Integrand size = 197, antiderivative size = 26 \[ \int \frac {e^{\frac {16 x-81 x^2-24 e^{\frac {1}{5} (5 x+\log (5))} x^2+9 e^{\frac {2}{5} (5 x+\log (5))} x^3}{16-24 e^{\frac {1}{5} (5 x+\log (5))} x+9 e^{\frac {2}{5} (5 x+\log (5))} x^2}} \left (-64+648 x-108 e^{\frac {2}{5} (5 x+\log (5))} x^2+27 e^{\frac {3}{5} (5 x+\log (5))} x^3+e^{\frac {1}{5} (5 x+\log (5))} \left (144 x+486 x^3\right )\right )}{-64+144 e^{\frac {1}{5} (5 x+\log (5))} x-108 e^{\frac {2}{5} (5 x+\log (5))} x^2+27 e^{\frac {3}{5} (5 x+\log (5))} x^3} \, dx=e^{-\frac {9}{\left (-\sqrt [5]{5} e^x+\frac {4}{3 x}\right )^2}+x} \] Output:
exp(x-9/(4/3/x-exp(1/5*ln(5)+x))^2)
Time = 0.21 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.92 \[ \int \frac {e^{\frac {16 x-81 x^2-24 e^{\frac {1}{5} (5 x+\log (5))} x^2+9 e^{\frac {2}{5} (5 x+\log (5))} x^3}{16-24 e^{\frac {1}{5} (5 x+\log (5))} x+9 e^{\frac {2}{5} (5 x+\log (5))} x^2}} \left (-64+648 x-108 e^{\frac {2}{5} (5 x+\log (5))} x^2+27 e^{\frac {3}{5} (5 x+\log (5))} x^3+e^{\frac {1}{5} (5 x+\log (5))} \left (144 x+486 x^3\right )\right )}{-64+144 e^{\frac {1}{5} (5 x+\log (5))} x-108 e^{\frac {2}{5} (5 x+\log (5))} x^2+27 e^{\frac {3}{5} (5 x+\log (5))} x^3} \, dx=e^{x-\frac {81 x^2}{\left (-4+3 \sqrt [5]{5} e^x x\right )^2}} \] Input:
Integrate[(E^((16*x - 81*x^2 - 24*E^((5*x + Log[5])/5)*x^2 + 9*E^((2*(5*x + Log[5]))/5)*x^3)/(16 - 24*E^((5*x + Log[5])/5)*x + 9*E^((2*(5*x + Log[5] ))/5)*x^2))*(-64 + 648*x - 108*E^((2*(5*x + Log[5]))/5)*x^2 + 27*E^((3*(5* x + Log[5]))/5)*x^3 + E^((5*x + Log[5])/5)*(144*x + 486*x^3)))/(-64 + 144* E^((5*x + Log[5])/5)*x - 108*E^((2*(5*x + Log[5]))/5)*x^2 + 27*E^((3*(5*x + Log[5]))/5)*x^3),x]
Output:
E^(x - (81*x^2)/(-4 + 3*5^(1/5)*E^x*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.
