Integrand size = 213, antiderivative size = 37 \[ \int \frac {300 x-100 x^2+e^x (-60+20 x)+e^{3 x} \left (-6 x-3 x^2-5 x^3+2 x^4\right )+e^{2 x} \left (55 x^3+15 x^4-10 x^5\right )+\left (e^{3 x} \left (6+6 x+10 x^2-4 x^3\right )+e^{2 x} \left (-70 x^2-40 x^3+20 x^4\right )\right ) \log \left (\frac {e^x (-3+x)+15 x-5 x^2}{x}\right )+\left (e^{3 x} \left (-3-5 x+2 x^2\right )+e^{2 x} \left (15 x+25 x^2-10 x^3\right )\right ) \log ^2\left (\frac {e^x (-3+x)+15 x-5 x^2}{x}\right )}{300 x-100 x^2+e^x (-60+20 x)} \, dx=x+\frac {1}{20} e^{2 x} x \left (-x+\log \left (\frac {(3-x) \left (-e^x+5 x\right )}{x}\right )\right )^2 \] Output:
1/20*(ln((5*x-exp(x))*(3-x)/x)-x)^2*exp(x)^2*x+x
Time = 0.08 (sec) , antiderivative size = 62, normalized size of antiderivative = 1.68 \[ \int \frac {300 x-100 x^2+e^x (-60+20 x)+e^{3 x} \left (-6 x-3 x^2-5 x^3+2 x^4\right )+e^{2 x} \left (55 x^3+15 x^4-10 x^5\right )+\left (e^{3 x} \left (6+6 x+10 x^2-4 x^3\right )+e^{2 x} \left (-70 x^2-40 x^3+20 x^4\right )\right ) \log \left (\frac {e^x (-3+x)+15 x-5 x^2}{x}\right )+\left (e^{3 x} \left (-3-5 x+2 x^2\right )+e^{2 x} \left (15 x+25 x^2-10 x^3\right )\right ) \log ^2\left (\frac {e^x (-3+x)+15 x-5 x^2}{x}\right )}{300 x-100 x^2+e^x (-60+20 x)} \, dx=\frac {1}{20} x \left (20+e^{2 x} x^2-2 e^{2 x} x \log \left (\frac {\left (e^x-5 x\right ) (-3+x)}{x}\right )+e^{2 x} \log ^2\left (\frac {\left (e^x-5 x\right ) (-3+x)}{x}\right )\right ) \] Input:
Integrate[(300*x - 100*x^2 + E^x*(-60 + 20*x) + E^(3*x)*(-6*x - 3*x^2 - 5* x^3 + 2*x^4) + E^(2*x)*(55*x^3 + 15*x^4 - 10*x^5) + (E^(3*x)*(6 + 6*x + 10 *x^2 - 4*x^3) + E^(2*x)*(-70*x^2 - 40*x^3 + 20*x^4))*Log[(E^x*(-3 + x) + 1 5*x - 5*x^2)/x] + (E^(3*x)*(-3 - 5*x + 2*x^2) + E^(2*x)*(15*x + 25*x^2 - 1 0*x^3))*Log[(E^x*(-3 + x) + 15*x - 5*x^2)/x]^2)/(300*x - 100*x^2 + E^x*(-6 0 + 20*x)),x]
Output:
(x*(20 + E^(2*x)*x^2 - 2*E^(2*x)*x*Log[((E^x - 5*x)*(-3 + x))/x] + E^(2*x) *Log[((E^x - 5*x)*(-3 + x))/x]^2))/20
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.
