Integrand size = 51, antiderivative size = 21 \[ \int \frac {e^{16/625}+e^{\frac {2 \left (-3-x+e^{16/625} (9+x)\right )}{e^{16/625}}} \left (-2 x+e^{16/625} (1+2 x)\right )}{e^{16/625}} \, dx=x+e^{18+2 x-\frac {2 (3+x)}{e^{16/625}}} x \] Output:
x+exp(9+x-(3+x)/exp(16/625))^2*x
Time = 0.46 (sec) , antiderivative size = 21, normalized size of antiderivative = 1.00 \[ \int \frac {e^{16/625}+e^{\frac {2 \left (-3-x+e^{16/625} (9+x)\right )}{e^{16/625}}} \left (-2 x+e^{16/625} (1+2 x)\right )}{e^{16/625}} \, dx=x+e^{2 \left (9+x-\frac {3+x}{e^{16/625}}\right )} x \] Input:
Integrate[(E^(16/625) + E^((2*(-3 - x + E^(16/625)*(9 + x)))/E^(16/625))*( -2*x + E^(16/625)*(1 + 2*x)))/E^(16/625),x]
Output:
x + E^(2*(9 + x - (3 + x)/E^(16/625)))*x
Leaf count is larger than twice the leaf count of optimal. \(192\) vs. \(2(21)=42\).
Time = 0.83 (sec) , antiderivative size = 192, normalized size of antiderivative = 9.14, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.039, Rules used = {27, 2009}
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.
| \(\displaystyle \int \frac {e^{\frac {2 \left (-x+e^{16/625} (x+9)-3\right )}{e^{16/625}}} \left (e^{16/625} (2 x+1)-2 x\right )+e^{16/625}}{e^{16/625}} \, dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {\int \left (e^{16/625}-e^{-\frac {2 \left (x-e^{16/625} (x+9)+3\right )}{e^{16/625}}} \left (2 x-e^{16/625} (2 x+1)\right )\right )dx}{e^{16/625}}\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle \frac {-\frac {x \exp \left (2 \left (\left (1-\frac {1}{e^{16/625}}\right ) x+3 \left (3-\frac {1}{e^{16/625}}\right )\right )\right )}{1-\frac {1}{e^{16/625}}}+\frac {\exp \left (2 \left (\left (1-\frac {1}{e^{16/625}}\right ) x+3 \left (3-\frac {1}{e^{16/625}}\right )\right )+\frac {32}{625}\right )}{2 \left (1-e^{16/625}\right )^2}+e^{16/625} x-\frac {e^{2 \left (1-\frac {1}{e^{16/625}}\right ) x+\frac {2}{625} \left (5633-\frac {1875}{e^{16/625}}\right )}}{2 \left (1-\frac {1}{e^{16/625}}\right )^2}+\frac {e^{2 \left (1-\frac {1}{e^{16/625}}\right ) x+\frac {2}{625} \left (5633-\frac {1875}{e^{16/625}}\right )} (2 x+1)}{2 \left (1-\frac {1}{e^{16/625}}\right )}}{e^{16/625}}\) |
Input:
Int[(E^(16/625) + E^((2*(-3 - x + E^(16/625)*(9 + x)))/E^(16/625))*(-2*x + E^(16/625)*(1 + 2*x)))/E^(16/625),x]
Output:
(-1/2*E^((2*(5633 - 1875/E^(16/625)))/625 + 2*(1 - E^(-16/625))*x)/(1 - E^ (-16/625))^2 + E^(32/625 + 2*(3*(3 - E^(-16/625)) + (1 - E^(-16/625))*x))/ (2*(1 - E^(16/625))^2) + E^(16/625)*x - (E^(2*(3*(3 - E^(-16/625)) + (1 - E^(-16/625))*x))*x)/(1 - E^(-16/625)) + (E^((2*(5633 - 1875/E^(16/625)))/6 25 + 2*(1 - E^(-16/625))*x)*(1 + 2*x))/(2*(1 - E^(-16/625))))/E^(16/625)
Int[(a_)*(Fx_), x_Symbol] :> Simp[a Int[Fx, x], x] /; FreeQ[a, x] && !Ma tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
Time = 0.31 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.10