| \(\displaystyle \int \frac {\left (27 x^3 e^{\frac {3}{5} (5 x+\log (5))}+\left (486 x^3+144 x\right ) e^{\frac {1}{5} (5 x+\log (5))}-108 x^2 e^{\frac {2}{5} (5 x+\log (5))}+648 x-64\right ) \exp \left (\frac {9 x^3 e^{\frac {2}{5} (5 x+\log (5))}-81 x^2-24 x^2 e^{\frac {1}{5} (5 x+\log (5))}+16 x}{9 x^2 e^{\frac {2}{5} (5 x+\log (5))}-24 x e^{\frac {1}{5} (5 x+\log (5))}+16}\right )}{27 x^3 e^{\frac {3}{5} (5 x+\log (5))}-108 x^2 e^{\frac {2}{5} (5 x+\log (5))}+144 x e^{\frac {1}{5} (5 x+\log (5))}-64} \, dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {\left (-27 x^3 e^{\frac {3}{5} (5 x+\log (5))}-\left (486 x^3+144 x\right ) e^{\frac {1}{5} (5 x+\log (5))}+108 x^2 e^{\frac {2}{5} (5 x+\log (5))}-648 x+64\right ) \exp \left (\frac {9 x^3 e^{\frac {2}{5} (5 x+\log (5))}-81 x^2-24 x^2 e^{\frac {1}{5} (5 x+\log (5))}+16 x}{\left (3 \sqrt [5]{5} e^x x-4\right )^2}\right )}{\left (4-3 \sqrt [5]{5} e^x x\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {27\ 5^{3/5} x^3 \exp \left (\frac {9 x^3 e^{\frac {2}{5} (5 x+\log (5))}-81 x^2-24 x^2 e^{\frac {1}{5} (5 x+\log (5))}+16 x}{\left (3 \sqrt [5]{5} e^x x-4\right )^2}+3 x\right )}{\left (3 \sqrt [5]{5} e^x x-4\right )^3}-\frac {108\ 5^{2/5} x^2 \exp \left (\frac {9 x^3 e^{\frac {2}{5} (5 x+\log (5))}-81 x^2-24 x^2 e^{\frac {1}{5} (5 x+\log (5))}+16 x}{\left (3 \sqrt [5]{5} e^x x-4\right )^2}+2 x\right )}{\left (3 \sqrt [5]{5} e^x x-4\right )^3}+\frac {18 \sqrt [5]{5} \left (27 x^2+8\right ) x \exp \left (\frac {9 x^3 e^{\frac {2}{5} (5 x+\log (5))}-81 x^2-24 x^2 e^{\frac {1}{5} (5 x+\log (5))}+16 x}{\left (3 \sqrt [5]{5} e^x x-4\right )^2}+x\right )}{\left (3 \sqrt [5]{5} e^x x-4\right )^3}+\frac {8 (81 x-8) \exp \left (\frac {9 x^3 e^{\frac {2}{5} (5 x+\log (5))}-81 x^2-24 x^2 e^{\frac {1}{5} (5 x+\log (5))}+16 x}{\left (3 \sqrt [5]{5} e^x x-4\right )^2}\right )}{\left (3 \sqrt [5]{5} e^x x-4\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (-27 \sqrt [5]{5} e^x \left (5^{2/5} e^{2 x}+18\right ) x^3+108\ 5^{2/5} e^{2 x} x^2-72 \left (2 \sqrt [5]{5} e^x+9\right ) x+64\right ) \exp \left (\frac {x \left (9\ 5^{2/5} e^{2 x} x^2-3 \left (8 \sqrt [5]{5} e^x+27\right ) x+16\right )}{\left (4-3 \sqrt [5]{5} e^x x\right )^2}\right )}{\left (4-3 \sqrt [5]{5} e^x x\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {162 x^2 \exp \left (\frac {x \left (9\ 5^{2/5} e^{2 x} x^2-3 \left (8 \sqrt [5]{5} e^x+27\right ) x+16\right )}{\left (4-3 \sqrt [5]{5} e^x x\right )^2}\right )}{\left (3 \sqrt [5]{5} e^x x-4\right )^2}+\frac {648 (x+1) x \exp \left (\frac {x \left (9\ 5^{2/5} e^{2 x} x^2-3 \left (8 \sqrt [5]{5} e^x+27\right ) x+16\right )}{\left (4-3 \sqrt [5]{5} e^x x\right )^2}\right )}{\left (3 \sqrt [5]{5} e^x x-4\right )^3}+\exp \left (\frac {x \left (9\ 5^{2/5} e^{2 x} x^2-3 \left (8 \sqrt [5]{5} e^x+27\right ) x+16\right )}{\left (4-3 \sqrt [5]{5} e^x x\right )^2}\right )\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle \int \exp \left (\frac {x \left (9\ 5^{2/5} e^{2 x} x^2-3 \left (27+8 \sqrt [5]{5} e^x\right ) x+16\right )}{\left (4-3 \sqrt [5]{5} e^x x\right )^2}\right )dx+648 \int \frac {\exp \left (\frac {x \left (9\ 5^{2/5} e^{2 x} x^2-3 \left (27+8 \sqrt [5]{5} e^x\right ) x+16\right )}{\left (4-3 \sqrt [5]{5} e^x x\right )^2}\right ) x}{\left (3 \sqrt [5]{5} e^x x-4\right )^3}dx+648 \int \frac {\exp \left (\frac {x \left (9\ 5^{2/5} e^{2 x} x^2-3 \left (27+8 \sqrt [5]{5} e^x\right ) x+16\right )}{\left (4-3 \sqrt [5]{5} e^x x\right )^2}\right ) x^2}{\left (3 \sqrt [5]{5} e^x x-4\right )^3}dx+162 \int \frac {\exp \left (\frac {x \left (9\ 5^{2/5} e^{2 x} x^2-3 \left (27+8 \sqrt [5]{5} e^x\right ) x+16\right )}{\left (4-3 \sqrt [5]{5} e^x x\right )^2}\right ) x^2}{\left (3 \sqrt [5]{5} e^x x-4\right )^2}dx\) |
Input:
Int[(E^((16*x - 81*x^2 - 24*E^((5*x + Log[5])/5)*x^2 + 9*E^((2*(5*x + Log[ 5]))/5)*x^3)/(16 - 24*E^((5*x + Log[5])/5)*x + 9*E^((2*(5*x + Log[5]))/5)* x^2))*(-64 + 648*x - 108*E^((2*(5*x + Log[5]))/5)*x^2 + 27*E^((3*(5*x + Lo g[5]))/5)*x^3 + E^((5*x + Log[5])/5)*(144*x + 486*x^3)))/(-64 + 144*E^((5* x + Log[5])/5)*x - 108*E^((2*(5*x + Log[5]))/5)*x^2 + 27*E^((3*(5*x + Log[ 5]))/5)*x^3),x]
Output:
$Aborted
Leaf count of result is larger than twice the leaf count of optimal. \(65\) vs. \(2(22)=44\).
Time = 3.50 (sec) , antiderivative size = 66, normalized size of antiderivative = 2.54
| method | result | size |
| parallelrisch | \({\mathrm e}^{\frac {9 x^{3} {\mathrm e}^{\frac {2 \ln \left (5\right )}{5}+2 x}-24 x^{2} {\mathrm e}^{\frac {\ln \left (5\right )}{5}+x}-81 x^{2}+16 x}{9 x^{2} {\mathrm e}^{\frac {2 \ln \left (5\right )}{5}+2 x}-24 x \,{\mathrm e}^{\frac {\ln \left (5\right )}{5}+x}+16}}\) | \(66\) |
Input:
int((27*x^3*exp(1/5*ln(5)+x)^3-108*x^2*exp(1/5*ln(5)+x)^2+(486*x^3+144*x)* exp(1/5*ln(5)+x)+648*x-64)*exp((9*x^3*exp(1/5*ln(5)+x)^2-24*x^2*exp(1/5*ln (5)+x)-81*x^2+16*x)/(9*x^2*exp(1/5*ln(5)+x)^2-24*x*exp(1/5*ln(5)+x)+16))/( 27*x^3*exp(1/5*ln(5)+x)^3-108*x^2*exp(1/5*ln(5)+x)^2+144*x*exp(1/5*ln(5)+x )-64),x,method=_RETURNVERBOSE)
Output:
exp((9*x^3*exp(1/5*ln(5)+x)^2-24*x^2*exp(1/5*ln(5)+x)-81*x^2+16*x)/(9*x^2* exp(1/5*ln(5)+x)^2-24*x*exp(1/5*ln(5)+x)+16))
Leaf count of result is larger than twice the leaf count of optimal. 65 vs. \(2 (22) = 44\).