| \(\displaystyle \int \frac {-100 x^2+\left (e^{3 x} \left (2 x^2-5 x-3\right )+e^{2 x} \left (-10 x^3+25 x^2+15 x\right )\right ) \log ^2\left (\frac {-5 x^2+15 x+e^x (x-3)}{x}\right )+e^{2 x} \left (-10 x^5+15 x^4+55 x^3\right )+e^{3 x} \left (2 x^4-5 x^3-3 x^2-6 x\right )+\left (e^{3 x} \left (-4 x^3+10 x^2+6 x+6\right )+e^{2 x} \left (20 x^4-40 x^3-70 x^2\right )\right ) \log \left (\frac {-5 x^2+15 x+e^x (x-3)}{x}\right )+300 x+e^x (20 x-60)}{-100 x^2+300 x+e^x (20 x-60)} \, dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {100 x^2-\left (e^{3 x} \left (2 x^2-5 x-3\right )+e^{2 x} \left (-10 x^3+25 x^2+15 x\right )\right ) \log ^2\left (\frac {-5 x^2+15 x+e^x (x-3)}{x}\right )-e^{2 x} \left (-10 x^5+15 x^4+55 x^3\right )-e^{3 x} \left (2 x^4-5 x^3-3 x^2-6 x\right )-\left (e^{3 x} \left (-4 x^3+10 x^2+6 x+6\right )+e^{2 x} \left (20 x^4-40 x^3-70 x^2\right )\right ) \log \left (\frac {-5 x^2+15 x+e^x (x-3)}{x}\right )-300 x-e^x (20 x-60)}{20 \left (e^x-5 x\right ) (3-x)}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {1}{20} \int \frac {100 x^2-300 x+\left (e^{3 x} \left (-2 x^2+5 x+3\right )-5 e^{2 x} \left (-2 x^3+5 x^2+3 x\right )\right ) \log ^2\left (-\frac {5 x^2-15 x+e^x (3-x)}{x}\right )+20 e^x (3-x)+e^{3 x} \left (-2 x^4+5 x^3+3 x^2+6 x\right )-5 e^{2 x} \left (-2 x^5+3 x^4+11 x^3\right )-2 \left (e^{3 x} \left (-2 x^3+5 x^2+3 x+3\right )-5 e^{2 x} \left (-2 x^4+4 x^3+7 x^2\right )\right ) \log \left (-\frac {5 x^2-15 x+e^x (3-x)}{x}\right )}{\left (e^x-5 x\right ) (3-x)}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {1}{20} \int \left (-\frac {250 (x-1) \left (x-\log \left (\frac {\left (e^x-5 x\right ) (x-3)}{x}\right )\right ) x^3}{e^x-5 x}-10 e^x (x-1) \left (x-\log \left (\frac {\left (e^x-5 x\right ) (x-3)}{x}\right )\right ) x-10 \left (5 x^4-5 \log \left (\frac {\left (e^x-5 x\right ) (x-3)}{x}\right ) x^3-5 x^3+5 \log \left (\frac {\left (e^x-5 x\right ) (x-3)}{x}\right ) x^2-2\right )+\frac {e^{2 x} \left (2 x^4-4 \log \left (\frac {\left (e^x-5 x\right ) (x-3)}{x}\right ) x^3-5 x^3+2 \log ^2\left (\frac {\left (e^x-5 x\right ) (x-3)}{x}\right ) x^2+10 \log \left (\frac {\left (e^x-5 x\right ) (x-3)}{x}\right ) x^2-3 x^2-5 \log ^2\left (\frac {\left (e^x-5 x\right ) (x-3)}{x}\right ) x+6 \log \left (\frac {\left (e^x-5 x\right ) (x-3)}{x}\right ) x-6 x-3 \log ^2\left (\frac {\left (e^x-5 x\right ) (x-3)}{x}\right )+6 \log \left (\frac {\left (e^x-5 x\right ) (x-3)}{x}\right )\right )}{x-3}\right )dx\) |
| \(\Big \downarrow \) 7299 |
| \(\displaystyle \frac {1}{20} \int \left (-\frac {250 (x-1) \left (x-\log \left (\frac {\left (e^x-5 x\right ) (x-3)}{x}\right )\right ) x^3}{e^x-5 x}-10 e^x (x-1) \left (x-\log \left (\frac {\left (e^x-5 x\right ) (x-3)}{x}\right )\right ) x-10 \left (5 x^4-5 \log \left (\frac {\left (e^x-5 x\right ) (x-3)}{x}\right ) x^3-5 x^3+5 \log \left (\frac {\left (e^x-5 x\right ) (x-3)}{x}\right ) x^2-2\right )+\frac {e^{2 x} \left (2 x^4-4 \log \left (\frac {\left (e^x-5 x\right ) (x-3)}{x}\right ) x^3-5 x^3+2 \log ^2\left (\frac {\left (e^x-5 x\right ) (x-3)}{x}\right ) x^2+10 \log \left (\frac {\left (e^x-5 x\right ) (x-3)}{x}\right ) x^2-3 x^2-5 \log ^2\left (\frac {\left (e^x-5 x\right ) (x-3)}{x}\right ) x+6 \log \left (\frac {\left (e^x-5 x\right ) (x-3)}{x}\right ) x-6 x-3 \log ^2\left (\frac {\left (e^x-5 x\right ) (x-3)}{x}\right )+6 \log \left (\frac {\left (e^x-5 x\right ) (x-3)}{x}\right )\right )}{x-3}\right )dx\) |
Input:
Int[(300*x - 100*x^2 + E^x*(-60 + 20*x) + E^(3*x)*(-6*x - 3*x^2 - 5*x^3 + 2*x^4) + E^(2*x)*(55*x^3 + 15*x^4 - 10*x^5) + (E^(3*x)*(6 + 6*x + 10*x^2 - 4*x^3) + E^(2*x)*(-70*x^2 - 40*x^3 + 20*x^4))*Log[(E^x*(-3 + x) + 15*x - 5*x^2)/x] + (E^(3*x)*(-3 - 5*x + 2*x^2) + E^(2*x)*(15*x + 25*x^2 - 10*x^3) )*Log[(E^x*(-3 + x) + 15*x - 5*x^2)/x]^2)/(300*x - 100*x^2 + E^x*(-60 + 20 *x)),x]
Output:
$Aborted
Leaf count of result is larger than twice the leaf count of optimal. \(70\) vs. \(2(33)=66\).