| method | result | size |
| risch | \(x +x \,{\mathrm e}^{2 \left ({\mathrm e}^{\frac {16}{625}} x +9 \,{\mathrm e}^{\frac {16}{625}}-x -3\right ) {\mathrm e}^{-\frac {16}{625}}}\) | \(23\) |
| norman | \(x +x \,{\mathrm e}^{2 \left (\left (x +9\right ) {\mathrm e}^{\frac {16}{625}}-3-x \right ) {\mathrm e}^{-\frac {16}{625}}}\) | \(24\) |
| parallelrisch | \({\mathrm e}^{-\frac {16}{625}} \left ({\mathrm e}^{\frac {16}{625}} x \,{\mathrm e}^{2 \left (\left (x +9\right ) {\mathrm e}^{\frac {16}{625}}-3-x \right ) {\mathrm e}^{-\frac {16}{625}}}+{\mathrm e}^{\frac {16}{625}} x \right )\) | \(34\) |
| parts | \(x +\frac {\frac {{\mathrm e}^{2 \left ({\mathrm e}^{\frac {16}{625}}-1\right ) {\mathrm e}^{-\frac {16}{625}} x +2 \left (9 \,{\mathrm e}^{\frac {16}{625}}-3\right ) {\mathrm e}^{-\frac {16}{625}}} {\mathrm e}^{\frac {16}{625}}}{2}-\frac {3 \,{\mathrm e}^{2 \left ({\mathrm e}^{\frac {16}{625}}-1\right ) {\mathrm e}^{-\frac {16}{625}} x +2 \left (9 \,{\mathrm e}^{\frac {16}{625}}-3\right ) {\mathrm e}^{-\frac {16}{625}}}}{{\mathrm e}^{\frac {16}{625}}-1}+\frac {12 \,{\mathrm e}^{2 \left ({\mathrm e}^{\frac {16}{625}}-1\right ) {\mathrm e}^{-\frac {16}{625}} x +2 \left (9 \,{\mathrm e}^{\frac {16}{625}}-3\right ) {\mathrm e}^{-\frac {16}{625}}} {\mathrm e}^{\frac {16}{625}}}{{\mathrm e}^{\frac {16}{625}}-1}-\frac {9 \,{\mathrm e}^{2 \left ({\mathrm e}^{\frac {16}{625}}-1\right ) {\mathrm e}^{-\frac {16}{625}} x +2 \left (9 \,{\mathrm e}^{\frac {16}{625}}-3\right ) {\mathrm e}^{-\frac {16}{625}}} {\mathrm e}^{\frac {32}{625}}}{{\mathrm e}^{\frac {16}{625}}-1}-\frac {2 \,{\mathrm e}^{\frac {16}{625}} \left (\frac {{\mathrm e}^{2 \left ({\mathrm e}^{\frac {16}{625}}-1\right ) {\mathrm e}^{-\frac {16}{625}} x +2 \left (9 \,{\mathrm e}^{\frac {16}{625}}-3\right ) {\mathrm e}^{-\frac {16}{625}}} \left (\left ({\mathrm e}^{\frac {16}{625}}-1\right ) {\mathrm e}^{-\frac {16}{625}} x +\left (9 \,{\mathrm e}^{\frac {16}{625}}-3\right ) {\mathrm e}^{-\frac {16}{625}}\right )}{2}-\frac {{\mathrm e}^{2 \left ({\mathrm e}^{\frac {16}{625}}-1\right ) {\mathrm e}^{-\frac {16}{625}} x +2 \left (9 \,{\mathrm e}^{\frac {16}{625}}-3\right ) {\mathrm e}^{-\frac {16}{625}}}}{4}\right )}{{\mathrm e}^{\frac {16}{625}}-1}+\frac {2 \,{\mathrm e}^{\frac {32}{625}} \left (\frac {{\mathrm e}^{2 \left ({\mathrm e}^{\frac {16}{625}}-1\right ) {\mathrm e}^{-\frac {16}{625}} x +2 \left (9 \,{\mathrm e}^{\frac {16}{625}}-3\right ) {\mathrm e}^{-\frac {16}{625}}} \left (\left ({\mathrm e}^{\frac {16}{625}}-1\right ) {\mathrm e}^{-\frac {16}{625}} x +\left (9 \,{\mathrm e}^{\frac {16}{625}}-3\right ) {\mathrm e}^{-\frac {16}{625}}\right )}{2}-\frac {{\mathrm e}^{2 \left ({\mathrm e}^{\frac {16}{625}}-1\right ) {\mathrm e}^{-\frac {16}{625}} x +2 \left (9 \,{\mathrm e}^{\frac {16}{625}}-3\right ) {\mathrm e}^{-\frac {16}{625}}}}{4}\right )}{{\mathrm e}^{\frac {16}{625}}-1}}{{\mathrm e}^{\frac {16}{625}}-1}\) | \(321\) |
