Integrand size = 326, antiderivative size = 29 \[ \int \frac {e^x \left (-4050 x-2025 x^2+81 x^3+\left (-2025-2106 x+81 x^2\right ) \log (5)\right )+e^{2+e^x} \left (e^{2 x} \left (2700 x^2-108 x^3+\left (2700 x-108 x^2\right ) \log (5)\right )+e^x \left (5400 x+2700 x^2-108 x^3+\left (2700+2808 x-108 x^2\right ) \log (5)\right )\right )+e^{6+3 e^x} \left (e^{2 x} \left (900 x^2-36 x^3+\left (900 x-36 x^2\right ) \log (5)\right )+e^x \left (600 x+300 x^2-12 x^3+\left (300+312 x-12 x^2\right ) \log (5)\right )\right )+e^{8+4 e^x} \left (e^x \left (-50 x-25 x^2+x^3+\left (-25-26 x+x^2\right ) \log (5)\right )+e^{2 x} \left (-100 x^2+4 x^3+\left (-100 x+4 x^2\right ) \log (5)\right )\right )+e^{4+2 e^x} \left (e^x \left (-2700 x-1350 x^2+54 x^3+\left (-1350-1404 x+54 x^2\right ) \log (5)\right )+e^{2 x} \left (-2700 x^2+108 x^3+\left (-2700 x+108 x^2\right ) \log (5)\right )\right )}{-15625+1875 x-75 x^2+x^3} \, dx=\frac {e^x \left (3-e^{2+e^x}\right )^4 x (x+\log (5))}{(25-x)^2} \] Output:
x*(3-exp(2+exp(x)))^4/(-x+25)^2*exp(x)*(ln(5)+x)
Time = 0.20 (sec) , antiderivative size = 25, normalized size of antiderivative = 0.86 \[ \int \frac {e^x \left (-4050 x-2025 x^2+81 x^3+\left (-2025-2106 x+81 x^2\right ) \log (5)\right )+e^{2+e^x} \left (e^{2 x} \left (2700 x^2-108 x^3+\left (2700 x-108 x^2\right ) \log (5)\right )+e^x \left (5400 x+2700 x^2-108 x^3+\left (2700+2808 x-108 x^2\right ) \log (5)\right )\right )+e^{6+3 e^x} \left (e^{2 x} \left (900 x^2-36 x^3+\left (900 x-36 x^2\right ) \log (5)\right )+e^x \left (600 x+300 x^2-12 x^3+\left (300+312 x-12 x^2\right ) \log (5)\right )\right )+e^{8+4 e^x} \left (e^x \left (-50 x-25 x^2+x^3+\left (-25-26 x+x^2\right ) \log (5)\right )+e^{2 x} \left (-100 x^2+4 x^3+\left (-100 x+4 x^2\right ) \log (5)\right )\right )+e^{4+2 e^x} \left (e^x \left (-2700 x-1350 x^2+54 x^3+\left (-1350-1404 x+54 x^2\right ) \log (5)\right )+e^{2 x} \left (-2700 x^2+108 x^3+\left (-2700 x+108 x^2\right ) \log (5)\right )\right )}{-15625+1875 x-75 x^2+x^3} \, dx=\frac {e^x \left (-3+e^{2+e^x}\right )^4 x (x+\log (5))}{(-25+x)^2} \] Input:
Integrate[(E^x*(-4050*x - 2025*x^2 + 81*x^3 + (-2025 - 2106*x + 81*x^2)*Lo g[5]) + E^(2 + E^x)*(E^(2*x)*(2700*x^2 - 108*x^3 + (2700*x - 108*x^2)*Log[ 5]) + E^x*(5400*x + 2700*x^2 - 108*x^3 + (2700 + 2808*x - 108*x^2)*Log[5]) ) + E^(6 + 3*E^x)*(E^(2*x)*(900*x^2 - 36*x^3 + (900*x - 36*x^2)*Log[5]) + E^x*(600*x + 300*x^2 - 12*x^3 + (300 + 312*x - 12*x^2)*Log[5])) + E^(8 + 4 *E^x)*(E^x*(-50*x - 25*x^2 + x^3 + (-25 - 26*x + x^2)*Log[5]) + E^(2*x)*(- 100*x^2 + 4*x^3 + (-100*x + 4*x^2)*Log[5])) + E^(4 + 2*E^x)*(E^x*(-2700*x - 1350*x^2 + 54*x^3 + (-1350 - 1404*x + 54*x^2)*Log[5]) + E^(2*x)*(-2700*x ^2 + 108*x^3 + (-2700*x + 108*x^2)*Log[5])))/(-15625 + 1875*x - 75*x^2 + x ^3),x]
Output:
(E^x*(-3 + E^(2 + E^x))^4*x*(x + Log[5]))/(-25 + x)^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.
