{-x-3+\log ^2(2)}} \left (3 x^2+e^x \left (-3 x^3-30 x^2+\left (3 x^2+24 x+36\right ) \log ^2(2)-87 x-78\right )+e^{\frac {e^x (-x-5)}{-x-3+\log ^2(2)}} \left (-2 x^3-11 x^2+\left (4 x^2+10 x-6\right ) \log ^2(2)-12 x+(1-2 x) \log ^4(2)+9\right )+18 x+(-6 x-18) \log ^2(2)+27+3 \log ^4(2)\right )}{x^2+6 x+(-2 x-6) \log ^2(2)+9+\log ^4(2)} \, dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {e^{-\frac {e^x (-x-5)}{-x-3+\log ^2(2)}} \left (3 x^2+e^x \left (-3 x^3-30 x^2+\left (3 x^2+24 x+36\right ) \log ^2(2)-87 x-78\right )+e^{\frac {e^x (-x-5)}{-x-3+\log ^2(2)}} \left (-2 x^3-11 x^2+\left (4 x^2+10 x-6\right ) \log ^2(2)-12 x+(1-2 x) \log ^4(2)+9\right )+18 x+(-6 x-18) \log ^2(2)+27 \left (1+\frac {\log ^4(2)}{9}\right )\right )}{x^2+2 x \left (3-\log ^2(2)\right )+\left (\log ^2(2)-3\right )^2}dx\) |
| \(\Big \downarrow \) 7277 |
| \(\displaystyle 4 \int \frac {e^{-\frac {e^x (x+5)}{x-\log ^2(2)+3}} \left (3 x^2+18 x-3 e^x \left (x^3+10 x^2+29 x-\left (x^2+8 x+12\right ) \log ^2(2)+26\right )+e^{\frac {e^x (x+5)}{x-\log ^2(2)+3}} \left (-2 x^3-11 x^2-12 x+(1-2 x) \log ^4(2)-2 \left (-2 x^2-5 x+3\right ) \log ^2(2)+9\right )+3 \left (9+\log ^4(2)\right )-6 (x+3) \log ^2(2)\right )}{4 \left (x-\log ^2(2)+3\right )^2}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \int \frac {e^{-\frac {e^x (x+5)}{x+3-\log ^2(2)}} \left (3 x^2-3 e^x \left (x^3+10 x^2-\left (x^2+8 x+12\right ) \log ^2(2)+29 x+26\right )+e^{\frac {e^x (x+5)}{x+3-\log ^2(2)}} \left (-2 x^3-11 x^2-2 \left (-2 x^2-5 x+3\right ) \log ^2(2)-12 x+(1-2 x) \log ^4(2)+9\right )+18 x-6 (x+3) \log ^2(2)+3 \left (9+\log ^4(2)\right )\right )}{\left (x+3-\log ^2(2)\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {3 x^2 e^{-\frac {e^x (x+5)}{x+3-\log ^2(2)}}}{\left (x+3-\log ^2(2)\right )^2}+\frac {3 (x+2) e^{x-\frac {e^x (x+5)}{x+3-\log ^2(2)}} \left (-x^2-x \left (8-\log ^2(2)\right )-13+6 \log ^2(2)\right )}{\left (x+3-\log ^2(2)\right )^2}-2 x+\frac {18 x e^{-\frac {e^x (x+5)}{x+3-\log ^2(2)}}}{\left (x+3-\log ^2(2)\right )^2}-\frac {6 (x+3) \log ^2(2) e^{-\frac {e^x (x+5)}{x+3-\log ^2(2)}}}{\left (x+3-\log ^2(2)\right )^2}+\frac {3 \left (9+\log ^4(2)\right ) e^{-\frac {e^x (x+5)}{x+3-\log ^2(2)}}}{\left (x+3-\log ^2(2)\right )^2}+1\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle 3 \int e^{-\frac {e^x (x+5)}{x-\log ^2(2)+3}}dx-3 \left (4+\log ^2(2)\right ) \int e^{x-\frac {e^x (x+5)}{x-\log ^2(2)+3}}dx-3 \int e^{x-\frac {e^x (x+5)}{x-\log ^2(2)+3}} xdx+3 \left (3-\log ^2(2)\right )^2 \int \frac {e^{-\frac {e^x (x+5)}{x-\log ^2(2)+3}}}{\left (x-\log ^2(2)+3\right )^2}dx-18 \left (3-\log ^2(2)\right ) \int \frac {e^{-\frac {e^x (x+5)}{x-\log ^2(2)+3}}}{\left (x-\log ^2(2)+3\right )^2}dx-6 \left (3-\log ^2(2)\right ) \int \frac {e^{-\frac {e^x (x+5)}{x-\log ^2(2)+3}}}{x-\log ^2(2)+3}dx-6 \log ^2(2) \int \frac {e^{-\frac {e^x (x+5)}{x-\log ^2(2)+3}}}{x-\log ^2(2)+3}dx+18 \int \frac {e^{-\frac {e^x (x+5)}{x-\log ^2(2)+3}}}{x-\log ^2(2)+3}dx+3 \left (9+\log ^4(2)\right ) \int \frac {e^{-\frac {e^x (x+5)}{x-\log ^2(2)+3}}}{\left (x-\log ^2(2)+3\right )^2}dx-3 \left (2-\log ^4(2)-\log ^2(2)\right ) \int \frac {e^{x-\frac {e^x (x+5)}{x-\log ^2(2)+3}}}{\left (x-\log ^2(2)+3\right )^2}dx+3 \left (4-\log ^4(2)\right ) \int \frac {e^{x-\frac {e^x (x+5)}{x-\log ^2(2)+3}}}{x-\log ^2(2)+3}dx-6 \log ^4(2) \int \frac {e^{-\frac {e^x (x+5)}{x-\log ^2(2)+3}}}{\left (-x+\log ^2(2)-3\right )^2}dx-x^2+x\) |
Input:
Int[(27 + 18*x + 3*x^2 + (-18 - 6*x)*Log[2]^2 + 3*Log[2]^4 + E^x*(-78 - 87 *x - 30*x^2 - 3*x^3 + (36 + 24*x + 3*x^2)*Log[2]^2) + E^((E^x*(-5 - x))/(- 3 - x + Log[2]^2))*(9 - 12*x - 11*x^2 - 2*x^3 + (-6 + 10*x + 4*x^2)*Log[2] ^2 + (1 - 2*x)*Log[2]^4))/(E^((E^x*(-5 - x))/(-3 - x + Log[2]^2))*(9 + 6*x + x^2 + (-6 - 2*x)*Log[2]^2 + Log[2]^4)),x]
Output:
$Aborted
Time = 0.97 (sec) , antiderivative size = 32, normalized size of antiderivative = 0.97
| method | result | size |
| risch | \(-x^{2}+x +\left (6+3 x \right ) {\mathrm e}^{\frac {\left (5+x \right ) {\mathrm e}^{x}}{\ln \left (2\right )^{2}-3-x}}\) | \(32\) |