Time = 2.68 (sec) , antiderivative size = 71, normalized size of antiderivative = 1.92
| method | result | size |
| parallelrisch | \(\frac {{\mathrm e}^{2 x} x^{3}}{20}-\frac {\ln \left (\frac {\left (-3+x \right ) {\mathrm e}^{x}-5 x^{2}+15 x}{x}\right ) {\mathrm e}^{2 x} x^{2}}{10}+\frac {\ln \left (\frac {\left (-3+x \right ) {\mathrm e}^{x}-5 x^{2}+15 x}{x}\right )^{2} {\mathrm e}^{2 x} x}{20}+\frac {3}{2}+x\) | \(71\) |
| risch | \(\text {Expression too large to display}\) | \(2157\) |
Input:
int((((2*x^2-5*x-3)*exp(x)^3+(-10*x^3+25*x^2+15*x)*exp(x)^2)*ln(((-3+x)*ex p(x)-5*x^2+15*x)/x)^2+((-4*x^3+10*x^2+6*x+6)*exp(x)^3+(20*x^4-40*x^3-70*x^ 2)*exp(x)^2)*ln(((-3+x)*exp(x)-5*x^2+15*x)/x)+(2*x^4-5*x^3-3*x^2-6*x)*exp( x)^3+(-10*x^5+15*x^4+55*x^3)*exp(x)^2+(20*x-60)*exp(x)-100*x^2+300*x)/((20 *x-60)*exp(x)-100*x^2+300*x),x,method=_RETURNVERBOSE)
Output:
1/20*exp(x)^2*x^3-1/10*exp(x)^2*ln(((-3+x)*exp(x)-5*x^2+15*x)/x)*x^2+1/20* exp(x)^2*ln(((-3+x)*exp(x)-5*x^2+15*x)/x)^2*x+3/2+x
Leaf count of result is larger than twice the leaf count of optimal. 73 vs. \(2 (32) = 64\).
Time = 0.09 (sec) , antiderivative size = 73, normalized size of antiderivative = 1.97 \[ \int \frac {300 x-100 x^2+e^x (-60+20 x)+e^{3 x} \left (-6 x-3 x^2-5 x^3+2 x^4\right )+e^{2 x} \left (55 x^3+15 x^4-10 x^5\right )+\left (e^{3 x} \left (6+6 x+10 x^2-4 x^3\right )+e^{2 x} \left (-70 x^2-40 x^3+20 x^4\right )\right ) \log \left (\frac {e^x (-3+x)+15 x-5 x^2}{x}\right )+\left (e^{3 x} \left (-3-5 x+2 x^2\right )+e^{2 x} \left (15 x+25 x^2-10 x^3\right )\right ) \log ^2\left (\frac {e^x (-3+x)+15 x-5 x^2}{x}\right )}{300 x-100 x^2+e^x (-60+20 x)} \, dx=\frac {1}{20} \, x^{3} e^{\left (2 \, x\right )} - \frac {1}{10} \, x^{2} e^{\left (2 \, x\right )} \log \left (-\frac {5 \, x^{2} - {\left (x - 3\right )} e^{x} - 15 \, x}{x}\right ) + \frac {1}{20} \, x e^{\left (2 \, x\right )} \log \left (-\frac {5 \, x^{2} - {\left (x - 3\right )} e^{x} - 15 \, x}{x}\right )^{2} + x \] Input:
integrate((((2*x^2-5*x-3)*exp(x)^3+(-10*x^3+25*x^2+15*x)*exp(x)^2)*log(((- 3+x)*exp(x)-5*x^2+15*x)/x)^2+((-4*x^3+10*x^2+6*x+6)*exp(x)^3+(20*x^4-40*x^ 3-70*x^2)*exp(x)^2)*log(((-3+x)*exp(x)-5*x^2+15*x)/x)+(2*x^4-5*x^3-3*x^2-6 *x)*exp(x)^3+(-10*x^5+15*x^4+55*x^3)*exp(x)^2+(20*x-60)*exp(x)-100*x^2+300 *x)/((20*x-60)*exp(x)-100*x^2+300*x),x, algorithm="fricas")
Output:
1/20*x^3*e^(2*x) - 1/10*x^2*e^(2*x)*log(-(5*x^2 - (x - 3)*e^x - 15*x)/x) + 1/20*x*e^(2*x)*log(-(5*x^2 - (x - 3)*e^x - 15*x)/x)^2 + x
Timed out. \[ \int \frac {300 x-100 x^2+e^x (-60+20 x)+e^{3 x} \left (-6 x-3 x^2-5 x^3+2 x^4\right )+e^{2 x} \left (55 x^3+15 x^4-10 x^5\right )+\left (e^{3 x} \left (6+6 x+10 x^2-4 x^3\right )+e^{2 x} \left (-70 x^2-40 x^3+20 x^4\right )\right ) \log \left (\frac {e^x (-3+x)+15 x-5 x^2}{x}\right )+\left (e^{3 x} \left (-3-5 x+2 x^2\right )+e^{2 x} \left (15 x+25 x^2-10 x^3\right )\right ) \log ^2\left (\frac {e^x (-3+x)+15 x-5 x^2}{x}\right )}{300 x-100 x^2+e^x (-60+20 x)} \, dx=\text {Timed out} \] Input:
integrate((((2*x**2-5*x-3)*exp(x)**3+(-10*x**3+25*x**2+15*x)*exp(x)**2)*ln (((-3+x)*exp(x)-5*x**2+15*x)/x)**2+((-4*x**3+10*x**2+6*x+6)*exp(x)**3+(20* x**4-40*x**3-70*x**2)*exp(x)**2)*ln(((-3+x)*exp(x)-5*x**2+15*x)/x)+(2*x**4 -5*x**3-3*x**2-6*x)*exp(x)**3+(-10*x**5+15*x**4+55*x**3)*exp(x)**2+(20*x-6 0)*exp(x)-100*x**2+300*x)/((20*x-60)*exp(x)-100*x**2+300*x),x)
Output:
Timed out
Leaf count of result is larger than twice the leaf count of optimal. 106 vs. \(2 (32) = 64\).
Time = 0.09 (sec) , antiderivative size = 106, normalized size of antiderivative = 2.86 \[ \int \frac {300 x-100 x^2+e^x (-60+20 x)+e^{3 x} \left (-6 x-3 x^2-5 x^3+2 x^4\right )+e^{2 x} \left (55 x^3+15 x^4-10 x^5\right )+\left (e^{3 x} \left (6+6 x+10 x^2-4 x^3\right )+e^{2 x} \left (-70 x^2-40 x^3+20 x^4\right )\right ) \log \left (\frac {e^x (-3+x)+15 x-5 x^2}{x}\right )+\left (e^{3 x} \left (-3-5 x+2 x^2\right )+e^{2 x} \left (15 x+25 x^2-10 x^3\right )\right ) \log ^2\left (\frac {e^x (-3+x)+15 x-5 x^2}{x}\right )}{300 x-100 x^2+e^x (-60+20 x)} \, dx=\frac {1}{20} \, x e^{\left (2 \, x\right )} \log \left (x - 3\right )^{2} + \frac {1}{20} \, x e^{\left (2 \, x\right )} \log \left (-5 \, x + e^{x}\right )^{2} - \frac {1}{10} \, {\left (x^{2} + x \log \left (x\right )\right )} e^{\left (2 \, x\right )} \log \left (x - 3\right ) + \frac {1}{20} \, {\left (x^{3} + 2 \, x^{2} \log \left (x\right ) + x \log \left (x\right )^{2}\right )} e^{\left (2 \, x\right )} + \frac {1}{10} \, {\left (x e^{\left (2 \, x\right )} \log \left (x - 3\right ) - {\left (x^{2} + x \log \left (x\right )\right )} e^{\left (2 \, x\right )}\right )} \log \left (-5 \, x + e^{x}\right ) + x \] Input:
integrate((((2*x^2-5*x-3)*exp(x)^3+(-10*x^3+25*x^2+15*x)*exp(x)^2)*log(((- 3+x)*exp(x)-5*x^2+15*x)/x)^2+((-4*x^3+10*x^2+6*x+6)*exp(x)^3+(20*x^4-40*x^ 3-70*x^2)*exp(x)^2)*log(((-3+x)*exp(x)-5*x^2+15*x)/x)+(2*x^4-5*x^3-3*x^2-6 *x)*exp(x)^3+(-10*x^5+15*x^4+55*x^3)*exp(x)^2+(20*x-60)*exp(x)-100*x^2+300 *x)/((20*x-60)*exp(x)-100*x^2+300*x),x, algorithm="maxima")
Output:
1/20*x*e^(2*x)*log(x - 3)^2 + 1/20*x*e^(2*x)*log(-5*x + e^x)^2 - 1/10*(x^2 + x*log(x))*e^(2*x)*log(x - 3) + 1/20*(x^3 + 2*x^2*log(x) + x*log(x)^2)*e ^(2*x) + 1/10*(x*e^(2*x)*log(x - 3) - (x^2 + x*log(x))*e^(2*x))*log(-5*x + e^x) + x
Leaf count of result is larger than twice the leaf count of optimal. 77 vs. \(2 (32) = 64\).
Time = 0.56 (sec) , antiderivative size = 77, normalized size of antiderivative = 2.08 \[ \int \frac {300 x-100 x^2+e^x (-60+20 x)+e^{3 x} \left (-6 x-3 x^2-5 x^3+2 x^4\right )+e^{2 x} \left (55 x^3+15 x^4-10 x^5\right )+\left (e^{3 x} \left (6+6 x+10 x^2-4 x^3\right )+e^{2 x} \left (-70 x^2-40 x^3+20 x^4\right )\right ) \log \left (\frac {e^x (-3+x)+15 x-5 x^2}{x}\right )+\left (e^{3 x} \left (-3-5 x+2 x^2\right )+e^{2 x} \left (15 x+25 x^2-10 x^3\right )\right ) \log ^2\left (\frac {e^x (-3+x)+15 x-5 x^2}{x}\right )}{300 x-100 x^2+e^x (-60+20 x)} \, dx=\frac {1}{20} \, x^{3} e^{\left (2 \, x\right )} - \frac {1}{10} \, x^{2} e^{\left (2 \, x\right )} \log \left (-\frac {5 \, x^{2} - x e^{x} - 15 \, x + 3 \, e^{x}}{x}\right ) + \frac {1}{20} \, x e^{\left (2 \, x\right )} \log \left (-\frac {5 \, x^{2} - x e^{x} - 15 \, x + 3 \, e^{x}}{x}\right )^{2} + x \] Input:
integrate((((2*x^2-5*x-3)*exp(x)^3+(-10*x^3+25*x^2+15*x)*exp(x)^2)*log(((- 3+x)*exp(x)-5*x^2+15*x)/x)^2+((-4*x^3+10*x^2+6*x+6)*exp(x)^3+(20*x^4-40*x^ 3-70*x^2)*exp(x)^2)*log(((-3+x)*exp(x)-5*x^2+15*x)/x)+(2*x^4-5*x^3-3*x^2-6 *x)*exp(x)^3+(-10*x^5+15*x^4+55*x^3)*exp(x)^2+(20*x-60)*exp(x)-100*x^2+300 *x)/((20*x-60)*exp(x)-100*x^2+300*x),x, algorithm="giac")
Output:
1/20*x^3*e^(2*x) - 1/10*x^2*e^(2*x)*log(-(5*x^2 - x*e^x - 15*x + 3*e^x)/x) + 1/20*x*e^(2*x)*log(-(5*x^2 - x*e^x - 15*x + 3*e^x)/x)^2 + x