| default | \({\mathrm e}^{-\frac {16}{625}} \left (\frac {{\mathrm e}^{\frac {16}{625}} \left (\frac {{\mathrm e}^{2 \left ({\mathrm e}^{\frac {16}{625}}-1\right ) {\mathrm e}^{-\frac {16}{625}} x +2 \left (9 \,{\mathrm e}^{\frac {16}{625}}-3\right ) {\mathrm e}^{-\frac {16}{625}}} {\mathrm e}^{\frac {16}{625}}}{2}-\frac {3 \,{\mathrm e}^{2 \left ({\mathrm e}^{\frac {16}{625}}-1\right ) {\mathrm e}^{-\frac {16}{625}} x +2 \left (9 \,{\mathrm e}^{\frac {16}{625}}-3\right ) {\mathrm e}^{-\frac {16}{625}}}}{{\mathrm e}^{\frac {16}{625}}-1}+\frac {12 \,{\mathrm e}^{2 \left ({\mathrm e}^{\frac {16}{625}}-1\right ) {\mathrm e}^{-\frac {16}{625}} x +2 \left (9 \,{\mathrm e}^{\frac {16}{625}}-3\right ) {\mathrm e}^{-\frac {16}{625}}} {\mathrm e}^{\frac {16}{625}}}{{\mathrm e}^{\frac {16}{625}}-1}-\frac {9 \,{\mathrm e}^{2 \left ({\mathrm e}^{\frac {16}{625}}-1\right ) {\mathrm e}^{-\frac {16}{625}} x +2 \left (9 \,{\mathrm e}^{\frac {16}{625}}-3\right ) {\mathrm e}^{-\frac {16}{625}}} {\mathrm e}^{\frac {32}{625}}}{{\mathrm e}^{\frac {16}{625}}-1}-\frac {2 \,{\mathrm e}^{\frac {16}{625}} \left (\frac {{\mathrm e}^{2 \left ({\mathrm e}^{\frac {16}{625}}-1\right ) {\mathrm e}^{-\frac {16}{625}} x +2 \left (9 \,{\mathrm e}^{\frac {16}{625}}-3\right ) {\mathrm e}^{-\frac {16}{625}}} \left (\left ({\mathrm e}^{\frac {16}{625}}-1\right ) {\mathrm e}^{-\frac {16}{625}} x +\left (9 \,{\mathrm e}^{\frac {16}{625}}-3\right ) {\mathrm e}^{-\frac {16}{625}}\right )}{2}-\frac {{\mathrm e}^{2 \left ({\mathrm e}^{\frac {16}{625}}-1\right ) {\mathrm e}^{-\frac {16}{625}} x +2 \left (9 \,{\mathrm e}^{\frac {16}{625}}-3\right ) {\mathrm e}^{-\frac {16}{625}}}}{4}\right )}{{\mathrm e}^{\frac {16}{625}}-1}+\frac {2 \,{\mathrm e}^{\frac {32}{625}} \left (\frac {{\mathrm e}^{2 \left ({\mathrm e}^{\frac {16}{625}}-1\right ) {\mathrm e}^{-\frac {16}{625}} x +2 \left (9 \,{\mathrm e}^{\frac {16}{625}}-3\right ) {\mathrm e}^{-\frac {16}{625}}} \left (\left ({\mathrm e}^{\frac {16}{625}}-1\right ) {\mathrm e}^{-\frac {16}{625}} x +\left (9 \,{\mathrm e}^{\frac {16}{625}}-3\right ) {\mathrm e}^{-\frac {16}{625}}\right )}{2}-\frac {{\mathrm e}^{2 \left ({\mathrm e}^{\frac {16}{625}}-1\right ) {\mathrm e}^{-\frac {16}{625}} x +2 \left (9 \,{\mathrm e}^{\frac {16}{625}}-3\right ) {\mathrm e}^{-\frac {16}{625}}}}{4}\right )}{{\mathrm e}^{\frac {16}{625}}-1}\right )}{{\mathrm e}^{\frac {16}{625}}-1}+{\mathrm e}^{\frac {16}{625}} x \right )\) | \(331\) |