Time = 0.09 (sec) , antiderivative size = 65, normalized size of antiderivative = 2.50 \[ \int \frac {e^{\frac {16 x-81 x^2-24 e^{\frac {1}{5} (5 x+\log (5))} x^2+9 e^{\frac {2}{5} (5 x+\log (5))} x^3}{16-24 e^{\frac {1}{5} (5 x+\log (5))} x+9 e^{\frac {2}{5} (5 x+\log (5))} x^2}} \left (-64+648 x-108 e^{\frac {2}{5} (5 x+\log (5))} x^2+27 e^{\frac {3}{5} (5 x+\log (5))} x^3+e^{\frac {1}{5} (5 x+\log (5))} \left (144 x+486 x^3\right )\right )}{-64+144 e^{\frac {1}{5} (5 x+\log (5))} x-108 e^{\frac {2}{5} (5 x+\log (5))} x^2+27 e^{\frac {3}{5} (5 x+\log (5))} x^3} \, dx=e^{\left (\frac {9 \, x^{3} e^{\left (2 \, x + \frac {2}{5} \, \log \left (5\right )\right )} - 24 \, x^{2} e^{\left (x + \frac {1}{5} \, \log \left (5\right )\right )} - 81 \, x^{2} + 16 \, x}{9 \, x^{2} e^{\left (2 \, x + \frac {2}{5} \, \log \left (5\right )\right )} - 24 \, x e^{\left (x + \frac {1}{5} \, \log \left (5\right )\right )} + 16}\right )} \] Input:
integrate((27*x^3*exp(1/5*log(5)+x)^3-108*x^2*exp(1/5*log(5)+x)^2+(486*x^3 +144*x)*exp(1/5*log(5)+x)+648*x-64)*exp((9*x^3*exp(1/5*log(5)+x)^2-24*x^2* exp(1/5*log(5)+x)-81*x^2+16*x)/(9*x^2*exp(1/5*log(5)+x)^2-24*x*exp(1/5*log (5)+x)+16))/(27*x^3*exp(1/5*log(5)+x)^3-108*x^2*exp(1/5*log(5)+x)^2+144*x* exp(1/5*log(5)+x)-64),x, algorithm="fricas")
Output:
e^((9*x^3*e^(2*x + 2/5*log(5)) - 24*x^2*e^(x + 1/5*log(5)) - 81*x^2 + 16*x )/(9*x^2*e^(2*x + 2/5*log(5)) - 24*x*e^(x + 1/5*log(5)) + 16))
Leaf count of result is larger than twice the leaf count of optimal. 66 vs. \(2 (19) = 38\).
Time = 2.21 (sec) , antiderivative size = 66, normalized size of antiderivative = 2.54 \[ \int \frac {e^{\frac {16 x-81 x^2-24 e^{\frac {1}{5} (5 x+\log (5))} x^2+9 e^{\frac {2}{5} (5 x+\log (5))} x^3}{16-24 e^{\frac {1}{5} (5 x+\log (5))} x+9 e^{\frac {2}{5} (5 x+\log (5))} x^2}} \left (-64+648 x-108 e^{\frac {2}{5} (5 x+\log (5))} x^2+27 e^{\frac {3}{5} (5 x+\log (5))} x^3+e^{\frac {1}{5} (5 x+\log (5))} \left (144 x+486 x^3\right )\right )}{-64+144 e^{\frac {1}{5} (5 x+\log (5))} x-108 e^{\frac {2}{5} (5 x+\log (5))} x^2+27 e^{\frac {3}{5} (5 x+\log (5))} x^3} \, dx=e^{\frac {9 \cdot 5^{\frac {2}{5}} x^{3} e^{2 x} - 24 \cdot \sqrt [5]{5} x^{2} e^{x} - 81 x^{2} + 16 x}{9 \cdot 5^{\frac {2}{5}} x^{2} e^{2 x} - 24 \cdot \sqrt [5]{5} x e^{x} + 16}} \] Input:
integrate((27*x**3*exp(1/5*ln(5)+x)**3-108*x**2*exp(1/5*ln(5)+x)**2+(486*x **3+144*x)*exp(1/5*ln(5)+x)+648*x-64)*exp((9*x**3*exp(1/5*ln(5)+x)**2-24*x **2*exp(1/5*ln(5)+x)-81*x**2+16*x)/(9*x**2*exp(1/5*ln(5)+x)**2-24*x*exp(1/ 5*ln(5)+x)+16))/(27*x**3*exp(1/5*ln(5)+x)**3-108*x**2*exp(1/5*ln(5)+x)**2+ 144*x*exp(1/5*ln(5)+x)-64),x)
Output:
exp((9*5**(2/5)*x**3*exp(2*x) - 24*5**(1/5)*x**2*exp(x) - 81*x**2 + 16*x)/ (9*5**(2/5)*x**2*exp(2*x) - 24*5**(1/5)*x*exp(x) + 16))
Exception generated. \[ \int \frac {e^{\frac {16 x-81 x^2-24 e^{\frac {1}{5} (5 x+\log (5))} x^2+9 e^{\frac {2}{5} (5 x+\log (5))} x^3}{16-24 e^{\frac {1}{5} (5 x+\log (5))} x+9 e^{\frac {2}{5} (5 x+\log (5))} x^2}} \left (-64+648 x-108 e^{\frac {2}{5} (5 x+\log (5))} x^2+27 e^{\frac {3}{5} (5 x+\log (5))} x^3+e^{\frac {1}{5} (5 x+\log (5))} \left (144 x+486 x^3\right )\right )}{-64+144 e^{\frac {1}{5} (5 x+\log (5))} x-108 e^{\frac {2}{5} (5 x+\log (5))} x^2+27 e^{\frac {3}{5} (5 x+\log (5))} x^3} \, dx=\text {Exception raised: RuntimeError} \] Input:
integrate((27*x^3*exp(1/5*log(5)+x)^3-108*x^2*exp(1/5*log(5)+x)^2+(486*x^3 +144*x)*exp(1/5*log(5)+x)+648*x-64)*exp((9*x^3*exp(1/5*log(5)+x)^2-24*x^2* exp(1/5*log(5)+x)-81*x^2+16*x)/(9*x^2*exp(1/5*log(5)+x)^2-24*x*exp(1/5*log (5)+x)+16))/(27*x^3*exp(1/5*log(5)+x)^3-108*x^2*exp(1/5*log(5)+x)^2+144*x* exp(1/5*log(5)+x)-64),x, algorithm="maxima")
Output:
Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is un defined.
