\(\int \frac {300 x-100 x^2+e^x (-60+20 x)+e^{3 x} (-6 x-3 x^2-5 x^3+2 x^4)+e^{2 x} (55 x^3+15 x^4-10 x^5)+(e^{3 x} (6+6 x+10 x^2-4 x^3)+e^{2 x} (-70 x^2-40 x^3+20 x^4)) \log (\frac {e^x (-3+x)+15 x-5 x^2}{x})+(e^{3 x} (-3-5 x+2 x^2)+e^{2 x} (15 x+25 x^2-10 x^3)) \log ^2(\frac {e^x (-3+x)+15 x-5 x^2}{x})}{300 x-100 x^2+e^x (-60+20 x)} \, dx\) [6877]

Optimal result

Integrand size = 213, antiderivative size = 37 \[ \int \frac {300 x-100 x^2+e^x (-60+20 x)+e^{3 x} \left (-6 x-3 x^2-5 x^3+2 x^4\right )+e^{2 x} \left (55 x^3+15 x^4-10 x^5\right )+\left (e^{3 x} \left (6+6 x+10 x^2-4 x^3\right )+e^{2 x} \left (-70 x^2-40 x^3+20 x^4\right )\right ) \log \left (\frac {e^x (-3+x)+15 x-5 x^2}{x}\right )+\left (e^{3 x} \left (-3-5 x+2 x^2\right )+e^{2 x} \left (15 x+25 x^2-10 x^3\right )\right ) \log ^2\left (\frac {e^x (-3+x)+15 x-5 x^2}{x}\right )}{300 x-100 x^2+e^x (-60+20 x)} \, dx=x+\frac {1}{20} e^{2 x} x \left (-x+\log \left (\frac {(3-x) \left (-e^x+5 x\right )}{x}\right )\right )^2 \]

[Out]

1/20*(ln((5*x-exp(x))*(-x+3)/x)-x)^2*exp(x)^2*x+x

Rubi [F]

\[ \int \frac {300 x-100 x^2+e^x (-60+20 x)+e^{3 x} \left (-6 x-3 x^2-5 x^3+2 x^4\right )+e^{2 x} \left (55 x^3+15 x^4-10 x^5\right )+\left (e^{3 x} \left (6+6 x+10 x^2-4 x^3\right )+e^{2 x} \left (-70 x^2-40 x^3+20 x^4\right )\right ) \log \left (\frac {e^x (-3+x)+15 x-5 x^2}{x}\right )+\left (e^{3 x} \left (-3-5 x+2 x^2\right )+e^{2 x} \left (15 x+25 x^2-10 x^3\right )\right ) \log ^2\left (\frac {e^x (-3+x)+15 x-5 x^2}{x}\right )}{300 x-100 x^2+e^x (-60+20 x)} \, dx=\int \frac {300 x-100 x^2+e^x (-60+20 x)+e^{3 x} \left (-6 x-3 x^2-5 x^3+2 x^4\right )+e^{2 x} \left (55 x^3+15 x^4-10 x^5\right )+\left (e^{3 x} \left (6+6 x+10 x^2-4 x^3\right )+e^{2 x} \left (-70 x^2-40 x^3+20 x^4\right )\right ) \log \left (\frac {e^x (-3+x)+15 x-5 x^2}{x}\right )+\left (e^{3 x} \left (-3-5 x+2 x^2\right )+e^{2 x} \left (15 x+25 x^2-10 x^3\right )\right ) \log ^2\left (\frac {e^x (-3+x)+15 x-5 x^2}{x}\right )}{300 x-100 x^2+e^x (-60+20 x)} \, dx \]

[In]

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]

[Out]