| derivativedivides | \(\frac {\frac {{\mathrm e}^{2 \left ({\mathrm e}^{\frac {16}{625}}-1\right ) {\mathrm e}^{-\frac {16}{625}} x +2 \left (9 \,{\mathrm e}^{\frac {16}{625}}-3\right ) {\mathrm e}^{-\frac {16}{625}}} {\mathrm e}^{\frac {16}{625}}}{2}-\frac {3 \,{\mathrm e}^{2 \left ({\mathrm e}^{\frac {16}{625}}-1\right ) {\mathrm e}^{-\frac {16}{625}} x +2 \left (9 \,{\mathrm e}^{\frac {16}{625}}-3\right ) {\mathrm e}^{-\frac {16}{625}}}}{{\mathrm e}^{\frac {16}{625}}-1}+\frac {12 \,{\mathrm e}^{2 \left ({\mathrm e}^{\frac {16}{625}}-1\right ) {\mathrm e}^{-\frac {16}{625}} x +2 \left (9 \,{\mathrm e}^{\frac {16}{625}}-3\right ) {\mathrm e}^{-\frac {16}{625}}} {\mathrm e}^{\frac {16}{625}}}{{\mathrm e}^{\frac {16}{625}}-1}-\frac {9 \,{\mathrm e}^{2 \left ({\mathrm e}^{\frac {16}{625}}-1\right ) {\mathrm e}^{-\frac {16}{625}} x +2 \left (9 \,{\mathrm e}^{\frac {16}{625}}-3\right ) {\mathrm e}^{-\frac {16}{625}}} {\mathrm e}^{\frac {32}{625}}}{{\mathrm e}^{\frac {16}{625}}-1}-\frac {2 \,{\mathrm e}^{\frac {16}{625}} \left (\frac {{\mathrm e}^{2 \left ({\mathrm e}^{\frac {16}{625}}-1\right ) {\mathrm e}^{-\frac {16}{625}} x +2 \left (9 \,{\mathrm e}^{\frac {16}{625}}-3\right ) {\mathrm e}^{-\frac {16}{625}}} \left (\left ({\mathrm e}^{\frac {16}{625}}-1\right ) {\mathrm e}^{-\frac {16}{625}} x +\left (9 \,{\mathrm e}^{\frac {16}{625}}-3\right ) {\mathrm e}^{-\frac {16}{625}}\right )}{2}-\frac {{\mathrm e}^{2 \left ({\mathrm e}^{\frac {16}{625}}-1\right ) {\mathrm e}^{-\frac {16}{625}} x +2 \left (9 \,{\mathrm e}^{\frac {16}{625}}-3\right ) {\mathrm e}^{-\frac {16}{625}}}}{4}\right )}{{\mathrm e}^{\frac {16}{625}}-1}+\frac {2 \,{\mathrm e}^{\frac {32}{625}} \left (\frac {{\mathrm e}^{2 \left ({\mathrm e}^{\frac {16}{625}}-1\right ) {\mathrm e}^{-\frac {16}{625}} x +2 \left (9 \,{\mathrm e}^{\frac {16}{625}}-3\right ) {\mathrm e}^{-\frac {16}{625}}} \left (\left ({\mathrm e}^{\frac {16}{625}}-1\right ) {\mathrm e}^{-\frac {16}{625}} x +\left (9 \,{\mathrm e}^{\frac {16}{625}}-3\right ) {\mathrm e}^{-\frac {16}{625}}\right )}{2}-\frac {{\mathrm e}^{2 \left ({\mathrm e}^{\frac {16}{625}}-1\right ) {\mathrm e}^{-\frac {16}{625}} x +2 \left (9 \,{\mathrm e}^{\frac {16}{625}}-3\right ) {\mathrm e}^{-\frac {16}{625}}}}{4}\right )}{{\mathrm e}^{\frac {16}{625}}-1}+\left (\left ({\mathrm e}^{\frac {16}{625}}-1\right ) {\mathrm e}^{-\frac {16}{625}} x +\left (9 \,{\mathrm e}^{\frac {16}{625}}-3\right ) {\mathrm e}^{-\frac {16}{625}}\right ) {\mathrm e}^{\frac {16}{625}}}{{\mathrm e}^{\frac {16}{625}}-1}\) | \(344\) |
Input:
int((((1+2*x)*exp(16/625)-2*x)*exp(((x+9)*exp(16/625)-3-x)/exp(16/625))^2+ exp(16/625))/exp(16/625),x,method=_RETURNVERBOSE)
Output:
x+x*exp(2*(exp(16/625)*x+9*exp(16/625)-x-3)*exp(-16/625))
Time = 0.08 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.95 \[ \int \frac {e^{16/625}+e^{\frac {2 \left (-3-x+e^{16/625} (9+x)\right )}{e^{16/625}}} \left (-2 x+e^{16/625} (1+2 x)\right )}{e^{16/625}} \, dx=x e^{\left (2 \, {\left ({\left (x + 9\right )} e^{\frac {16}{625}} - x - 3\right )} e^{\left (-\frac {16}{625}\right )}\right )} + x \] Input:
integrate((((1+2*x)*exp(16/625)-2*x)*exp(((x+9)*exp(16/625)-3-x)/exp(16/62 5))^2+exp(16/625))/exp(16/625),x, algorithm="fricas")
Output:
x*e^(2*((x + 9)*e^(16/625) - x - 3)*e^(-16/625)) + x
Time = 0.07 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.14 \[ \int \frac {e^{16/625}+e^{\frac {2 \left (-3-x+e^{16/625} (9+x)\right )}{e^{16/625}}} \left (-2 x+e^{16/625} (1+2 x)\right )}{e^{16/625}} \, dx=x e^{\frac {2 \left (- x + \left (x + 9\right ) e^{\frac {16}{625}} - 3\right )}{e^{\frac {16}{625}}}} + x \] Input:
integrate((((1+2*x)*exp(16/625)-2*x)*exp(((x+9)*exp(16/625)-3-x)/exp(16/62 5))**2+exp(16/625))/exp(16/625),x)
Output:
x*exp(2*(-x + (x + 9)*exp(16/625) - 3)*exp(-16/625)) + x
Leaf count of result is larger than twice the leaf count of optimal. 134 vs. \(2 (17) = 34\).
Time = 0.05 (sec) , antiderivative size = 134, normalized size of antiderivative = 6.38 \[ \int \frac {e^{16/625}+e^{\frac {2 \left (-3-x+e^{16/625} (9+x)\right )}{e^{16/625}}} \left (-2 x+e^{16/625} (1+2 x)\right )}{e^{16/625}} \, dx=\frac {1}{2} \, {\left (2 \, x e^{\frac {16}{625}} + \frac {{\left (2 \, x {\left (e^{\frac {11298}{625}} - e^{\frac {11282}{625}}\right )} - e^{\frac {11298}{625}}\right )} e^{\left (-2 \, x e^{\left (-\frac {16}{625}\right )} + 2 \, x\right )}}{e^{\left (6 \, e^{\left (-\frac {16}{625}\right )}\right )} + e^{\left (6 \, e^{\left (-\frac {16}{625}\right )} + \frac {32}{625}\right )} - 2 \, e^{\left (6 \, e^{\left (-\frac {16}{625}\right )} + \frac {16}{625}\right )}} - \frac {{\left (2 \, x {\left (e^{\frac {11282}{625}} - e^{\frac {11266}{625}}\right )} - e^{\frac {11282}{625}}\right )} e^{\left (-2 \, x e^{\left (-\frac {16}{625}\right )} + 2 \, x\right )}}{e^{\left (6 \, e^{\left (-\frac {16}{625}\right )}\right )} + e^{\left (6 \, e^{\left (-\frac {16}{625}\right )} + \frac {32}{625}\right )} - 2 \, e^{\left (6 \, e^{\left (-\frac {16}{625}\right )} + \frac {16}{625}\right )}} - \frac {e^{\left (-2 \, x e^{\left (-\frac {16}{625}\right )} + 2 \, x - 6 \, e^{\left (-\frac {16}{625}\right )} + \frac {11266}{625}\right )}}{e^{\left (-\frac {16}{625}\right )} - 1}\right )} e^{\left (-\frac {16}{625}\right )} \] Input:
integrate((((1+2*x)*exp(16/625)-2*x)*exp(((x+9)*exp(16/625)-3-x)/exp(16/62 5))^2+exp(16/625))/exp(16/625),x, algorithm="maxima")
Output:
1/2*(2*x*e^(16/625) + (2*x*(e^(11298/625) - e^(11282/625)) - e^(11298/625) )*e^(-2*x*e^(-16/625) + 2*x)/(e^(6*e^(-16/625)) + e^(6*e^(-16/625) + 32/62 5) - 2*e^(6*e^(-16/625) + 16/625)) - (2*x*(e^(11282/625) - e^(11266/625)) - e^(11282/625))*e^(-2*x*e^(-16/625) + 2*x)/(e^(6*e^(-16/625)) + e^(6*e^(- 16/625) + 32/625) - 2*e^(6*e^(-16/625) + 16/625)) - e^(-2*x*e^(-16/625) + 2*x - 6*e^(-16/625) + 11266/625)/(e^(-16/625) - 1))*e^(-16/625)
Leaf count of result is larger than twice the leaf count of optimal. 88 vs. \(2 (17) = 34\).
