Integrand size = 216, antiderivative size = 31 \[ \int \frac {-x^5+e^{2 \left (2 x-e^{25} x+x^2-x \log (x)\right )} \left (-4+2 x-2 e^{25} x+4 x^2-2 x \log (x)\right )+e^{\frac {3}{2} \left (2 x-e^{25} x+x^2-x \log (x)\right )} \left (-12 x+6 x^2-6 e^{25} x^2+12 x^3-6 x^2 \log (x)\right )+e^{2 x-e^{25} x+x^2-x \log (x)} \left (-12 x^2+6 x^3-6 e^{25} x^3+12 x^4-6 x^3 \log (x)\right )+e^{\frac {1}{2} \left (2 x-e^{25} x+x^2-x \log (x)\right )} \left (-4 x^3+2 x^4-2 e^{25} x^4+4 x^5-2 x^4 \log (x)\right )}{x^5} \, dx=-x+\frac {\left (e^{\frac {1}{2} x \left (2-e^{25}+x-\log (x)\right )}+x\right )^4}{x^4} \] Output:
(exp(1/2*x*(2-exp(25)+x-ln(x)))+x)^4/x^4-x
Leaf count is larger than twice the leaf count of optimal. \(113\) vs. \(2(31)=62\).
Time = 2.76 (sec) , antiderivative size = 113, normalized size of antiderivative = 3.65 \[ \int \frac {-x^5+e^{2 \left (2 x-e^{25} x+x^2-x \log (x)\right )} \left (-4+2 x-2 e^{25} x+4 x^2-2 x \log (x)\right )+e^{\frac {3}{2} \left (2 x-e^{25} x+x^2-x \log (x)\right )} \left (-12 x+6 x^2-6 e^{25} x^2+12 x^3-6 x^2 \log (x)\right )+e^{2 x-e^{25} x+x^2-x \log (x)} \left (-12 x^2+6 x^3-6 e^{25} x^3+12 x^4-6 x^3 \log (x)\right )+e^{\frac {1}{2} \left (2 x-e^{25} x+x^2-x \log (x)\right )} \left (-4 x^3+2 x^4-2 e^{25} x^4+4 x^5-2 x^4 \log (x)\right )}{x^5} \, dx=-x+e^{-2 \left (-2+e^{25}\right ) x+2 x^2} x^{-4-2 x}+4 e^{-\frac {3}{2} \left (-2+e^{25}\right ) x+\frac {3 x^2}{2}} x^{-3-\frac {3 x}{2}}+6 e^{-\left (\left (-2+e^{25}\right ) x\right )+x^2} x^{-2-x}+4 e^{-\frac {1}{2} \left (-2+e^{25}\right ) x+\frac {x^2}{2}} x^{-1-\frac {x}{2}} \] Input:
Integrate[(-x^5 + E^(2*(2*x - E^25*x + x^2 - x*Log[x]))*(-4 + 2*x - 2*E^25 *x + 4*x^2 - 2*x*Log[x]) + E^((3*(2*x - E^25*x + x^2 - x*Log[x]))/2)*(-12* x + 6*x^2 - 6*E^25*x^2 + 12*x^3 - 6*x^2*Log[x]) + E^(2*x - E^25*x + x^2 - x*Log[x])*(-12*x^2 + 6*x^3 - 6*E^25*x^3 + 12*x^4 - 6*x^3*Log[x]) + E^((2*x - E^25*x + x^2 - x*Log[x])/2)*(-4*x^3 + 2*x^4 - 2*E^25*x^4 + 4*x^5 - 2*x^ 4*Log[x]))/x^5,x]
Output:
-x + E^(-2*(-2 + E^25)*x + 2*x^2)*x^(-4 - 2*x) + 4*E^((-3*(-2 + E^25)*x)/2 + (3*x^2)/2)*x^(-3 - (3*x)/2) + 6*E^(-((-2 + E^25)*x) + x^2)*x^(-2 - x) + 4*E^(-1/2*((-2 + E^25)*x) + x^2/2)*x^(-1 - 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.