| \(\displaystyle \int \frac {e^x \left (81 x^3-2025 x^2+\left (81 x^2-2106 x-2025\right ) \log (5)-4050 x\right )+e^{e^x+2} \left (e^{2 x} \left (-108 x^3+2700 x^2+\left (2700 x-108 x^2\right ) \log (5)\right )+e^x \left (-108 x^3+2700 x^2+\left (-108 x^2+2808 x+2700\right ) \log (5)+5400 x\right )\right )+e^{3 e^x+6} \left (e^{2 x} \left (-36 x^3+900 x^2+\left (900 x-36 x^2\right ) \log (5)\right )+e^x \left (-12 x^3+300 x^2+\left (-12 x^2+312 x+300\right ) \log (5)+600 x\right )\right )+e^{4 e^x+8} \left (e^x \left (x^3-25 x^2+\left (x^2-26 x-25\right ) \log (5)-50 x\right )+e^{2 x} \left (4 x^3-100 x^2+\left (4 x^2-100 x\right ) \log (5)\right )\right )+e^{2 e^x+4} \left (e^x \left (54 x^3-1350 x^2+\left (54 x^2-1404 x-1350\right ) \log (5)-2700 x\right )+e^{2 x} \left (108 x^3-2700 x^2+\left (108 x^2-2700 x\right ) \log (5)\right )\right )}{x^3-75 x^2+1875 x-15625} \, dx\) |
| \(\Big \downarrow \) 2007 |
| \(\displaystyle \int \frac {e^x \left (81 x^3-2025 x^2+\left (81 x^2-2106 x-2025\right ) \log (5)-4050 x\right )+e^{e^x+2} \left (e^{2 x} \left (-108 x^3+2700 x^2+\left (2700 x-108 x^2\right ) \log (5)\right )+e^x \left (-108 x^3+2700 x^2+\left (-108 x^2+2808 x+2700\right ) \log (5)+5400 x\right )\right )+e^{3 e^x+6} \left (e^{2 x} \left (-36 x^3+900 x^2+\left (900 x-36 x^2\right ) \log (5)\right )+e^x \left (-12 x^3+300 x^2+\left (-12 x^2+312 x+300\right ) \log (5)+600 x\right )\right )+e^{4 e^x+8} \left (e^x \left (x^3-25 x^2+\left (x^2-26 x-25\right ) \log (5)-50 x\right )+e^{2 x} \left (4 x^3-100 x^2+\left (4 x^2-100 x\right ) \log (5)\right )\right )+e^{2 e^x+4} \left (e^x \left (54 x^3-1350 x^2+\left (54 x^2-1404 x-1350\right ) \log (5)-2700 x\right )+e^{2 x} \left (108 x^3-2700 x^2+\left (108 x^2-2700 x\right ) \log (5)\right )\right )}{(x-25)^3}dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {e^x \left (3-e^{e^x+2}\right )^3 \left (\left (e^{e^x+2}+4 e^{x+e^x+2}-3\right ) x^3+\left (e^{e^x+2}+4 e^{x+e^x+2}-3\right ) x^2 (\log (5)-25)-2 x \left (50 e^{x+e^x+2} \log (5)+e^{e^x+2} (25+13 \log (5))-75-39 \log (5)\right )-25 \left (e^{e^x+2}-3\right ) \log (5)\right )}{(25-x)^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {3 e^x x^3 \left (e^{e^x+2}-3\right )^3}{(x-25)^3}+\frac {e^{x+e^x+2} x^3 \left (e^{e^x+2}-3\right )^3}{(x-25)^3}-\frac {3 e^x x^2 \left (e^{e^x+2}-3\right )^3 (\log (5)-25)}{(x-25)^3}+\frac {e^{x+e^x+2} x^2 \left (e^{e^x+2}-3\right )^3 (\log (5)-25)}{(x-25)^3}-\frac {25 e^x \left (e^{e^x+2}-3\right )^4 \log (5)}{(x-25)^3}+\frac {4 e^{2 x+e^x+2} x \left (e^{e^x+2}-3\right )^3 (x+\log (5))}{(x-25)^2}-\frac {2 e^{x+e^x+2} x \left (e^{e^x+2}-3\right )^3 (25+13 \log (5))}{(x-25)^3}+\frac {150 e^x x \left (e^{e^x+2}-3\right )^3 \left (1+\frac {13 \log (5)}{25}\right )}{(x-25)^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {e^x \left (3-e^{e^x+2}\right )^3 \left (\left (e^{e^x+2}+4 e^{x+e^x+2}-3\right ) x^3+\left (e^{e^x+2}+4 e^{x+e^x+2}-3\right ) x^2 (\log (5)-25)-2 x \left (50 e^{x+e^x+2} \log (5)+e^{e^x+2} (25+13 \log (5))-75-39 \log (5)\right )-25 \left (e^{e^x+2}-3\right ) \log (5)\right )}{(25-x)^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {3 e^x x^3 \left (e^{e^x+2}-3\right )^3}{(x-25)^3}+\frac {e^{x+e^x+2} x^3 \left (e^{e^x+2}-3\right )^3}{(x-25)^3}-\frac {3 e^x x^2 \left (e^{e^x+2}-3\right )^3 (\log (5)-25)}{(x-25)^3}+\frac {e^{x+e^x+2} x^2 \left (e^{e^x+2}-3\right )^3 (\log (5)-25)}{(x-25)^3}-\frac {25 e^x \left (e^{e^x+2}-3\right )^4 \log (5)}{(x-25)^3}+\frac {4 e^{2 x+e^x+2} x \left (e^{e^x+2}-3\right )^3 (x+\log (5))}{(x-25)^2}-\frac {2 e^{x+e^x+2} x \left (e^{e^x+2}-3\right )^3 (25+13 \log (5))}{(x-25)^3}+\frac {150 e^x x \left (e^{e^x+2}-3\right )^3 \left (1+\frac {13 \log (5)}{25}\right )}{(x-25)^3}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -2187 e^{25} (25+13 \log (5)) \operatorname {ExpIntegralEi}(x-25)-\frac {2025}{2} e^{25} \log (5) \operatorname {ExpIntegralEi}(x-25)-\frac {58887}{2} e^{25} (25-\log (5)) \operatorname {ExpIntegralEi}(x-25)+\frac {1581525}{2} e^{25} \operatorname {ExpIntegralEi}(x-25)+27 e^{4+2 e^x}+\frac {1}{4} e^{8+4 e^x}+81 e^x-108 e^{x+e^x+2}-12 e^{x+3 e^x+6}+108 \int e^{2 \left (x+e^x+2\right )}dx+4 \int e^{2 \left (x+2 e^x+4\right )}dx-300 \log (5) \int \frac {e^{3 \left (2+e^x\right )+x}}{(25-x)^3}dx+27 (25-\log (5)) \int \frac {e^{2 \left (2+e^x\right )+x}}{25-x}dx-9 (25-\log (5)) \int \frac {e^{2 \left (2+e^x\right )+e^x+x+2}}{25-x}dx+5400 (25+13 \log (5)) \int \frac {e^{x+e^x+2}}{(x-25)^3}dx+2700 \log (5) \int \frac {e^{x+e^x+2}}{(x-25)^3}dx+67500 (25-\log (5)) \int \frac {e^{x+e^x+2}}{(x-25)^3}dx-1687500 \int \frac {e^{x+e^x+2}}{(x-25)^3}dx-1350 (25+13 \log (5)) \int \frac {e^{x+2 e^x+4}}{(x-25)^3}dx-16875 (25-\log (5)) \int \frac {e^{x+2 e^x+4}}{(x-25)^3}dx+421875 \int \frac {e^{x+2 e^x+4}}{(x-25)^3}dx-1350 (25+13 \log (5)) \int \frac {e^{2 \left (2+e^x\right )+x}}{(x-25)^3}dx-1350 \log (5) \int \frac {e^{2 \left (2+e^x\right )+x}}{(x-25)^3}dx-16875 (25-\log (5)) \int \frac {e^{2 \left (2+e^x\right )+x}}{(x-25)^3}dx+421875 \int \frac {e^{2 \left (2+e^x\right )+x}}{(x-25)^3}dx+450 (25+13 \log (5)) \int \frac {e^{2 \left (2+e^x\right )+e^x+x+2}}{(x-25)^3}dx+5625 (25-\log (5)) \int \frac {e^{2 \left (2+e^x\right )+e^x+x+2}}{(x-25)^3}dx-140625 \int \frac {e^{2 \left (2+e^x\right )+e^x+x+2}}{(x-25)^3}dx+150 (25+13 \log (5)) \int \frac {e^{3 \left (2+e^x\right )+x}}{(x-25)^3}dx+1875 (25-\log (5)) \int \frac {e^{3 \left (2+e^x\right )+x}}{(x-25)^3}dx-46875 \int \frac {e^{3 \left (2+e^x\right )+x}}{(x-25)^3}dx-50 (25+13 \log (5)) \int \frac {e^{3 \left (2+e^x\right )+e^x+x+2}}{(x-25)^3}dx-625 (25-\log (5)) \int \frac {e^{3 \left (2+e^x\right )+e^x+x+2}}{(x-25)^3}dx+15625 \int \frac {e^{3 \left (2+e^x\right )+e^x+x+2}}{(x-25)^3}dx-25 \log (5) \int \frac {e^{4 \left (2+e^x\right )+x}}{(x-25)^3}dx+216 (25+13 \log (5)) \int \frac {e^{x+e^x+2}}{(x-25)^2}dx+5400 (25-\log (5)) \int \frac {e^{x+e^x+2}}{(x-25)^2}dx-202500 \int \frac {e^{x+e^x+2}}{(x-25)^2}dx+2700 (25+\log (5)) \int \frac {e^{2 \left (x+e^x+2\right )}}{(x-25)^2}dx-54 (25+13 \log (5)) \int \frac {e^{x+2 e^x+4}}{(x-25)^2}dx-1350 (25-\log (5)) \int \frac {e^{x+2 e^x+4}}{(x-25)^2}dx+50625 \int \frac {e^{x+2 e^x+4}}{(x-25)^2}dx+100 (25+\log (5)) \int \frac {e^{2 \left (x+2 e^x+4\right )}}{(x-25)^2}dx-54 (25+13 \log (5)) \int \frac {e^{2 \left (2+e^x\right )+x}}{(x-25)^2}dx-1350 (25-\log (5)) \int \frac {e^{2 \left (2+e^x\right )+x}}{(x-25)^2}dx+50625 \int \frac {e^{2 \left (2+e^x\right )+x}}{(x-25)^2}dx+18 (25+13 \log (5)) \int \frac {e^{2 \left (2+e^x\right )+e^x+x+2}}{(x-25)^2}dx+450 (25-\log (5)) \int \frac {e^{2 \left (2+e^x\right )+e^x+x+2}}{(x-25)^2}dx-16875 \int \frac {e^{2 \left (2+e^x\right )+e^x+x+2}}{(x-25)^2}dx+6 (25+13 \log (5)) \int \frac {e^{3 \left (2+e^x\right )+x}}{(x-25)^2}dx+150 (25-\log (5)) \int \frac {e^{3 \left (2+e^x\right )+x}}{(x-25)^2}dx-5625 \int \frac {e^{3 \left (2+e^x\right )+x}}{(x-25)^2}dx-2 (25+13 \log (5)) \int \frac {e^{3 \left (2+e^x\right )+e^x+x+2}}{(x-25)^2}dx-50 (25-\log (5)) \int \frac {e^{3 \left (2+e^x\right )+e^x+x+2}}{(x-25)^2}dx+1875 \int \frac {e^{3 \left (2+e^x\right )+e^x+x+2}}{(x-25)^2}dx-2700 (25+\log (5)) \int \frac {e^{2 x+e^x+2}}{(x-25)^2}dx-900 (25+\log (5)) \int \frac {e^{2 \left (2+e^x\right )+e^x+2 x+2}}{(x-25)^2}dx+108 (25-\log (5)) \int \frac {e^{x+e^x+2}}{x-25}dx-8100 \int \frac {e^{x+e^x+2}}{x-25}dx+108 (50+\log (5)) \int \frac {e^{2 \left (x+e^x+2\right )}}{x-25}dx-27 (25-\log (5)) \int \frac {e^{x+2 e^x+4}}{x-25}dx+2025 \int \frac {e^{x+2 e^x+4}}{x-25}dx+4 (50+\log (5)) \int \frac {e^{2 \left (x+2 e^x+4\right )}}{x-25}dx+2025 \int \frac {e^{2 \left (2+e^x\right )+x}}{x-25}dx-675 \int \frac {e^{2 \left (2+e^x\right )+e^x+x+2}}{x-25}dx+3 (25-\log (5)) \int \frac {e^{3 \left (2+e^x\right )+x}}{x-25}dx-225 \int \frac {e^{3 \left (2+e^x\right )+x}}{x-25}dx-(25-\log (5)) \int \frac {e^{3 \left (2+e^x\right )+e^x+x+2}}{x-25}dx+75 \int \frac {e^{3 \left (2+e^x\right )+e^x+x+2}}{x-25}dx-108 (50+\log (5)) \int \frac {e^{2 x+e^x+2}}{x-25}dx-36 (50+\log (5)) \int \frac {e^{2 \left (2+e^x\right )+e^x+2 x+2}}{x-25}dx+\frac {1569375 e^x}{2 (25-x)}-\frac {1265625 e^x}{2 (25-x)^2}-\frac {2187 e^x (25+13 \log (5))}{25-x}+\frac {2025 e^x (25+13 \log (5))}{(25-x)^2}-\frac {2025 e^x \log (5)}{2 (25-x)}+\frac {2025 e^x \log (5)}{2 (25-x)^2}-\frac {58725 e^x (25-\log (5))}{2 (25-x)}+\frac {50625 e^x (25-\log (5))}{2 (25-x)^2}\) |
Input:
Int[(E^x*(-4050*x - 2025*x^2 + 81*x^3 + (-2025 - 2106*x + 81*x^2)*Log[5]) + E^(2 + E^x)*(E^(2*x)*(2700*x^2 - 108*x^3 + (2700*x - 108*x^2)*Log[5]) + E^x*(5400*x + 2700*x^2 - 108*x^3 + (2700 + 2808*x - 108*x^2)*Log[5])) + E^ (6 + 3*E^x)*(E^(2*x)*(900*x^2 - 36*x^3 + (900*x - 36*x^2)*Log[5]) + E^x*(6 00*x + 300*x^2 - 12*x^3 + (300 + 312*x - 12*x^2)*Log[5])) + E^(8 + 4*E^x)* (E^x*(-50*x - 25*x^2 + x^3 + (-25 - 26*x + x^2)*Log[5]) + E^(2*x)*(-100*x^ 2 + 4*x^3 + (-100*x + 4*x^2)*Log[5])) + E^(4 + 2*E^x)*(E^x*(-2700*x - 1350 *x^2 + 54*x^3 + (-1350 - 1404*x + 54*x^2)*Log[5]) + E^(2*x)*(-2700*x^2 + 1 08*x^3 + (-2700*x + 108*x^2)*Log[5])))/(-15625 + 1875*x - 75*x^2 + x^3),x]
Output:
$Aborted
Leaf count of result is larger than twice the leaf count of optimal. \(112\) vs. \(2(26)=52\).