| norman | \(\frac {\left (x^{3} {\mathrm e}^{\frac {\left (-x -5\right ) {\mathrm e}^{x}}{\ln \left (2\right )^{2}-3-x}}+\left (-15+3 \ln \left (2\right )^{2}\right ) x +\left (\ln \left (2\right )^{4}-6 \ln \left (2\right )^{2}+9\right ) {\mathrm e}^{\frac {\left (-x -5\right ) {\mathrm e}^{x}}{\ln \left (2\right )^{2}-3-x}}+\left (2-\ln \left (2\right )^{2}\right ) x^{2} {\mathrm e}^{\frac {\left (-x -5\right ) {\mathrm e}^{x}}{\ln \left (2\right )^{2}-3-x}}-3 x^{2}+6 \ln \left (2\right )^{2}-18\right ) {\mathrm e}^{-\frac {\left (-x -5\right ) {\mathrm e}^{x}}{\ln \left (2\right )^{2}-3-x}}}{\ln \left (2\right )^{2}-3-x}\) | \(147\) |
| parallelrisch | \(\frac {\left (6 \ln \left (2\right )^{6} {\mathrm e}^{\frac {\left (-x -5\right ) {\mathrm e}^{x}}{\ln \left (2\right )^{2}-3-x}}-6 \,{\mathrm e}^{\frac {\left (-x -5\right ) {\mathrm e}^{x}}{\ln \left (2\right )^{2}-3-x}} \ln \left (2\right )^{4} x -50 \,{\mathrm e}^{\frac {\left (-x -5\right ) {\mathrm e}^{x}}{\ln \left (2\right )^{2}-3-x}} \ln \left (2\right )^{4}-18-{\mathrm e}^{\frac {\left (-x -5\right ) {\mathrm e}^{x}}{\ln \left (2\right )^{2}-3-x}} \ln \left (2\right )^{2} x^{2}+33 \,{\mathrm e}^{\frac {\left (-x -5\right ) {\mathrm e}^{x}}{\ln \left (2\right )^{2}-3-x}} \ln \left (2\right )^{2} x +x^{3} {\mathrm e}^{\frac {\left (-x -5\right ) {\mathrm e}^{x}}{\ln \left (2\right )^{2}-3-x}}+3 x \ln \left (2\right )^{2}+138 \,{\mathrm e}^{\frac {\left (-x -5\right ) {\mathrm e}^{x}}{\ln \left (2\right )^{2}-3-x}} \ln \left (2\right )^{2}+2 \,{\mathrm e}^{\frac {\left (-x -5\right ) {\mathrm e}^{x}}{\ln \left (2\right )^{2}-3-x}} x^{2}+6 \ln \left (2\right )^{2}-3 x^{2}-45 \,{\mathrm e}^{\frac {\left (-x -5\right ) {\mathrm e}^{x}}{\ln \left (2\right )^{2}-3-x}} x -15 x -126 \,{\mathrm e}^{\frac {\left (-x -5\right ) {\mathrm e}^{x}}{\ln \left (2\right )^{2}-3-x}}\right ) {\mathrm e}^{-\frac {\left (-x -5\right ) {\mathrm e}^{x}}{\ln \left (2\right )^{2}-3-x}}}{\ln \left (2\right )^{2}-3-x}\) | \(313\) |
Input:
int((((1-2*x)*ln(2)^4+(4*x^2+10*x-6)*ln(2)^2-2*x^3-11*x^2-12*x+9)*exp((-x- 5)*exp(x)/(ln(2)^2-3-x))+((3*x^2+24*x+36)*ln(2)^2-3*x^3-30*x^2-87*x-78)*ex p(x)+3*ln(2)^4+(-6*x-18)*ln(2)^2+3*x^2+18*x+27)/(ln(2)^4+(-2*x-6)*ln(2)^2+ x^2+6*x+9)/exp((-x-5)*exp(x)/(ln(2)^2-3-x)),x,method=_RETURNVERBOSE)