| \(\displaystyle \int \frac {-x^5+e^{2 \left (x^2-e^{25} x+2 x-x \log (x)\right )} \left (4 x^2-2 e^{25} x+2 x-2 x \log (x)-4\right )+e^{\frac {3}{2} \left (x^2-e^{25} x+2 x-x \log (x)\right )} \left (12 x^3-6 e^{25} x^2+6 x^2-6 x^2 \log (x)-12 x\right )+e^{x^2-e^{25} x+2 x-x \log (x)} \left (12 x^4-6 e^{25} x^3+6 x^3-6 x^3 \log (x)-12 x^2\right )+e^{\frac {1}{2} \left (x^2-e^{25} x+2 x-x \log (x)\right )} \left (4 x^5-2 e^{25} x^4+2 x^4-2 x^4 \log (x)-4 x^3\right )}{x^5} \, dx\) |
| \(\Big \downarrow \) 2010 |
| \(\displaystyle \int \left (2 e^{2 x \left (x-e^{25}+2\right )} x^{-2 x-5} \left (2 x^2+\left (1-e^{25}\right ) x-x \log (x)-2\right )+6 e^{\frac {3}{2} x \left (x-e^{25}+2\right )} x^{-\frac {3 x}{2}-4} \left (2 x^2+\left (1-e^{25}\right ) x-x \log (x)-2\right )+6 e^{x^2+\left (2-e^{25}\right ) x} x^{-x-3} \left (2 x^2+\left (1-e^{25}\right ) x-x \log (x)-2\right )+2 e^{\frac {1}{2} x \left (x-e^{25}+2\right )} x^{-\frac {x}{2}-2} \left (2 x^2+\left (1-e^{25}\right ) x-x \log (x)-2\right )-1\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -4 \int e^{2 x \left (x-e^{25}+2\right )} x^{-2 x-5}dx+2 \left (1-e^{25}\right ) \int e^{2 x \left (x-e^{25}+2\right )} x^{-2 x-4}dx+4 \int e^{2 x \left (x-e^{25}+2\right )} x^{-2 x-3}dx-12 \int e^{\frac {3}{2} x \left (x-e^{25}+2\right )} x^{-\frac {3 x}{2}-4}dx+6 \left (1-e^{25}\right ) \int e^{\frac {3}{2} x \left (x-e^{25}+2\right )} x^{-\frac {3 x}{2}-3}dx+12 \int e^{\frac {3}{2} x \left (x-e^{25}+2\right )} x^{-\frac {3 x}{2}-2}dx-4 \int e^{\frac {1}{2} x \left (x-e^{25}+2\right )} x^{-\frac {x}{2}-2}dx+2 \left (1-e^{25}\right ) \int e^{\frac {1}{2} x \left (x-e^{25}+2\right )} x^{-\frac {x}{2}-1}dx+4 \int e^{\frac {1}{2} x \left (x-e^{25}+2\right )} x^{-x/2}dx+2 \int \frac {\int e^{2 x \left (x-e^{25}+2\right )} x^{-2 x-4}dx}{x}dx+6 \int \frac {\int e^{\frac {3}{2} x \left (x-e^{25}+2\right )} x^{-\frac {3 x}{2}-3}dx}{x}dx+2 \int \frac {\int e^{\frac {1}{2} x \left (x-e^{25}+2\right )} x^{-\frac {x}{2}-1}dx}{x}dx-2 \log (x) \int e^{2 x \left (x-e^{25}+2\right )} x^{-2 x-4}dx-6 \log (x) \int e^{\frac {3}{2} x \left (x-e^{25}+2\right )} x^{-\frac {3 x}{2}-3}dx-2 \log (x) \int e^{\frac {1}{2} x \left (x-e^{25}+2\right )} x^{-\frac {x}{2}-1}dx-12 \int e^{x^2+\left (2-e^{25}\right ) x} x^{-x-3}dx+6 \left (1-e^{25}\right ) \int e^{x^2+\left (2-e^{25}\right ) x} x^{-x-2}dx+12 \int e^{x^2+\left (2-e^{25}\right ) x} x^{-x-1}dx+6 \int \frac {\int e^{x^2+\left (2-e^{25}\right ) x} x^{-x-2}dx}{x}dx-6 \log (x) \int e^{x^2+\left (2-e^{25}\right ) x} x^{-x-2}dx-x\) |
Input:
Int[(-x^5 + E^(2*(2*x - E^25*x + x^2 - x*Log[x]))*(-4 + 2*x - 2*E^25*x + 4 *x^2 - 2*x*Log[x]) + E^((3*(2*x - E^25*x + x^2 - x*Log[x]))/2)*(-12*x + 6* x^2 - 6*E^25*x^2 + 12*x^3 - 6*x^2*Log[x]) + E^(2*x - E^25*x + x^2 - x*Log[ x])*(-12*x^2 + 6*x^3 - 6*E^25*x^3 + 12*x^4 - 6*x^3*Log[x]) + E^((2*x - E^2 5*x + x^2 - x*Log[x])/2)*(-4*x^3 + 2*x^4 - 2*E^25*x^4 + 4*x^5 - 2*x^4*Log[ x]))/x^5,x]
Output:
$Aborted
Leaf count of result is larger than twice the leaf count of optimal. \(81\) vs. \(2(27)=54\).