Time = 1.79 (sec) , antiderivative size = 113, normalized size of antiderivative = 3.90
| method | result | size |
| risch | \(\frac {81 x \left (\ln \left (5\right )+x \right ) {\mathrm e}^{x}}{\left (x -25\right )^{2}}+\frac {\left (\ln \left (5\right )+x \right ) x \,{\mathrm e}^{x +4 \,{\mathrm e}^{x}+8}}{x^{2}-50 x +625}-\frac {12 \left (\ln \left (5\right )+x \right ) x \,{\mathrm e}^{x +3 \,{\mathrm e}^{x}+6}}{x^{2}-50 x +625}+\frac {54 \left (\ln \left (5\right )+x \right ) x \,{\mathrm e}^{x +2 \,{\mathrm e}^{x}+4}}{x^{2}-50 x +625}-\frac {108 \left (\ln \left (5\right )+x \right ) x \,{\mathrm e}^{{\mathrm e}^{x}+x +2}}{x^{2}-50 x +625}\) | \(113\) |
| parallelrisch | \(\frac {-108 \,{\mathrm e}^{{\mathrm e}^{x}+2} {\mathrm e}^{x} \ln \left (5\right ) x -108 \,{\mathrm e}^{{\mathrm e}^{x}+2} {\mathrm e}^{x} x^{2}-12 \,{\mathrm e}^{x} \ln \left (5\right ) {\mathrm e}^{3 \,{\mathrm e}^{x}+6} x -12 \,{\mathrm e}^{x} {\mathrm e}^{3 \,{\mathrm e}^{x}+6} x^{2}+{\mathrm e}^{x} \ln \left (5\right ) {\mathrm e}^{4 \,{\mathrm e}^{x}+8} x +{\mathrm e}^{x} {\mathrm e}^{4 \,{\mathrm e}^{x}+8} x^{2}+81 \ln \left (5\right ) {\mathrm e}^{x} x +81 \,{\mathrm e}^{x} x^{2}+54 \,{\mathrm e}^{x} \ln \left (5\right ) {\mathrm e}^{2 \,{\mathrm e}^{x}+4} x +54 \,{\mathrm e}^{x} {\mathrm e}^{2 \,{\mathrm e}^{x}+4} x^{2}}{x^{2}-50 x +625}\) | \(133\) |
Input:
int(((((4*x^2-100*x)*ln(5)+4*x^3-100*x^2)*exp(x)^2+((x^2-26*x-25)*ln(5)+x^ 3-25*x^2-50*x)*exp(x))*exp(exp(x)+2)^4+(((-36*x^2+900*x)*ln(5)-36*x^3+900* x^2)*exp(x)^2+((-12*x^2+312*x+300)*ln(5)-12*x^3+300*x^2+600*x)*exp(x))*exp (exp(x)+2)^3+(((108*x^2-2700*x)*ln(5)+108*x^3-2700*x^2)*exp(x)^2+((54*x^2- 1404*x-1350)*ln(5)+54*x^3-1350*x^2-2700*x)*exp(x))*exp(exp(x)+2)^2+(((-108 *x^2+2700*x)*ln(5)-108*x^3+2700*x^2)*exp(x)^2+((-108*x^2+2808*x+2700)*ln(5 )-108*x^3+2700*x^2+5400*x)*exp(x))*exp(exp(x)+2)+((81*x^2-2106*x-2025)*ln( 5)+81*x^3-2025*x^2-4050*x)*exp(x))/(x^3-75*x^2+1875*x-15625),x,method=_RET URNVERBOSE)
Output:
81*x*(ln(5)+x)/(x-25)^2*exp(x)+1/(x^2-50*x+625)*(ln(5)+x)*x*exp(x+4*exp(x) +8)-12/(x^2-50*x+625)*(ln(5)+x)*x*exp(x+3*exp(x)+6)+54/(x^2-50*x+625)*(ln( 5)+x)*x*exp(x+2*exp(x)+4)-108/(x^2-50*x+625)*(ln(5)+x)*x*exp(exp(x)+x+2)
Leaf count of result is larger than twice the leaf count of optimal. 93 vs. \(2 (22) = 44\).
Time = 0.10 (sec) , antiderivative size = 93, normalized size of antiderivative = 3.21 \[ \int \frac {e^x \left (-4050 x-2025 x^2+81 x^3+\left (-2025-2106 x+81 x^2\right ) \log (5)\right )+e^{2+e^x} \left (e^{2 x} \left (2700 x^2-108 x^3+\left (2700 x-108 x^2\right ) \log (5)\right )+e^x \left (5400 x+2700 x^2-108 x^3+\left (2700+2808 x-108 x^2\right ) \log (5)\right )\right )+e^{6+3 e^x} \left (e^{2 x} \left (900 x^2-36 x^3+\left (900 x-36 x^2\right ) \log (5)\right )+e^x \left (600 x+300 x^2-12 x^3+\left (300+312 x-12 x^2\right ) \log (5)\right )\right )+e^{8+4 e^x} \left (e^x \left (-50 x-25 x^2+x^3+\left (-25-26 x+x^2\right ) \log (5)\right )+e^{2 x} \left (-100 x^2+4 x^3+\left (-100 x+4 x^2\right ) \log (5)\right )\right )+e^{4+2 e^x} \left (e^x \left (-2700 x-1350 x^2+54 x^3+\left (-1350-1404 x+54 x^2\right ) \log (5)\right )+e^{2 x} \left (-2700 x^2+108 x^3+\left (-2700 x+108 x^2\right ) \log (5)\right )\right )}{-15625+1875 x-75 x^2+x^3} \, dx=\frac {{\left (x^{2} + x \log \left (5\right )\right )} e^{\left (x + 4 \, e^{x} + 8\right )} - 12 \, {\left (x^{2} + x \log \left (5\right )\right )} e^{\left (x + 3 \, e^{x} + 6\right )} + 54 \, {\left (x^{2} + x \log \left (5\right )\right )} e^{\left (x + 2 \, e^{x} + 4\right )} - 108 \, {\left (x^{2} + x \log \left (5\right )\right )} e^{\left (x + e^{x} + 2\right )} + 81 \, {\left (x^{2} + x \log \left (5\right )\right )} e^{x}}{x^{2} - 50 \, x + 625} \] Input:
integrate(((((4*x^2-100*x)*log(5)+4*x^3-100*x^2)*exp(x)^2+((x^2-26*x-25)*l og(5)+x^3-25*x^2-50*x)*exp(x))*exp(2+exp(x))^4+(((-36*x^2+900*x)*log(5)-36 *x^3+900*x^2)*exp(x)^2+((-12*x^2+312*x+300)*log(5)-12*x^3+300*x^2+600*x)*e xp(x))*exp(2+exp(x))^3+(((108*x^2-2700*x)*log(5)+108*x^3-2700*x^2)*exp(x)^ 2+((54*x^2-1404*x-1350)*log(5)+54*x^3-1350*x^2-2700*x)*exp(x))*exp(2+exp(x ))^2+(((-108*x^2+2700*x)*log(5)-108*x^3+2700*x^2)*exp(x)^2+((-108*x^2+2808 *x+2700)*log(5)-108*x^3+2700*x^2+5400*x)*exp(x))*exp(2+exp(x))+((81*x^2-21 06*x-2025)*log(5)+81*x^3-2025*x^2-4050*x)*exp(x))/(x^3-75*x^2+1875*x-15625 ),x, algorithm="fricas")
Output:
((x^2 + x*log(5))*e^(x + 4*e^x + 8) - 12*(x^2 + x*log(5))*e^(x + 3*e^x + 6 ) + 54*(x^2 + x*log(5))*e^(x + 2*e^x + 4) - 108*(x^2 + x*log(5))*e^(x + e^ x + 2) + 81*(x^2 + x*log(5))*e^x)/(x^2 - 50*x + 625)
Leaf count of result is larger than twice the leaf count of optimal. 654 vs. \(2 (24) = 48\).