Output:
-x^2+x+(6+3*x)*exp((5+x)*exp(x)/(ln(2)^2-3-x))
Time = 0.09 (sec) , antiderivative size = 30, normalized size of antiderivative = 0.91 \[ \int \frac {e^{-\frac {e^x (-5-x)}{-3-x+\log ^2(2)}} \left (27+18 x+3 x^2+(-18-6 x) \log ^2(2)+3 \log ^4(2)+e^x \left (-78-87 x-30 x^2-3 x^3+\left (36+24 x+3 x^2\right ) \log ^2(2)\right )+e^{\frac {e^x (-5-x)}{-3-x+\log ^2(2)}} \left (9-12 x-11 x^2-2 x^3+\left (-6+10 x+4 x^2\right ) \log ^2(2)+(1-2 x) \log ^4(2)\right )\right )}{9+6 x+x^2+(-6-2 x) \log ^2(2)+\log ^4(2)} \, dx=-x^{2} + 3 \, {\left (x + 2\right )} e^{\left (\frac {{\left (x + 5\right )} e^{x}}{\log \left (2\right )^{2} - x - 3}\right )} + x \] Input:
integrate((((1-2*x)*log(2)^4+(4*x^2+10*x-6)*log(2)^2-2*x^3-11*x^2-12*x+9)* exp((-x-5)*exp(x)/(log(2)^2-3-x))+((3*x^2+24*x+36)*log(2)^2-3*x^3-30*x^2-8 7*x-78)*exp(x)+3*log(2)^4+(-6*x-18)*log(2)^2+3*x^2+18*x+27)/(log(2)^4+(-2* x-6)*log(2)^2+x^2+6*x+9)/exp((-x-5)*exp(x)/(log(2)^2-3-x)),x, algorithm="f ricas")
Output:
-x^2 + 3*(x + 2)*e^((x + 5)*e^x/(log(2)^2 - x - 3)) + x
Time = 11.84 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.82 \[ \int \frac {e^{-\frac {e^x (-5-x)}{-3-x+\log ^2(2)}} \left (27+18 x+3 x^2+(-18-6 x) \log ^2(2)+3 \log ^4(2)+e^x \left (-78-87 x-30 x^2-3 x^3+\left (36+24 x+3 x^2\right ) \log ^2(2)\right )+e^{\frac {e^x (-5-x)}{-3-x+\log ^2(2)}} \left (9-12 x-11 x^2-2 x^3+\left (-6+10 x+4 x^2\right ) \log ^2(2)+(1-2 x) \log ^4(2)\right )\right )}{9+6 x+x^2+(-6-2 x) \log ^2(2)+\log ^4(2)} \, dx=- x^{2} + x + \left (3 x + 6\right ) e^{- \frac {\left (- x - 5\right ) e^{x}}{- x - 3 + \log {\left (2 \right )}^{2}}} \] Input:
integrate((((1-2*x)*ln(2)**4+(4*x**2+10*x-6)*ln(2)**2-2*x**3-11*x**2-12*x+ 9)*exp((-x-5)*exp(x)/(ln(2)**2-3-x))+((3*x**2+24*x+36)*ln(2)**2-3*x**3-30* x**2-87*x-78)*exp(x)+3*ln(2)**4+(-6*x-18)*ln(2)**2+3*x**2+18*x+27)/(ln(2)* *4+(-2*x-6)*ln(2)**2+x**2+6*x+9)/exp((-x-5)*exp(x)/(ln(2)**2-3-x)),x)
Output:
-x**2 + x + (3*x + 6)*exp(-(-x - 5)*exp(x)/(-x - 3 + log(2)**2))
Leaf count of result is larger than twice the leaf count of optimal. 357 vs. \(2 (30) = 60\).