Time = 1.13 (sec) , antiderivative size = 82, normalized size of antiderivative = 2.65
| method | result | size |
| parallelrisch | \(\frac {-x^{5}+4 \,{\mathrm e}^{-\frac {x \left (\ln \left (x \right )+{\mathrm e}^{25}-x -2\right )}{2}} x^{3}+6 \,{\mathrm e}^{-x \left (\ln \left (x \right )+{\mathrm e}^{25}-x -2\right )} x^{2}+4 \,{\mathrm e}^{-\frac {3 x \left (\ln \left (x \right )+{\mathrm e}^{25}-x -2\right )}{2}} x +{\mathrm e}^{-2 x \left (\ln \left (x \right )+{\mathrm e}^{25}-x -2\right )}}{x^{4}}\) | \(82\) |
| risch | \(-x +\frac {x^{-2 x} {\mathrm e}^{-2 x \left ({\mathrm e}^{25}-x -2\right )}}{x^{4}}+\frac {4 x^{-\frac {3 x}{2}} {\mathrm e}^{-\frac {3 x \left ({\mathrm e}^{25}-x -2\right )}{2}}}{x^{3}}+\frac {6 x^{-x} {\mathrm e}^{-x \left ({\mathrm e}^{25}-x -2\right )}}{x^{2}}+\frac {4 x^{-\frac {x}{2}} {\mathrm e}^{-\frac {x \left ({\mathrm e}^{25}-x -2\right )}{2}}}{x}\) | \(94\) |
Input:
int(((-2*x*ln(x)-2*x*exp(25)+4*x^2+2*x-4)*exp(-1/2*x*ln(x)-1/2*x*exp(25)+1 /2*x^2+x)^4+(-6*x^2*ln(x)-6*x^2*exp(25)+12*x^3+6*x^2-12*x)*exp(-1/2*x*ln(x )-1/2*x*exp(25)+1/2*x^2+x)^3+(-6*x^3*ln(x)-6*x^3*exp(25)+12*x^4+6*x^3-12*x ^2)*exp(-1/2*x*ln(x)-1/2*x*exp(25)+1/2*x^2+x)^2+(-2*x^4*ln(x)-2*x^4*exp(25 )+4*x^5+2*x^4-4*x^3)*exp(-1/2*x*ln(x)-1/2*x*exp(25)+1/2*x^2+x)-x^5)/x^5,x, method=_RETURNVERBOSE)
Output:
1/x^4*(-x^5+4*exp(-1/2*x*(ln(x)+exp(25)-x-2))*x^3+6*exp(-1/2*x*(ln(x)+exp( 25)-x-2))^2*x^2+4*exp(-1/2*x*(ln(x)+exp(25)-x-2))^3*x+exp(-1/2*x*(ln(x)+ex p(25)-x-2))^4)
Leaf count of result is larger than twice the leaf count of optimal. 100 vs. \(2 (27) = 54\).