Exception generated. \[ \int \frac {e^{\frac {16 x-81 x^2-24 e^{\frac {1}{5} (5 x+\log (5))} x^2+9 e^{\frac {2}{5} (5 x+\log (5))} x^3}{16-24 e^{\frac {1}{5} (5 x+\log (5))} x+9 e^{\frac {2}{5} (5 x+\log (5))} x^2}} \left (-64+648 x-108 e^{\frac {2}{5} (5 x+\log (5))} x^2+27 e^{\frac {3}{5} (5 x+\log (5))} x^3+e^{\frac {1}{5} (5 x+\log (5))} \left (144 x+486 x^3\right )\right )}{-64+144 e^{\frac {1}{5} (5 x+\log (5))} x-108 e^{\frac {2}{5} (5 x+\log (5))} x^2+27 e^{\frac {3}{5} (5 x+\log (5))} x^3} \, dx=\text {Exception raised: TypeError} \] Input:
integrate((27*x^3*exp(1/5*log(5)+x)^3-108*x^2*exp(1/5*log(5)+x)^2+(486*x^3 +144*x)*exp(1/5*log(5)+x)+648*x-64)*exp((9*x^3*exp(1/5*log(5)+x)^2-24*x^2* exp(1/5*log(5)+x)-81*x^2+16*x)/(9*x^2*exp(1/5*log(5)+x)^2-24*x*exp(1/5*log (5)+x)+16))/(27*x^3*exp(1/5*log(5)+x)^3-108*x^2*exp(1/5*log(5)+x)^2+144*x* exp(1/5*log(5)+x)-64),x, algorithm="giac")
Output:
Exception raised: TypeError >> an error occurred running a Giac command:IN PUT:sage2:=int(sage0,sageVARx):;OUTPUT:Unable to divide, perhaps due to ro unding error%%%{-51257812500000000,[2,12,0,1,0]%%%}+%%%{123018750000000000 ,[2,11,1,
Time = 4.36 (sec) , antiderivative size = 131, normalized size of antiderivative = 5.04 \[ \int \frac {e^{\frac {16 x-81 x^2-24 e^{\frac {1}{5} (5 x+\log (5))} x^2+9 e^{\frac {2}{5} (5 x+\log (5))} x^3}{16-24 e^{\frac {1}{5} (5 x+\log (5))} x+9 e^{\frac {2}{5} (5 x+\log (5))} x^2}} \left (-64+648 x-108 e^{\frac {2}{5} (5 x+\log (5))} x^2+27 e^{\frac {3}{5} (5 x+\log (5))} x^3+e^{\frac {1}{5} (5 x+\log (5))} \left (144 x+486 x^3\right )\right )}{-64+144 e^{\frac {1}{5} (5 x+\log (5))} x-108 e^{\frac {2}{5} (5 x+\log (5))} x^2+27 e^{\frac {3}{5} (5 x+\log (5))} x^3} \, dx={\mathrm {e}}^{-\frac {81\,x^2}{9\,5^{2/5}\,x^2\,{\mathrm {e}}^{2\,x}-24\,5^{1/5}\,x\,{\mathrm {e}}^x+16}}\,{\mathrm {e}}^{-\frac {24\,5^{1/5}\,x^2\,{\mathrm {e}}^x}{9\,5^{2/5}\,x^2\,{\mathrm {e}}^{2\,x}-24\,5^{1/5}\,x\,{\mathrm {e}}^x+16}}\,{\mathrm {e}}^{\frac {9\,5^{2/5}\,x^3\,{\mathrm {e}}^{2\,x}}{9\,5^{2/5}\,x^2\,{\mathrm {e}}^{2\,x}-24\,5^{1/5}\,x\,{\mathrm {e}}^x+16}}\,{\mathrm {e}}^{\frac {16\,x}{9\,5^{2/5}\,x^2\,{\mathrm {e}}^{2\,x}-24\,5^{1/5}\,x\,{\mathrm {e}}^x+16}} \] Input:
int(-(exp((16*x - 24*x^2*exp(x + log(5)/5) + 9*x^3*exp(2*x + (2*log(5))/5) - 81*x^2)/(9*x^2*exp(2*x + (2*log(5))/5) - 24*x*exp(x + log(5)/5) + 16))* (648*x - 108*x^2*exp(2*x + (2*log(5))/5) + 27*x^3*exp(3*x + (3*log(5))/5) + exp(x + log(5)/5)*(144*x + 486*x^3) - 64))/(108*x^2*exp(2*x + (2*log(5)) /5) - 27*x^3*exp(3*x + (3*log(5))/5) - 144*x*exp(x + log(5)/5) + 64),x)
Output:
exp(-(81*x^2)/(9*5^(2/5)*x^2*exp(2*x) - 24*5^(1/5)*x*exp(x) + 16))*exp(-(2 4*5^(1/5)*x^2*exp(x))/(9*5^(2/5)*x^2*exp(2*x) - 24*5^(1/5)*x*exp(x) + 16)) *exp((9*5^(2/5)*x^3*exp(2*x))/(9*5^(2/5)*x^2*exp(2*x) - 24*5^(1/5)*x*exp(x ) + 16))*exp((16*x)/(9*5^(2/5)*x^2*exp(2*x) - 24*5^(1/5)*x*exp(x) + 16))
Time = 0.19 (sec) , antiderivative size = 39, normalized size of antiderivative = 1.50 \[ \int \frac {e^{\frac {16 x-81 x^2-24 e^{\frac {1}{5} (5 x+\log (5))} x^2+9 e^{\frac {2}{5} (5 x+\log (5))} x^3}{16-24 e^{\frac {1}{5} (5 x+\log (5))} x+9 e^{\frac {2}{5} (5 x+\log (5))} x^2}} \left (-64+648 x-108 e^{\frac {2}{5} (5 x+\log (5))} x^2+27 e^{\frac {3}{5} (5 x+\log (5))} x^3+e^{\frac {1}{5} (5 x+\log (5))} \left (144 x+486 x^3\right )\right )}{-64+144 e^{\frac {1}{5} (5 x+\log (5))} x-108 e^{\frac {2}{5} (5 x+\log (5))} x^2+27 e^{\frac {3}{5} (5 x+\log (5))} x^3} \, dx=\frac {e^{x}}{e^{\frac {81 x^{2}}{9 e^{2 x} 5^{\frac {2}{5}} x^{2}-24 e^{x} 5^{\frac {1}{5}} x +16}}} \] Input:
int((27*x^3*exp(1/5*log(5)+x)^3-108*x^2*exp(1/5*log(5)+x)^2+(486*x^3+144*x )*exp(1/5*log(5)+x)+648*x-64)*exp((9*x^3*exp(1/5*log(5)+x)^2-24*x^2*exp(1/ 5*log(5)+x)-81*x^2+16*x)/(9*x^2*exp(1/5*log(5)+x)^2-24*x*exp(1/5*log(5)+x) +16))/(27*x^3*exp(1/5*log(5)+x)^3-108*x^2*exp(1/5*log(5)+x)^2+144*x*exp(1/ 5*log(5)+x)-64),x)
Output:
e**x/e**((81*x**2)/(9*e**(2*x)*5**(2/5)*x**2 - 24*e**x*5**(1/5)*x + 16))