Time = 0.23 (sec) , antiderivative size = 357, normalized size of antiderivative = 10.82 \[ \int \frac {e^{-\frac {e^x (-5-x)}{-3-x+\log ^2(2)}} \left (27+18 x+3 x^2+(-18-6 x) \log ^2(2)+3 \log ^4(2)+e^x \left (-78-87 x-30 x^2-3 x^3+\left (36+24 x+3 x^2\right ) \log ^2(2)\right )+e^{\frac {e^x (-5-x)}{-3-x+\log ^2(2)}} \left (9-12 x-11 x^2-2 x^3+\left (-6+10 x+4 x^2\right ) \log ^2(2)+(1-2 x) \log ^4(2)\right )\right )}{9+6 x+x^2+(-6-2 x) \log ^2(2)+\log ^4(2)} \, dx=-2 \, {\left (\frac {\log \left (2\right )^{2} - 3}{\log \left (2\right )^{2} - x - 3} + \log \left (-\log \left (2\right )^{2} + x + 3\right )\right )} \log \left (2\right )^{4} + 4 \, {\left (2 \, {\left (\log \left (2\right )^{2} - 3\right )} \log \left (-\log \left (2\right )^{2} + x + 3\right ) + x + \frac {\log \left (2\right )^{4} - 6 \, \log \left (2\right )^{2} + 9}{\log \left (2\right )^{2} - x - 3}\right )} \log \left (2\right )^{2} + 10 \, {\left (\frac {\log \left (2\right )^{2} - 3}{\log \left (2\right )^{2} - x - 3} + \log \left (-\log \left (2\right )^{2} + x + 3\right )\right )} \log \left (2\right )^{2} + \frac {\log \left (2\right )^{4}}{\log \left (2\right )^{2} - x - 3} - 4 \, {\left (\log \left (2\right )^{2} - 3\right )} x - x^{2} + 3 \, {\left (x + 2\right )} e^{\left (\frac {e^{x} \log \left (2\right )^{2}}{\log \left (2\right )^{2} - x - 3} + \frac {2 \, e^{x}}{\log \left (2\right )^{2} - x - 3} - e^{x}\right )} - 6 \, {\left (\log \left (2\right )^{4} - 6 \, \log \left (2\right )^{2} + 9\right )} \log \left (-\log \left (2\right )^{2} + x + 3\right ) - 22 \, {\left (\log \left (2\right )^{2} - 3\right )} \log \left (-\log \left (2\right )^{2} + x + 3\right ) - 11 \, x - \frac {6 \, \log \left (2\right )^{2}}{\log \left (2\right )^{2} - x - 3} - \frac {2 \, {\left (\log \left (2\right )^{6} - 9 \, \log \left (2\right )^{4} + 27 \, \log \left (2\right )^{2} - 27\right )}}{\log \left (2\right )^{2} - x - 3} - \frac {11 \, {\left (\log \left (2\right )^{4} - 6 \, \log \left (2\right )^{2} + 9\right )}}{\log \left (2\right )^{2} - x - 3} - \frac {12 \, {\left (\log \left (2\right )^{2} - 3\right )}}{\log \left (2\right )^{2} - x - 3} + \frac {9}{\log \left (2\right )^{2} - x - 3} - 12 \, \log \left (-\log \left (2\right )^{2} + x + 3\right ) \] Input:
integrate((((1-2*x)*log(2)^4+(4*x^2+10*x-6)*log(2)^2-2*x^3-11*x^2-12*x+9)* exp((-x-5)*exp(x)/(log(2)^2-3-x))+((3*x^2+24*x+36)*log(2)^2-3*x^3-30*x^2-8 7*x-78)*exp(x)+3*log(2)^4+(-6*x-18)*log(2)^2+3*x^2+18*x+27)/(log(2)^4+(-2* x-6)*log(2)^2+x^2+6*x+9)/exp((-x-5)*exp(x)/(log(2)^2-3-x)),x, algorithm="m axima")
Output:
-2*((log(2)^2 - 3)/(log(2)^2 - x - 3) + log(-log(2)^2 + x + 3))*log(2)^4 + 4*(2*(log(2)^2 - 3)*log(-log(2)^2 + x + 3) + x + (log(2)^4 - 6*log(2)^2 + 9)/(log(2)^2 - x - 3))*log(2)^2 + 10*((log(2)^2 - 3)/(log(2)^2 - x - 3) + log(-log(2)^2 + x + 3))*log(2)^2 + log(2)^4/(log(2)^2 - x - 3) - 4*(log(2 )^2 - 3)*x - x^2 + 3*(x + 2)*e^(e^x*log(2)^2/(log(2)^2 - x - 3) + 2*e^x/(l og(2)^2 - x - 3) - e^x) - 6*(log(2)^4 - 6*log(2)^2 + 9)*log(-log(2)^2 + x + 3) - 22*(log(2)^2 - 3)*log(-log(2)^2 + x + 3) - 11*x - 6*log(2)^2/(log(2 )^2 - x - 3) - 2*(log(2)^6 - 9*log(2)^4 + 27*log(2)^2 - 27)/(log(2)^2 - x - 3) - 11*(log(2)^4 - 6*log(2)^2 + 9)/(log(2)^2 - x - 3) - 12*(log(2)^2 - 3)/(log(2)^2 - x - 3) + 9/(log(2)^2 - x - 3) - 12*log(-log(2)^2 + x + 3)
\[ \int \frac {e^{-\frac {e^x (-5-x)}{-3-x+\log ^2(2)}} \left (27+18 x+3 x^2+(-18-6 x) \log ^2(2)+3 \log ^4(2)+e^x \left (-78-87 x-30 x^2-3 x^3+\left (36+24 x+3 x^2\right ) \log ^2(2)\right )+e^{\frac {e^x (-5-x)}{-3-x+\log ^2(2)}} \left (9-12 x-11 x^2-2 x^3+\left (-6+10 x+4 x^2\right ) \log ^2(2)+(1-2 x) \log ^4(2)\right )\right )}{9+6 x+x^2+(-6-2 x) \log ^2(2)+\log ^4(2)} \, dx=\int { \frac {{\left (3 \, \log \left (2\right )^{4} - 6 \, {\left (x + 3\right )} \log \left (2\right )^{2} + 3 \, x^{2} - 3 \, {\left (x^{3} - {\left (x^{2} + 8 \, x + 12\right )} \log \left (2\right )^{2} + 10 \, x^{2} + 29 \, x + 26\right )} e^{x} - {\left ({\left (2 \, x - 1\right )} \log \left (2\right )^{4} + 2 \, x^{3} - 2 \, {\left (2 \, x^{2} + 5 \, x - 3\right )} \log \left (2\right )^{2} + 11 \, x^{2} + 12 \, x - 9\right )} e^{\left (-\frac {{\left (x + 5\right )} e^{x}}{\log \left (2\right )^{2} - x - 3}\right )} + 18 \, x + 27\right )} e^{\left (\frac {{\left (x + 5\right )} e^{x}}{\log \left (2\right )^{2} - x - 3}\right )}}{\log \left (2\right )^{4} - 2 \, {\left (x + 3\right )} \log \left (2\right )^{2} + x^{2} + 6 \, x + 9} \,d x } \] Input:
integrate((((1-2*x)*log(2)^4+(4*x^2+10*x-6)*log(2)^2-2*x^3-11*x^2-12*x+9)* exp((-x-5)*exp(x)/(log(2)^2-3-x))+((3*x^2+24*x+36)*log(2)^2-3*x^3-30*x^2-8 7*x-78)*exp(x)+3*log(2)^4+(-6*x-18)*log(2)^2+3*x^2+18*x+27)/(log(2)^4+(-2* x-6)*log(2)^2+x^2+6*x+9)/exp((-x-5)*exp(x)/(log(2)^2-3-x)),x, algorithm="g iac")
Output:
integrate((3*log(2)^4 - 6*(x + 3)*log(2)^2 + 3*x^2 - 3*(x^3 - (x^2 + 8*x + 12)*log(2)^2 + 10*x^2 + 29*x + 26)*e^x - ((2*x - 1)*log(2)^4 + 2*x^3 - 2* (2*x^2 + 5*x - 3)*log(2)^2 + 11*x^2 + 12*x - 9)*e^(-(x + 5)*e^x/(log(2)^2 - x - 3)) + 18*x + 27)*e^((x + 5)*e^x/(log(2)^2 - x - 3))/(log(2)^4 - 2*(x + 3)*log(2)^2 + x^2 + 6*x + 9), x)
Time = 3.15 (sec) , antiderivative size = 46, normalized size of antiderivative = 1.39 \[ \int \frac {e^{-\frac {e^x (-5-x)}{-3-x+\log ^2(2)}} \left (27+18 x+3 x^2+(-18-6 x) \log ^2(2)+3 \log ^4(2)+e^x \left (-78-87 x-30 x^2-3 x^3+\left (36+24 x+3 x^2\right ) \log ^2(2)\right )+e^{\frac {e^x (-5-x)}{-3-x+\log ^2(2)}} \left (9-12 x-11 x^2-2 x^3+\left (-6+10 x+4 x^2\right ) \log ^2(2)+(1-2 x) \log ^4(2)\right )\right )}{9+6 x+x^2+(-6-2 x) \log ^2(2)+\log ^4(2)} \, dx=x+{\mathrm {e}}^{-\frac {5\,{\mathrm {e}}^x}{x-{\ln \left (2\right )}^2+3}-\frac {x\,{\mathrm {e}}^x}{x-{\ln \left (2\right )}^2+3}}\,\left (3\,x+6\right )-x^2 \] Input:
int((exp(-(exp(x)*(x + 5))/(x - log(2)^2 + 3))*(18*x - log(2)^2*(6*x + 18) - exp(x)*(87*x - log(2)^2*(24*x + 3*x^2 + 36) + 30*x^2 + 3*x^3 + 78) + 3* log(2)^4 + 3*x^2 - exp((exp(x)*(x + 5))/(x - log(2)^2 + 3))*(12*x + log(2) ^4*(2*x - 1) - log(2)^2*(10*x + 4*x^2 - 6) + 11*x^2 + 2*x^3 - 9) + 27))/(6 *x - log(2)^2*(2*x + 6) + log(2)^4 + x^2 + 9),x)
Output:
x + exp(- (5*exp(x))/(x - log(2)^2 + 3) - (x*exp(x))/(x - log(2)^2 + 3))*( 3*x + 6) - x^2
Time = 0.19 (sec) , antiderivative size = 62, normalized size of antiderivative = 1.88 \[ \int \frac {e^{-\frac {e^x (-5-x)}{-3-x+\log ^2(2)}} \left (27+18 x+3 x^2+(-18-6 x) \log ^2(2)+3 \log ^4(2)+e^x \left (-78-87 x-30 x^2-3 x^3+\left (36+24 x+3 x^2\right ) \log ^2(2)\right )+e^{\frac {e^x (-5-x)}{-3-x+\log ^2(2)}} \left (9-12 x-11 x^2-2 x^3+\left (-6+10 x+4 x^2\right ) \log ^2(2)+(1-2 x) \log ^4(2)\right )\right )}{9+6 x+x^2+(-6-2 x) \log ^2(2)+\log ^4(2)} \, dx=3 e^{\frac {e^{x} x +5 e^{x}}{\mathrm {log}\left (2\right )^{2}-x -3}} x +6 e^{\frac {e^{x} x +5 e^{x}}{\mathrm {log}\left (2\right )^{2}-x -3}}-x^{2}+x \] Input:
int((((1-2*x)*log(2)^4+(4*x^2+10*x-6)*log(2)^2-2*x^3-11*x^2-12*x+9)*exp((- x-5)*exp(x)/(log(2)^2-3-x))+((3*x^2+24*x+36)*log(2)^2-3*x^3-30*x^2-87*x-78 )*exp(x)+3*log(2)^4+(-6*x-18)*log(2)^2+3*x^2+18*x+27)/(log(2)^4+(-2*x-6)*l og(2)^2+x^2+6*x+9)/exp((-x-5)*exp(x)/(log(2)^2-3-x)),x)
Output:
3*e**((e**x*x + 5*e**x)/(log(2)**2 - x - 3))*x + 6*e**((e**x*x + 5*e**x)/( log(2)**2 - x - 3)) - x**2 + x