Time = 0.10 (sec) , antiderivative size = 100, normalized size of antiderivative = 3.23 \[ \int \frac {-x^5+e^{2 \left (2 x-e^{25} x+x^2-x \log (x)\right )} \left (-4+2 x-2 e^{25} x+4 x^2-2 x \log (x)\right )+e^{\frac {3}{2} \left (2 x-e^{25} x+x^2-x \log (x)\right )} \left (-12 x+6 x^2-6 e^{25} x^2+12 x^3-6 x^2 \log (x)\right )+e^{2 x-e^{25} x+x^2-x \log (x)} \left (-12 x^2+6 x^3-6 e^{25} x^3+12 x^4-6 x^3 \log (x)\right )+e^{\frac {1}{2} \left (2 x-e^{25} x+x^2-x \log (x)\right )} \left (-4 x^3+2 x^4-2 e^{25} x^4+4 x^5-2 x^4 \log (x)\right )}{x^5} \, dx=-\frac {x^{5} - 4 \, x^{3} e^{\left (\frac {1}{2} \, x^{2} - \frac {1}{2} \, x e^{25} - \frac {1}{2} \, x \log \left (x\right ) + x\right )} - 6 \, x^{2} e^{\left (x^{2} - x e^{25} - x \log \left (x\right ) + 2 \, x\right )} - 4 \, x e^{\left (\frac {3}{2} \, x^{2} - \frac {3}{2} \, x e^{25} - \frac {3}{2} \, x \log \left (x\right ) + 3 \, x\right )} - e^{\left (2 \, x^{2} - 2 \, x e^{25} - 2 \, x \log \left (x\right ) + 4 \, x\right )}}{x^{4}} \] Input:
integrate(((-2*x*log(x)-2*x*exp(25)+4*x^2+2*x-4)*exp(-1/2*x*log(x)-1/2*x*e xp(25)+1/2*x^2+x)^4+(-6*x^2*log(x)-6*x^2*exp(25)+12*x^3+6*x^2-12*x)*exp(-1 /2*x*log(x)-1/2*x*exp(25)+1/2*x^2+x)^3+(-6*x^3*log(x)-6*x^3*exp(25)+12*x^4 +6*x^3-12*x^2)*exp(-1/2*x*log(x)-1/2*x*exp(25)+1/2*x^2+x)^2+(-2*x^4*log(x) -2*x^4*exp(25)+4*x^5+2*x^4-4*x^3)*exp(-1/2*x*log(x)-1/2*x*exp(25)+1/2*x^2+ x)-x^5)/x^5,x, algorithm="fricas")
Output:
-(x^5 - 4*x^3*e^(1/2*x^2 - 1/2*x*e^25 - 1/2*x*log(x) + x) - 6*x^2*e^(x^2 - x*e^25 - x*log(x) + 2*x) - 4*x*e^(3/2*x^2 - 3/2*x*e^25 - 3/2*x*log(x) + 3 *x) - e^(2*x^2 - 2*x*e^25 - 2*x*log(x) + 4*x))/x^4
Leaf count of result is larger than twice the leaf count of optimal. 116 vs. \(2 (22) = 44\).
Time = 0.22 (sec) , antiderivative size = 116, normalized size of antiderivative = 3.74 \[ \int \frac {-x^5+e^{2 \left (2 x-e^{25} x+x^2-x \log (x)\right )} \left (-4+2 x-2 e^{25} x+4 x^2-2 x \log (x)\right )+e^{\frac {3}{2} \left (2 x-e^{25} x+x^2-x \log (x)\right )} \left (-12 x+6 x^2-6 e^{25} x^2+12 x^3-6 x^2 \log (x)\right )+e^{2 x-e^{25} x+x^2-x \log (x)} \left (-12 x^2+6 x^3-6 e^{25} x^3+12 x^4-6 x^3 \log (x)\right )+e^{\frac {1}{2} \left (2 x-e^{25} x+x^2-x \log (x)\right )} \left (-4 x^3+2 x^4-2 e^{25} x^4+4 x^5-2 x^4 \log (x)\right )}{x^5} \, dx=- x + \frac {4 x^{9} e^{\frac {x^{2}}{2} - \frac {x \log {\left (x \right )}}{2} - \frac {x e^{25}}{2} + x} + 6 x^{8} e^{x^{2} - x \log {\left (x \right )} - x e^{25} + 2 x} + 4 x^{7} e^{\frac {3 x^{2}}{2} - \frac {3 x \log {\left (x \right )}}{2} - \frac {3 x e^{25}}{2} + 3 x} + x^{6} e^{2 x^{2} - 2 x \log {\left (x \right )} - 2 x e^{25} + 4 x}}{x^{10}} \] Input:
integrate(((-2*x*ln(x)-2*x*exp(25)+4*x**2+2*x-4)*exp(-1/2*x*ln(x)-1/2*x*ex p(25)+1/2*x**2+x)**4+(-6*x**2*ln(x)-6*x**2*exp(25)+12*x**3+6*x**2-12*x)*ex p(-1/2*x*ln(x)-1/2*x*exp(25)+1/2*x**2+x)**3+(-6*x**3*ln(x)-6*x**3*exp(25)+ 12*x**4+6*x**3-12*x**2)*exp(-1/2*x*ln(x)-1/2*x*exp(25)+1/2*x**2+x)**2+(-2* x**4*ln(x)-2*x**4*exp(25)+4*x**5+2*x**4-4*x**3)*exp(-1/2*x*ln(x)-1/2*x*exp (25)+1/2*x**2+x)-x**5)/x**5,x)
Output:
-x + (4*x**9*exp(x**2/2 - x*log(x)/2 - x*exp(25)/2 + x) + 6*x**8*exp(x**2 - x*log(x) - x*exp(25) + 2*x) + 4*x**7*exp(3*x**2/2 - 3*x*log(x)/2 - 3*x*e xp(25)/2 + 3*x) + x**6*exp(2*x**2 - 2*x*log(x) - 2*x*exp(25) + 4*x))/x**10
Leaf count of result is larger than twice the leaf count of optimal. 99 vs. \(2 (27) = 54\).