Time = 0.13 (sec) , antiderivative size = 88, normalized size of antiderivative = 4.19 \[ \int \frac {e^{16/625}+e^{\frac {2 \left (-3-x+e^{16/625} (9+x)\right )}{e^{16/625}}} \left (-2 x+e^{16/625} (1+2 x)\right )}{e^{16/625}} \, dx=\frac {1}{2} \, {\left (2 \, x e^{\frac {16}{625}} + \frac {{\left (2 \, x e^{\left (-\frac {16}{625}\right )} - 2 \, x + e^{\left (-\frac {16}{625}\right )}\right )} e^{\left (-2 \, x e^{\left (-\frac {16}{625}\right )} + 2 \, x - 6 \, e^{\left (-\frac {16}{625}\right )} + \frac {11266}{625}\right )}}{2 \, e^{\left (-\frac {16}{625}\right )} - e^{\left (-\frac {32}{625}\right )} - 1} - \frac {{\left (2 \, x e^{\left (-\frac {16}{625}\right )} - 2 \, x + 1\right )} e^{\left (-2 \, x e^{\left (-\frac {16}{625}\right )} + 2 \, x - 6 \, e^{\left (-\frac {16}{625}\right )} + 18\right )}}{2 \, e^{\left (-\frac {16}{625}\right )} - e^{\left (-\frac {32}{625}\right )} - 1}\right )} e^{\left (-\frac {16}{625}\right )} \] Input:
integrate((((1+2*x)*exp(16/625)-2*x)*exp(((x+9)*exp(16/625)-3-x)/exp(16/62 5))^2+exp(16/625))/exp(16/625),x, algorithm="giac")
Output:
1/2*(2*x*e^(16/625) + (2*x*e^(-16/625) - 2*x + e^(-16/625))*e^(-2*x*e^(-16 /625) + 2*x - 6*e^(-16/625) + 11266/625)/(2*e^(-16/625) - e^(-32/625) - 1) - (2*x*e^(-16/625) - 2*x + 1)*e^(-2*x*e^(-16/625) + 2*x - 6*e^(-16/625) + 18)/(2*e^(-16/625) - e^(-32/625) - 1))*e^(-16/625)
Time = 0.13 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.05 \[ \int \frac {e^{16/625}+e^{\frac {2 \left (-3-x+e^{16/625} (9+x)\right )}{e^{16/625}}} \left (-2 x+e^{16/625} (1+2 x)\right )}{e^{16/625}} \, dx=x\,\left ({\mathrm {e}}^{-6\,{\mathrm {e}}^{-\frac {16}{625}}}\,{\mathrm {e}}^{2\,x}\,{\mathrm {e}}^{18}\,{\mathrm {e}}^{-2\,x\,{\mathrm {e}}^{-\frac {16}{625}}}+1\right ) \] Input:
int(exp(-16/625)*(exp(16/625) - exp(-2*exp(-16/625)*(x - exp(16/625)*(x + 9) + 3))*(2*x - exp(16/625)*(2*x + 1))),x)
Output:
x*(exp(-6*exp(-16/625))*exp(2*x)*exp(18)*exp(-2*x*exp(-16/625)) + 1)
Time = 0.21 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.71 \[ \int \frac {e^{16/625}+e^{\frac {2 \left (-3-x+e^{16/625} (9+x)\right )}{e^{16/625}}} \left (-2 x+e^{16/625} (1+2 x)\right )}{e^{16/625}} \, dx=\frac {x \left (e^{\frac {2 x +6}{e^{\frac {16}{625}}}}+e^{2 x} e^{18}\right )}{e^{\frac {2 x +6}{e^{\frac {16}{625}}}}} \] Input:
int((((1+2*x)*exp(16/625)-2*x)*exp(((x+9)*exp(16/625)-3-x)/exp(16/625))^2+ exp(16/625))/exp(16/625),x)
Output:
(x*(e**((2*x + 6)/e**(16/625)) + e**(2*x)*e**18))/e**((2*x + 6)/e**(16/625 ))