Time = 0.47 (sec) , antiderivative size = 654, normalized size of antiderivative = 22.55 \[ \int \frac {e^x \left (-4050 x-2025 x^2+81 x^3+\left (-2025-2106 x+81 x^2\right ) \log (5)\right )+e^{2+e^x} \left (e^{2 x} \left (2700 x^2-108 x^3+\left (2700 x-108 x^2\right ) \log (5)\right )+e^x \left (5400 x+2700 x^2-108 x^3+\left (2700+2808 x-108 x^2\right ) \log (5)\right )\right )+e^{6+3 e^x} \left (e^{2 x} \left (900 x^2-36 x^3+\left (900 x-36 x^2\right ) \log (5)\right )+e^x \left (600 x+300 x^2-12 x^3+\left (300+312 x-12 x^2\right ) \log (5)\right )\right )+e^{8+4 e^x} \left (e^x \left (-50 x-25 x^2+x^3+\left (-25-26 x+x^2\right ) \log (5)\right )+e^{2 x} \left (-100 x^2+4 x^3+\left (-100 x+4 x^2\right ) \log (5)\right )\right )+e^{4+2 e^x} \left (e^x \left (-2700 x-1350 x^2+54 x^3+\left (-1350-1404 x+54 x^2\right ) \log (5)\right )+e^{2 x} \left (-2700 x^2+108 x^3+\left (-2700 x+108 x^2\right ) \log (5)\right )\right )}{-15625+1875 x-75 x^2+x^3} \, dx =\text {Too large to display} \] Input:
integrate(((((4*x**2-100*x)*ln(5)+4*x**3-100*x**2)*exp(x)**2+((x**2-26*x-2 5)*ln(5)+x**3-25*x**2-50*x)*exp(x))*exp(2+exp(x))**4+(((-36*x**2+900*x)*ln (5)-36*x**3+900*x**2)*exp(x)**2+((-12*x**2+312*x+300)*ln(5)-12*x**3+300*x* *2+600*x)*exp(x))*exp(2+exp(x))**3+(((108*x**2-2700*x)*ln(5)+108*x**3-2700 *x**2)*exp(x)**2+((54*x**2-1404*x-1350)*ln(5)+54*x**3-1350*x**2-2700*x)*ex p(x))*exp(2+exp(x))**2+(((-108*x**2+2700*x)*ln(5)-108*x**3+2700*x**2)*exp( x)**2+((-108*x**2+2808*x+2700)*ln(5)-108*x**3+2700*x**2+5400*x)*exp(x))*ex p(2+exp(x))+((81*x**2-2106*x-2025)*ln(5)+81*x**3-2025*x**2-4050*x)*exp(x)) /(x**3-75*x**2+1875*x-15625),x)
Output:
(81*x**2 + 81*x*log(5))*exp(x)/(x**2 - 50*x + 625) + ((-108*x**8*exp(x) - 108*x**7*exp(x)*log(5) + 16200*x**7*exp(x) - 1012500*x**6*exp(x) + 16200*x **6*exp(x)*log(5) - 1012500*x**5*exp(x)*log(5) + 33750000*x**5*exp(x) - 63 2812500*x**4*exp(x) + 33750000*x**4*exp(x)*log(5) - 632812500*x**3*exp(x)* log(5) + 6328125000*x**3*exp(x) - 26367187500*x**2*exp(x) + 6328125000*x** 2*exp(x)*log(5) - 26367187500*x*exp(x)*log(5))*exp(exp(x) + 2) + (-12*x**8 *exp(x) - 12*x**7*exp(x)*log(5) + 1800*x**7*exp(x) - 112500*x**6*exp(x) + 1800*x**6*exp(x)*log(5) - 112500*x**5*exp(x)*log(5) + 3750000*x**5*exp(x) - 70312500*x**4*exp(x) + 3750000*x**4*exp(x)*log(5) - 70312500*x**3*exp(x) *log(5) + 703125000*x**3*exp(x) - 2929687500*x**2*exp(x) + 703125000*x**2* exp(x)*log(5) - 2929687500*x*exp(x)*log(5))*exp(3*exp(x) + 6) + (x**8*exp( x) - 150*x**7*exp(x) + x**7*exp(x)*log(5) - 150*x**6*exp(x)*log(5) + 9375* x**6*exp(x) - 312500*x**5*exp(x) + 9375*x**5*exp(x)*log(5) - 312500*x**4*e xp(x)*log(5) + 5859375*x**4*exp(x) - 58593750*x**3*exp(x) + 5859375*x**3*e xp(x)*log(5) - 58593750*x**2*exp(x)*log(5) + 244140625*x**2*exp(x) + 24414 0625*x*exp(x)*log(5))*exp(4*exp(x) + 8) + (54*x**8*exp(x) - 8100*x**7*exp( x) + 54*x**7*exp(x)*log(5) - 8100*x**6*exp(x)*log(5) + 506250*x**6*exp(x) - 16875000*x**5*exp(x) + 506250*x**5*exp(x)*log(5) - 16875000*x**4*exp(x)* log(5) + 316406250*x**4*exp(x) - 3164062500*x**3*exp(x) + 316406250*x**3*e xp(x)*log(5) - 3164062500*x**2*exp(x)*log(5) + 13183593750*x**2*exp(x) ...