Time = 0.12 (sec) , antiderivative size = 99, normalized size of antiderivative = 3.19 \[ \int \frac {-x^5+e^{2 \left (2 x-e^{25} x+x^2-x \log (x)\right )} \left (-4+2 x-2 e^{25} x+4 x^2-2 x \log (x)\right )+e^{\frac {3}{2} \left (2 x-e^{25} x+x^2-x \log (x)\right )} \left (-12 x+6 x^2-6 e^{25} x^2+12 x^3-6 x^2 \log (x)\right )+e^{2 x-e^{25} x+x^2-x \log (x)} \left (-12 x^2+6 x^3-6 e^{25} x^3+12 x^4-6 x^3 \log (x)\right )+e^{\frac {1}{2} \left (2 x-e^{25} x+x^2-x \log (x)\right )} \left (-4 x^3+2 x^4-2 e^{25} x^4+4 x^5-2 x^4 \log (x)\right )}{x^5} \, dx=-x + \frac {4 \, x^{3} e^{\left (\frac {1}{2} \, x^{2} - \frac {1}{2} \, x e^{25} + \frac {3}{2} \, x \log \left (x\right ) + x\right )} + 6 \, x^{2} e^{\left (x^{2} - x e^{25} + x \log \left (x\right ) + 2 \, x\right )} + 4 \, x e^{\left (\frac {3}{2} \, x^{2} - \frac {3}{2} \, x e^{25} + \frac {1}{2} \, x \log \left (x\right ) + 3 \, x\right )} + e^{\left (2 \, x^{2} - 2 \, x e^{25} + 4 \, x\right )}}{x^{4} x^{2 \, x}} \] Input:
integrate(((-2*x*log(x)-2*x*exp(25)+4*x^2+2*x-4)*exp(-1/2*x*log(x)-1/2*x*e xp(25)+1/2*x^2+x)^4+(-6*x^2*log(x)-6*x^2*exp(25)+12*x^3+6*x^2-12*x)*exp(-1 /2*x*log(x)-1/2*x*exp(25)+1/2*x^2+x)^3+(-6*x^3*log(x)-6*x^3*exp(25)+12*x^4 +6*x^3-12*x^2)*exp(-1/2*x*log(x)-1/2*x*exp(25)+1/2*x^2+x)^2+(-2*x^4*log(x) -2*x^4*exp(25)+4*x^5+2*x^4-4*x^3)*exp(-1/2*x*log(x)-1/2*x*exp(25)+1/2*x^2+ x)-x^5)/x^5,x, algorithm="maxima")
Output:
-x + (4*x^3*e^(1/2*x^2 - 1/2*x*e^25 + 3/2*x*log(x) + x) + 6*x^2*e^(x^2 - x *e^25 + x*log(x) + 2*x) + 4*x*e^(3/2*x^2 - 3/2*x*e^25 + 1/2*x*log(x) + 3*x ) + e^(2*x^2 - 2*x*e^25 + 4*x))/(x^4*x^(2*x))
Leaf count of result is larger than twice the leaf count of optimal. 100 vs. \(2 (27) = 54\).