Time = 3.42 (sec) , antiderivative size = 69, normalized size of antiderivative = 1.86 \[ \int \frac {300 x-100 x^2+e^x (-60+20 x)+e^{3 x} \left (-6 x-3 x^2-5 x^3+2 x^4\right )+e^{2 x} \left (55 x^3+15 x^4-10 x^5\right )+\left (e^{3 x} \left (6+6 x+10 x^2-4 x^3\right )+e^{2 x} \left (-70 x^2-40 x^3+20 x^4\right )\right ) \log \left (\frac {e^x (-3+x)+15 x-5 x^2}{x}\right )+\left (e^{3 x} \left (-3-5 x+2 x^2\right )+e^{2 x} \left (15 x+25 x^2-10 x^3\right )\right ) \log ^2\left (\frac {e^x (-3+x)+15 x-5 x^2}{x}\right )}{300 x-100 x^2+e^x (-60+20 x)} \, dx=x+\frac {x^3\,{\mathrm {e}}^{2\,x}}{20}+\frac {x\,{\ln \left (\frac {15\,x+{\mathrm {e}}^x\,\left (x-3\right )-5\,x^2}{x}\right )}^2\,{\mathrm {e}}^{2\,x}}{20}-\frac {x^2\,\ln \left (\frac {15\,x+{\mathrm {e}}^x\,\left (x-3\right )-5\,x^2}{x}\right )\,{\mathrm {e}}^{2\,x}}{10} \] Input:
int((300*x + exp(x)*(20*x - 60) - exp(3*x)*(6*x + 3*x^2 + 5*x^3 - 2*x^4) - log((15*x + exp(x)*(x - 3) - 5*x^2)/x)^2*(exp(3*x)*(5*x - 2*x^2 + 3) - ex p(2*x)*(15*x + 25*x^2 - 10*x^3)) + exp(2*x)*(55*x^3 + 15*x^4 - 10*x^5) + l og((15*x + exp(x)*(x - 3) - 5*x^2)/x)*(exp(3*x)*(6*x + 10*x^2 - 4*x^3 + 6) - exp(2*x)*(70*x^2 + 40*x^3 - 20*x^4)) - 100*x^2)/(300*x + exp(x)*(20*x - 60) - 100*x^2),x)
Output:
x + (x^3*exp(2*x))/20 + (x*log((15*x + exp(x)*(x - 3) - 5*x^2)/x)^2*exp(2* x))/20 - (x^2*log((15*x + exp(x)*(x - 3) - 5*x^2)/x)*exp(2*x))/10
Time = 0.20 (sec) , antiderivative size = 78, normalized size of antiderivative = 2.11 \[ \int \frac {300 x-100 x^2+e^x (-60+20 x)+e^{3 x} \left (-6 x-3 x^2-5 x^3+2 x^4\right )+e^{2 x} \left (55 x^3+15 x^4-10 x^5\right )+\left (e^{3 x} \left (6+6 x+10 x^2-4 x^3\right )+e^{2 x} \left (-70 x^2-40 x^3+20 x^4\right )\right ) \log \left (\frac {e^x (-3+x)+15 x-5 x^2}{x}\right )+\left (e^{3 x} \left (-3-5 x+2 x^2\right )+e^{2 x} \left (15 x+25 x^2-10 x^3\right )\right ) \log ^2\left (\frac {e^x (-3+x)+15 x-5 x^2}{x}\right )}{300 x-100 x^2+e^x (-60+20 x)} \, dx=\frac {x \left (e^{2 x} \mathrm {log}\left (\frac {e^{x} x -3 e^{x}-5 x^{2}+15 x}{x}\right )^{2}-2 e^{2 x} \mathrm {log}\left (\frac {e^{x} x -3 e^{x}-5 x^{2}+15 x}{x}\right ) x +e^{2 x} x^{2}+20\right )}{20} \] Input:
int((((2*x^2-5*x-3)*exp(x)^3+(-10*x^3+25*x^2+15*x)*exp(x)^2)*log(((-3+x)*e xp(x)-5*x^2+15*x)/x)^2+((-4*x^3+10*x^2+6*x+6)*exp(x)^3+(20*x^4-40*x^3-70*x ^2)*exp(x)^2)*log(((-3+x)*exp(x)-5*x^2+15*x)/x)+(2*x^4-5*x^3-3*x^2-6*x)*ex p(x)^3+(-10*x^5+15*x^4+55*x^3)*exp(x)^2+(20*x-60)*exp(x)-100*x^2+300*x)/(( 20*x-60)*exp(x)-100*x^2+300*x),x)
Output:
(x*(e**(2*x)*log((e**x*x - 3*e**x - 5*x**2 + 15*x)/x)**2 - 2*e**(2*x)*log( (e**x*x - 3*e**x - 5*x**2 + 15*x)/x)*x + e**(2*x)*x**2 + 20))/20