\[ \int \frac {e^x \left (-4050 x-2025 x^2+81 x^3+\left (-2025-2106 x+81 x^2\right ) \log (5)\right )+e^{2+e^x} \left (e^{2 x} \left (2700 x^2-108 x^3+\left (2700 x-108 x^2\right ) \log (5)\right )+e^x \left (5400 x+2700 x^2-108 x^3+\left (2700+2808 x-108 x^2\right ) \log (5)\right )\right )+e^{6+3 e^x} \left (e^{2 x} \left (900 x^2-36 x^3+\left (900 x-36 x^2\right ) \log (5)\right )+e^x \left (600 x+300 x^2-12 x^3+\left (300+312 x-12 x^2\right ) \log (5)\right )\right )+e^{8+4 e^x} \left (e^x \left (-50 x-25 x^2+x^3+\left (-25-26 x+x^2\right ) \log (5)\right )+e^{2 x} \left (-100 x^2+4 x^3+\left (-100 x+4 x^2\right ) \log (5)\right )\right )+e^{4+2 e^x} \left (e^x \left (-2700 x-1350 x^2+54 x^3+\left (-1350-1404 x+54 x^2\right ) \log (5)\right )+e^{2 x} \left (-2700 x^2+108 x^3+\left (-2700 x+108 x^2\right ) \log (5)\right )\right )}{-15625+1875 x-75 x^2+x^3} \, dx=\int { \frac {81 \, {\left (x^{3} - 25 \, x^{2} + {\left (x^{2} - 26 \, x - 25\right )} \log \left (5\right ) - 50 \, x\right )} e^{x} + {\left (4 \, {\left (x^{3} - 25 \, x^{2} + {\left (x^{2} - 25 \, x\right )} \log \left (5\right )\right )} e^{\left (2 \, x\right )} + {\left (x^{3} - 25 \, x^{2} + {\left (x^{2} - 26 \, x - 25\right )} \log \left (5\right ) - 50 \, x\right )} e^{x}\right )} e^{\left (4 \, e^{x} + 8\right )} - 12 \, {\left (3 \, {\left (x^{3} - 25 \, x^{2} + {\left (x^{2} - 25 \, x\right )} \log \left (5\right )\right )} e^{\left (2 \, x\right )} + {\left (x^{3} - 25 \, x^{2} + {\left (x^{2} - 26 \, x - 25\right )} \log \left (5\right ) - 50 \, x\right )} e^{x}\right )} e^{\left (3 \, e^{x} + 6\right )} + 54 \, {\left (2 \, {\left (x^{3} - 25 \, x^{2} + {\left (x^{2} - 25 \, x\right )} \log \left (5\right )\right )} e^{\left (2 \, x\right )} + {\left (x^{3} - 25 \, x^{2} + {\left (x^{2} - 26 \, x - 25\right )} \log \left (5\right ) - 50 \, x\right )} e^{x}\right )} e^{\left (2 \, e^{x} + 4\right )} - 108 \, {\left ({\left (x^{3} - 25 \, x^{2} + {\left (x^{2} - 25 \, x\right )} \log \left (5\right )\right )} e^{\left (2 \, x\right )} + {\left (x^{3} - 25 \, x^{2} + {\left (x^{2} - 26 \, x - 25\right )} \log \left (5\right ) - 50 \, x\right )} e^{x}\right )} e^{\left (e^{x} + 2\right )}}{x^{3} - 75 \, x^{2} + 1875 \, x - 15625} \,d x } \] Input:
integrate(((((4*x^2-100*x)*log(5)+4*x^3-100*x^2)*exp(x)^2+((x^2-26*x-25)*l og(5)+x^3-25*x^2-50*x)*exp(x))*exp(2+exp(x))^4+(((-36*x^2+900*x)*log(5)-36 *x^3+900*x^2)*exp(x)^2+((-12*x^2+312*x+300)*log(5)-12*x^3+300*x^2+600*x)*e xp(x))*exp(2+exp(x))^3+(((108*x^2-2700*x)*log(5)+108*x^3-2700*x^2)*exp(x)^ 2+((54*x^2-1404*x-1350)*log(5)+54*x^3-1350*x^2-2700*x)*exp(x))*exp(2+exp(x ))^2+(((-108*x^2+2700*x)*log(5)-108*x^3+2700*x^2)*exp(x)^2+((-108*x^2+2808 *x+2700)*log(5)-108*x^3+2700*x^2+5400*x)*exp(x))*exp(2+exp(x))+((81*x^2-21 06*x-2025)*log(5)+81*x^3-2025*x^2-4050*x)*exp(x))/(x^3-75*x^2+1875*x-15625 ),x, algorithm="maxima")
Output:
2025*integrate(e^x/(x^3 - 75*x^2 + 1875*x - 15625), x)*log(5) + 2025*e^25* exp_integral_e(3, -x + 25)*log(5)/(x - 25)^2 + ((x^2*e^8 + x*e^8*log(5))*e ^(x + 4*e^x) - 12*(x^2*e^6 + x*e^6*log(5))*e^(x + 3*e^x) + 54*(x^2*e^4 + x *e^4*log(5))*e^(x + 2*e^x) - 108*(x^2*e^2 + x*e^2*log(5))*e^(x + e^x) + 81 *(x^2 + x*log(5))*e^x)/(x^2 - 50*x + 625)
\[ \int \frac {e^x \left (-4050 x-2025 x^2+81 x^3+\left (-2025-2106 x+81 x^2\right ) \log (5)\right )+e^{2+e^x} \left (e^{2 x} \left (2700 x^2-108 x^3+\left (2700 x-108 x^2\right ) \log (5)\right )+e^x \left (5400 x+2700 x^2-108 x^3+\left (2700+2808 x-108 x^2\right ) \log (5)\right )\right )+e^{6+3 e^x} \left (e^{2 x} \left (900 x^2-36 x^3+\left (900 x-36 x^2\right ) \log (5)\right )+e^x \left (600 x+300 x^2-12 x^3+\left (300+312 x-12 x^2\right ) \log (5)\right )\right )+e^{8+4 e^x} \left (e^x \left (-50 x-25 x^2+x^3+\left (-25-26 x+x^2\right ) \log (5)\right )+e^{2 x} \left (-100 x^2+4 x^3+\left (-100 x+4 x^2\right ) \log (5)\right )\right )+e^{4+2 e^x} \left (e^x \left (-2700 x-1350 x^2+54 x^3+\left (-1350-1404 x+54 x^2\right ) \log (5)\right )+e^{2 x} \left (-2700 x^2+108 x^3+\left (-2700 x+108 x^2\right ) \log (5)\right )\right )}{-15625+1875 x-75 x^2+x^3} \, dx=\int { \frac {81 \, {\left (x^{3} - 25 \, x^{2} + {\left (x^{2} - 26 \, x - 25\right )} \log \left (5\right ) - 50 \, x\right )} e^{x} + {\left (4 \, {\left (x^{3} - 25 \, x^{2} + {\left (x^{2} - 25 \, x\right )} \log \left (5\right )\right )} e^{\left (2 \, x\right )} + {\left (x^{3} - 25 \, x^{2} + {\left (x^{2} - 26 \, x - 25\right )} \log \left (5\right ) - 50 \, x\right )} e^{x}\right )} e^{\left (4 \, e^{x} + 8\right )} - 12 \, {\left (3 \, {\left (x^{3} - 25 \, x^{2} + {\left (x^{2} - 25 \, x\right )} \log \left (5\right )\right )} e^{\left (2 \, x\right )} + {\left (x^{3} - 25 \, x^{2} + {\left (x^{2} - 26 \, x - 25\right )} \log \left (5\right ) - 50 \, x\right )} e^{x}\right )} e^{\left (3 \, e^{x} + 6\right )} + 54 \, {\left (2 \, {\left (x^{3} - 25 \, x^{2} + {\left (x^{2} - 25 \, x\right )} \log \left (5\right )\right )} e^{\left (2 \, x\right )} + {\left (x^{3} - 25 \, x^{2} + {\left (x^{2} - 26 \, x - 25\right )} \log \left (5\right ) - 50 \, x\right )} e^{x}\right )} e^{\left (2 \, e^{x} + 4\right )} - 108 \, {\left ({\left (x^{3} - 25 \, x^{2} + {\left (x^{2} - 25 \, x\right )} \log \left (5\right )\right )} e^{\left (2 \, x\right )} + {\left (x^{3} - 25 \, x^{2} + {\left (x^{2} - 26 \, x - 25\right )} \log \left (5\right ) - 50 \, x\right )} e^{x}\right )} e^{\left (e^{x} + 2\right )}}{x^{3} - 75 \, x^{2} + 1875 \, x - 15625} \,d x } \] Input:
integrate(((((4*x^2-100*x)*log(5)+4*x^3-100*x^2)*exp(x)^2+((x^2-26*x-25)*l og(5)+x^3-25*x^2-50*x)*exp(x))*exp(2+exp(x))^4+(((-36*x^2+900*x)*log(5)-36 *x^3+900*x^2)*exp(x)^2+((-12*x^2+312*x+300)*log(5)-12*x^3+300*x^2+600*x)*e xp(x))*exp(2+exp(x))^3+(((108*x^2-2700*x)*log(5)+108*x^3-2700*x^2)*exp(x)^ 2+((54*x^2-1404*x-1350)*log(5)+54*x^3-1350*x^2-2700*x)*exp(x))*exp(2+exp(x ))^2+(((-108*x^2+2700*x)*log(5)-108*x^3+2700*x^2)*exp(x)^2+((-108*x^2+2808 *x+2700)*log(5)-108*x^3+2700*x^2+5400*x)*exp(x))*exp(2+exp(x))+((81*x^2-21 06*x-2025)*log(5)+81*x^3-2025*x^2-4050*x)*exp(x))/(x^3-75*x^2+1875*x-15625 ),x, algorithm="giac")
Output:
integrate((81*(x^3 - 25*x^2 + (x^2 - 26*x - 25)*log(5) - 50*x)*e^x + (4*(x ^3 - 25*x^2 + (x^2 - 25*x)*log(5))*e^(2*x) + (x^3 - 25*x^2 + (x^2 - 26*x - 25)*log(5) - 50*x)*e^x)*e^(4*e^x + 8) - 12*(3*(x^3 - 25*x^2 + (x^2 - 25*x )*log(5))*e^(2*x) + (x^3 - 25*x^2 + (x^2 - 26*x - 25)*log(5) - 50*x)*e^x)* e^(3*e^x + 6) + 54*(2*(x^3 - 25*x^2 + (x^2 - 25*x)*log(5))*e^(2*x) + (x^3 - 25*x^2 + (x^2 - 26*x - 25)*log(5) - 50*x)*e^x)*e^(2*e^x + 4) - 108*((x^3 - 25*x^2 + (x^2 - 25*x)*log(5))*e^(2*x) + (x^3 - 25*x^2 + (x^2 - 26*x - 2 5)*log(5) - 50*x)*e^x)*e^(e^x + 2))/(x^3 - 75*x^2 + 1875*x - 15625), x)
Time = 4.38 (sec) , antiderivative size = 155, normalized size of antiderivative = 5.34 \[ \int \frac {e^x \left (-4050 x-2025 x^2+81 x^3+\left (-2025-2106 x+81 x^2\right ) \log (5)\right )+e^{2+e^x} \left (e^{2 x} \left (2700 x^2-108 x^3+\left (2700 x-108 x^2\right ) \log (5)\right )+e^x \left (5400 x+2700 x^2-108 x^3+\left (2700+2808 x-108 x^2\right ) \log (5)\right )\right )+e^{6+3 e^x} \left (e^{2 x} \left (900 x^2-36 x^3+\left (900 x-36 x^2\right ) \log (5)\right )+e^x \left (600 x+300 x^2-12 x^3+\left (300+312 x-12 x^2\right ) \log (5)\right )\right )+e^{8+4 e^x} \left (e^x \left (-50 x-25 x^2+x^3+\left (-25-26 x+x^2\right ) \log (5)\right )+e^{2 x} \left (-100 x^2+4 x^3+\left (-100 x+4 x^2\right ) \log (5)\right )\right )+e^{4+2 e^x} \left (e^x \left (-2700 x-1350 x^2+54 x^3+\left (-1350-1404 x+54 x^2\right ) \log (5)\right )+e^{2 x} \left (-2700 x^2+108 x^3+\left (-2700 x+108 x^2\right ) \log (5)\right )\right )}{-15625+1875 x-75 x^2+x^3} \, dx=\frac {{\mathrm {e}}^{4\,{\mathrm {e}}^x+8}\,\left (x^2\,{\mathrm {e}}^x+x\,{\mathrm {e}}^x\,\ln \left (5\right )\right )}{x^2-50\,x+625}-\frac {{\mathrm {e}}^{{\mathrm {e}}^x+2}\,\left (108\,x^2\,{\mathrm {e}}^x+108\,x\,{\mathrm {e}}^x\,\ln \left (5\right )\right )}{x^2-50\,x+625}-\frac {{\mathrm {e}}^{3\,{\mathrm {e}}^x+6}\,\left (12\,x^2\,{\mathrm {e}}^x+12\,x\,{\mathrm {e}}^x\,\ln \left (5\right )\right )}{x^2-50\,x+625}+\frac {{\mathrm {e}}^{2\,{\mathrm {e}}^x+4}\,\left (54\,x^2\,{\mathrm {e}}^x+54\,x\,{\mathrm {e}}^x\,\ln \left (5\right )\right )}{x^2-50\,x+625}+\frac {{\mathrm {e}}^x\,\left (81\,x^2+81\,\ln \left (5\right )\,x\right )}{x^2-50\,x+625} \] Input:
int(-(exp(x)*(4050*x + log(5)*(2106*x - 81*x^2 + 2025) + 2025*x^2 - 81*x^3 ) - exp(exp(x) + 2)*(exp(x)*(5400*x + log(5)*(2808*x - 108*x^2 + 2700) + 2 700*x^2 - 108*x^3) + exp(2*x)*(log(5)*(2700*x - 108*x^2) + 2700*x^2 - 108* x^3)) + exp(4*exp(x) + 8)*(exp(x)*(50*x + log(5)*(26*x - x^2 + 25) + 25*x^ 2 - x^3) + exp(2*x)*(log(5)*(100*x - 4*x^2) + 100*x^2 - 4*x^3)) - exp(3*ex p(x) + 6)*(exp(x)*(600*x + log(5)*(312*x - 12*x^2 + 300) + 300*x^2 - 12*x^ 3) + exp(2*x)*(log(5)*(900*x - 36*x^2) + 900*x^2 - 36*x^3)) + exp(2*exp(x) + 4)*(exp(x)*(2700*x + log(5)*(1404*x - 54*x^2 + 1350) + 1350*x^2 - 54*x^ 3) + exp(2*x)*(log(5)*(2700*x - 108*x^2) + 2700*x^2 - 108*x^3)))/(1875*x - 75*x^2 + x^3 - 15625),x)
Output:
(exp(4*exp(x) + 8)*(x^2*exp(x) + x*exp(x)*log(5)))/(x^2 - 50*x + 625) - (e xp(exp(x) + 2)*(108*x^2*exp(x) + 108*x*exp(x)*log(5)))/(x^2 - 50*x + 625) - (exp(3*exp(x) + 6)*(12*x^2*exp(x) + 12*x*exp(x)*log(5)))/(x^2 - 50*x + 6 25) + (exp(2*exp(x) + 4)*(54*x^2*exp(x) + 54*x*exp(x)*log(5)))/(x^2 - 50*x + 625) + (exp(x)*(81*x*log(5) + 81*x^2))/(x^2 - 50*x + 625)
Time = 0.18 (sec) , antiderivative size = 125, normalized size of antiderivative = 4.31 \[ \int \frac {e^x \left (-4050 x-2025 x^2+81 x^3+\left (-2025-2106 x+81 x^2\right ) \log (5)\right )+e^{2+e^x} \left (e^{2 x} \left (2700 x^2-108 x^3+\left (2700 x-108 x^2\right ) \log (5)\right )+e^x \left (5400 x+2700 x^2-108 x^3+\left (2700+2808 x-108 x^2\right ) \log (5)\right )\right )+e^{6+3 e^x} \left (e^{2 x} \left (900 x^2-36 x^3+\left (900 x-36 x^2\right ) \log (5)\right )+e^x \left (600 x+300 x^2-12 x^3+\left (300+312 x-12 x^2\right ) \log (5)\right )\right )+e^{8+4 e^x} \left (e^x \left (-50 x-25 x^2+x^3+\left (-25-26 x+x^2\right ) \log (5)\right )+e^{2 x} \left (-100 x^2+4 x^3+\left (-100 x+4 x^2\right ) \log (5)\right )\right )+e^{4+2 e^x} \left (e^x \left (-2700 x-1350 x^2+54 x^3+\left (-1350-1404 x+54 x^2\right ) \log (5)\right )+e^{2 x} \left (-2700 x^2+108 x^3+\left (-2700 x+108 x^2\right ) \log (5)\right )\right )}{-15625+1875 x-75 x^2+x^3} \, dx=\frac {e^{x} x \left (e^{4 e^{x}} \mathrm {log}\left (5\right ) e^{8}+e^{4 e^{x}} e^{8} x -12 e^{3 e^{x}} \mathrm {log}\left (5\right ) e^{6}-12 e^{3 e^{x}} e^{6} x +54 e^{2 e^{x}} \mathrm {log}\left (5\right ) e^{4}+54 e^{2 e^{x}} e^{4} x -108 e^{e^{x}} \mathrm {log}\left (5\right ) e^{2}-108 e^{e^{x}} e^{2} x +81 \,\mathrm {log}\left (5\right )+81 x \right )}{x^{2}-50 x +625} \] Input:
int(((((4*x^2-100*x)*log(5)+4*x^3-100*x^2)*exp(x)^2+((x^2-26*x-25)*log(5)+ x^3-25*x^2-50*x)*exp(x))*exp(2+exp(x))^4+(((-36*x^2+900*x)*log(5)-36*x^3+9 00*x^2)*exp(x)^2+((-12*x^2+312*x+300)*log(5)-12*x^3+300*x^2+600*x)*exp(x)) *exp(2+exp(x))^3+(((108*x^2-2700*x)*log(5)+108*x^3-2700*x^2)*exp(x)^2+((54 *x^2-1404*x-1350)*log(5)+54*x^3-1350*x^2-2700*x)*exp(x))*exp(2+exp(x))^2+( ((-108*x^2+2700*x)*log(5)-108*x^3+2700*x^2)*exp(x)^2+((-108*x^2+2808*x+270 0)*log(5)-108*x^3+2700*x^2+5400*x)*exp(x))*exp(2+exp(x))+((81*x^2-2106*x-2 025)*log(5)+81*x^3-2025*x^2-4050*x)*exp(x))/(x^3-75*x^2+1875*x-15625),x)
Output:
(e**x*x*(e**(4*e**x)*log(5)*e**8 + e**(4*e**x)*e**8*x - 12*e**(3*e**x)*log (5)*e**6 - 12*e**(3*e**x)*e**6*x + 54*e**(2*e**x)*log(5)*e**4 + 54*e**(2*e **x)*e**4*x - 108*e**(e**x)*log(5)*e**2 - 108*e**(e**x)*e**2*x + 81*log(5) + 81*x))/(x**2 - 50*x + 625)