Time = 0.22 (sec) , antiderivative size = 100, normalized size of antiderivative = 3.23 \[ \int \frac {-x^5+e^{2 \left (2 x-e^{25} x+x^2-x \log (x)\right )} \left (-4+2 x-2 e^{25} x+4 x^2-2 x \log (x)\right )+e^{\frac {3}{2} \left (2 x-e^{25} x+x^2-x \log (x)\right )} \left (-12 x+6 x^2-6 e^{25} x^2+12 x^3-6 x^2 \log (x)\right )+e^{2 x-e^{25} x+x^2-x \log (x)} \left (-12 x^2+6 x^3-6 e^{25} x^3+12 x^4-6 x^3 \log (x)\right )+e^{\frac {1}{2} \left (2 x-e^{25} x+x^2-x \log (x)\right )} \left (-4 x^3+2 x^4-2 e^{25} x^4+4 x^5-2 x^4 \log (x)\right )}{x^5} \, dx=-\frac {x^{5} - 4 \, x^{3} e^{\left (\frac {1}{2} \, x^{2} - \frac {1}{2} \, x e^{25} - \frac {1}{2} \, x \log \left (x\right ) + x\right )} - 6 \, x^{2} e^{\left (x^{2} - x e^{25} - x \log \left (x\right ) + 2 \, x\right )} - 4 \, x e^{\left (\frac {3}{2} \, x^{2} - \frac {3}{2} \, x e^{25} - \frac {3}{2} \, x \log \left (x\right ) + 3 \, x\right )} - e^{\left (2 \, x^{2} - 2 \, x e^{25} - 2 \, x \log \left (x\right ) + 4 \, x\right )}}{x^{4}} \] Input:
integrate(((-2*x*log(x)-2*x*exp(25)+4*x^2+2*x-4)*exp(-1/2*x*log(x)-1/2*x*e xp(25)+1/2*x^2+x)^4+(-6*x^2*log(x)-6*x^2*exp(25)+12*x^3+6*x^2-12*x)*exp(-1 /2*x*log(x)-1/2*x*exp(25)+1/2*x^2+x)^3+(-6*x^3*log(x)-6*x^3*exp(25)+12*x^4 +6*x^3-12*x^2)*exp(-1/2*x*log(x)-1/2*x*exp(25)+1/2*x^2+x)^2+(-2*x^4*log(x) -2*x^4*exp(25)+4*x^5+2*x^4-4*x^3)*exp(-1/2*x*log(x)-1/2*x*exp(25)+1/2*x^2+ x)-x^5)/x^5,x, algorithm="giac")
Output:
-(x^5 - 4*x^3*e^(1/2*x^2 - 1/2*x*e^25 - 1/2*x*log(x) + x) - 6*x^2*e^(x^2 - x*e^25 - x*log(x) + 2*x) - 4*x*e^(3/2*x^2 - 3/2*x*e^25 - 3/2*x*log(x) + 3 *x) - e^(2*x^2 - 2*x*e^25 - 2*x*log(x) + 4*x))/x^4
Time = 3.97 (sec) , antiderivative size = 101, normalized size of antiderivative = 3.26 \[ \int \frac {-x^5+e^{2 \left (2 x-e^{25} x+x^2-x \log (x)\right )} \left (-4+2 x-2 e^{25} x+4 x^2-2 x \log (x)\right )+e^{\frac {3}{2} \left (2 x-e^{25} x+x^2-x \log (x)\right )} \left (-12 x+6 x^2-6 e^{25} x^2+12 x^3-6 x^2 \log (x)\right )+e^{2 x-e^{25} x+x^2-x \log (x)} \left (-12 x^2+6 x^3-6 e^{25} x^3+12 x^4-6 x^3 \log (x)\right )+e^{\frac {1}{2} \left (2 x-e^{25} x+x^2-x \log (x)\right )} \left (-4 x^3+2 x^4-2 e^{25} x^4+4 x^5-2 x^4 \log (x)\right )}{x^5} \, dx=\frac {4\,{\mathrm {e}}^{3\,x-\frac {3\,x\,{\mathrm {e}}^{25}}{2}-\frac {3\,x\,\ln \left (x\right )}{2}+\frac {3\,x^2}{2}}}{x^3}-x+\frac {4\,{\mathrm {e}}^{x-\frac {x\,{\mathrm {e}}^{25}}{2}-\frac {x\,\ln \left (x\right )}{2}+\frac {x^2}{2}}}{x}+\frac {6\,{\mathrm {e}}^{2\,x-x\,{\mathrm {e}}^{25}+x^2}}{x^x\,x^2}+\frac {{\mathrm {e}}^{4\,x-2\,x\,{\mathrm {e}}^{25}+2\,x^2}}{x^{2\,x}\,x^4} \] Input:
int(-(exp(3*x - (3*x*exp(25))/2 - (3*x*log(x))/2 + (3*x^2)/2)*(12*x + 6*x^ 2*log(x) + 6*x^2*exp(25) - 6*x^2 - 12*x^3) + exp(x - (x*exp(25))/2 - (x*lo g(x))/2 + x^2/2)*(2*x^4*log(x) + 2*x^4*exp(25) + 4*x^3 - 2*x^4 - 4*x^5) + exp(2*x - x*exp(25) - x*log(x) + x^2)*(6*x^3*log(x) + 6*x^3*exp(25) + 12*x ^2 - 6*x^3 - 12*x^4) + exp(4*x - 2*x*exp(25) - 2*x*log(x) + 2*x^2)*(2*x*ex p(25) - 2*x + 2*x*log(x) - 4*x^2 + 4) + x^5)/x^5,x)
Output:
(4*exp(3*x - (3*x*exp(25))/2 - (3*x*log(x))/2 + (3*x^2)/2))/x^3 - x + (4*e xp(x - (x*exp(25))/2 - (x*log(x))/2 + x^2/2))/x + (6*exp(2*x - x*exp(25) + x^2))/(x^x*x^2) + exp(4*x - 2*x*exp(25) + 2*x^2)/(x^(2*x)*x^4)
Time = 0.20 (sec) , antiderivative size = 123, normalized size of antiderivative = 3.97 \[ \int \frac {-x^5+e^{2 \left (2 x-e^{25} x+x^2-x \log (x)\right )} \left (-4+2 x-2 e^{25} x+4 x^2-2 x \log (x)\right )+e^{\frac {3}{2} \left (2 x-e^{25} x+x^2-x \log (x)\right )} \left (-12 x+6 x^2-6 e^{25} x^2+12 x^3-6 x^2 \log (x)\right )+e^{2 x-e^{25} x+x^2-x \log (x)} \left (-12 x^2+6 x^3-6 e^{25} x^3+12 x^4-6 x^3 \log (x)\right )+e^{\frac {1}{2} \left (2 x-e^{25} x+x^2-x \log (x)\right )} \left (-4 x^3+2 x^4-2 e^{25} x^4+4 x^5-2 x^4 \log (x)\right )}{x^5} \, dx=\frac {e^{2 x^{2}+4 x}+6 x^{x} e^{e^{25} x +x^{2}+2 x} x^{2}+4 x^{\frac {x}{2}} e^{\frac {1}{2} e^{25} x +\frac {3}{2} x^{2}+3 x} x +4 x^{\frac {3 x}{2}} e^{\frac {3}{2} e^{25} x +\frac {1}{2} x^{2}+x} x^{3}-x^{2 x} e^{2 e^{25} x} x^{5}}{x^{2 x} e^{2 e^{25} x} x^{4}} \] Input:
int(((-2*x*log(x)-2*x*exp(25)+4*x^2+2*x-4)*exp(-1/2*x*log(x)-1/2*x*exp(25) +1/2*x^2+x)^4+(-6*x^2*log(x)-6*x^2*exp(25)+12*x^3+6*x^2-12*x)*exp(-1/2*x*l og(x)-1/2*x*exp(25)+1/2*x^2+x)^3+(-6*x^3*log(x)-6*x^3*exp(25)+12*x^4+6*x^3 -12*x^2)*exp(-1/2*x*log(x)-1/2*x*exp(25)+1/2*x^2+x)^2+(-2*x^4*log(x)-2*x^4 *exp(25)+4*x^5+2*x^4-4*x^3)*exp(-1/2*x*log(x)-1/2*x*exp(25)+1/2*x^2+x)-x^5 )/x^5,x)
Output:
(e**(2*x**2 + 4*x) + 6*x**x*e**(e**25*x + x**2 + 2*x)*x**2 + 4*x**(x/2)*e* *((e**25*x + 3*x**2 + 6*x)/2)*x + 4*x**((3*x)/2)*e**((3*e**25*x + x**2 + 2 *x)/2)*x**3 - x**(2*x)*e**(2*e**25*x)*x**5)/(x**(2*x)*e**(2*e**25*x)*x**4)