(-13*E^x)/2 + (7*E^(2*x))/40 - (67*x)/8 + (27*E^x*x)/8 - (E^(2*x)*x)/40 - (15*x^2)/8 - (3*E^x*x^2)/4 + (E^(2*x
)*x^3)/20 - (5*x^4)/48 - x^5/8 - (E^6*ExpIntegralEi[-2*(3 - x)])/8 - (3*E^3*ExpIntegralEi[-3 + x])/2 + (3*ExpI
ntegralEi[x])/2 - ExpIntegralEi[2*x]/40 + (3*E^6*(3 - x)*ExpIntegralEi[-6 + 2*x])/10 - (225*Log[3 - x])/8 + (3
*E^x*Log[-(((E^x - 5*x)*(3 - x))/x)])/2 - (E^(2*x)*Log[-(((E^x - 5*x)*(3 - x))/x)])/40 - (3*E^x*x*Log[-(((E^x
- 5*x)*(3 - x))/x)])/2 + (E^(2*x)*x*Log[-(((E^x - 5*x)*(3 - x))/x)])/20 + (E^x*x^2*Log[-(((E^x - 5*x)*(3 - x))
/x)])/2 - (E^(2*x)*x^2*Log[-(((E^x - 5*x)*(3 - x))/x)])/10 - (5*x^3*Log[-(((E^x - 5*x)*(3 - x))/x)])/6 + (5*x^
4*Log[-(((E^x - 5*x)*(3 - x))/x)])/8 + (3*E^6*ExpIntegralEi[-2*(3 - x)]*Log[-(((E^x - 5*x)*(3 - x))/x)])/10 +
(15*Defer[Int][E^x/(E^x - 5*x), x])/2 - 15*Defer[Int][(E^x*x)/(E^x - 5*x), x] - (25*Defer[Int][x^2/(E^x - 5*x)
, x])/8 + 10*Defer[Int][(E^x*x^2)/(E^x - 5*x), x] + (125*Defer[Int][x^3/(E^x - 5*x), x])/24 - (25*Log[-(((E^x
- 5*x)*(3 - x))/x)]*Defer[Int][x^3/(E^x - 5*x), x])/2 - (5*Defer[Int][(E^x*x^3)/(E^x - 5*x), x])/2 + (25*Defer
[Int][x^4/(E^x - 5*x), x])/24 + (25*Log[-(((E^x - 5*x)*(3 - x))/x)]*Defer[Int][x^4/(E^x - 5*x), x])/2 - (25*De
fer[Int][x^5/(E^x - 5*x), x])/8 + (3*E^6*Defer[Int][ExpIntegralEi[-6 + 2*x]/(E^x - 5*x), x])/2 - (3*E^6*Defer[
Int][ExpIntegralEi[-6 + 2*x]/(-3 + x), x])/10 + (3*E^6*Defer[Int][ExpIntegralEi[-6 + 2*x]/x, x])/10 - (3*E^6*D
efer[Int][(x*ExpIntegralEi[-6 + 2*x])/(E^x - 5*x), x])/2 + Defer[Int][E^(2*x)*Log[((E^x - 5*x)*(-3 + x))/x]^2,
x]/20 + Defer[Int][E^(2*x)*x*Log[((E^x - 5*x)*(-3 + x))/x]^2, x]/10 + (25*Defer[Int][Defer[Int][x^3/(E^x - 5*
x), x], x])/2 - (125*Defer[Int][Defer[Int][x^3/(E^x - 5*x), x]/(E^x - 5*x), x])/2 + (25*Defer[Int][Defer[Int][
x^3/(E^x - 5*x), x]/(-3 + x), x])/2 - (25*Defer[Int][Defer[Int][x^3/(E^x - 5*x), x]/x, x])/2 + (125*Defer[Int]
[(x*Defer[Int][x^3/(E^x - 5*x), x])/(E^x - 5*x), x])/2 - (25*Defer[Int][Defer[Int][x^4/(E^x - 5*x), x], x])/2
+ (125*Defer[Int][Defer[Int][x^4/(E^x - 5*x), x]/(E^x - 5*x), x])/2 - (25*Defer[Int][Defer[Int][x^4/(E^x - 5*x
), x]/(-3 + x), x])/2 + (25*Defer[Int][Defer[Int][x^4/(E^x - 5*x), x]/x, x])/2 - (125*Defer[Int][(x*Defer[Int]
[x^4/(E^x - 5*x), x])/(E^x - 5*x), x])/2

Rubi steps \begin{align*} \text {integral}& = \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 )}{20 \left (e^x-5 x\right ) (3-x)} \, dx \\ & = \frac {1}{20} \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 )}{\left (e^x-5 x\right ) (3-x)} \, dx \\ & = \frac {1}{20} \int \left (-10 e^x (-1+x) x \left (x-\log \left (\frac {\left (e^x-5 x\right ) (-3+x)}{x}\right )\right )-\frac {250 (-1+x) x^3 \left (x-\log \left (\frac {\left (e^x-5 x\right ) (-3+x)}{x}\right )\right )}{e^x-5 x}-10 \left (-2-5 x^3+5 x^4+5 x^2 \log \left (\frac {\left (e^x-5 x\right ) (-3+x)}{x}\right )-5 x^3 \log \left (\frac {\left (e^x-5 x\right ) (-3+x)}{x}\right )\right )+\frac {e^{2 x} \left (-6 x-3 x^2-5 x^3+2 x^4+6 \log \left (\frac {\left (e^x-5 x\right ) (-3+x)}{x}\right )+6 x \log \left (\frac {\left (e^x-5 x\right ) (-3+x)}{x}\right )+10 x^2 \log \left (\frac {\left (e^x-5 x\right ) (-3+x)}{x}\right )-4 x^3 \log \left (\frac {\left (e^x-5 x\right ) (-3+x)}{x}\right )-3 \log ^2\left (\frac {\left (e^x-5 x\right ) (-3+x)}{x}\right )-5 x \log ^2\left (\frac {\left (e^x-5 x\right ) (-3+x)}{x}\right )+2 x^2 \log ^2\left (\frac {\left (e^x-5 x\right ) (-3+x)}{x}\right )\right )}{-3+x}\right ) \, dx \\ & = \frac {1}{20} \int \frac {e^{2 x} \left (-6 x-3 x^2-5 x^3+2 x^4+6 \log \left (\frac {\left (e^x-5 x\right ) (-3+x)}{x}\right )+6 x \log \left (\frac {\left (e^x-5 x\right ) (-3+x)}{x}\right )+10 x^2 \log \left (\frac {\left (e^x-5 x\right ) (-3+x)}{x}\right )-4 x^3 \log \left (\frac {\left (e^x-5 x\right ) (-3+x)}{x}\right )-3 \log ^2\left (\frac {\left (e^x-5 x\right ) (-3+x)}{x}\right )-5 x \log ^2\left (\frac {\left (e^x-5 x\right ) (-3+x)}{x}\right )+2 x^2 \log ^2\left (\frac {\left (e^x-5 x\right ) (-3+x)}{x}\right )\right )}{-3+x} \, dx-\frac {1}{2} \int e^x (-1+x) x \left (x-\log \left (\frac {\left (e^x-5 x\right ) (-3+x)}{x}\right )\right ) \, dx-\frac {1}{2} \int \left (-2-5 x^3+5 x^4+5 x^2 \log \left (\frac {\left (e^x-5 x\right ) (-3+x)}{x}\right )-5 x^3 \log \left (\frac {\left (e^x-5 x\right ) (-3+x)}{x}\right )\right ) \, dx-\frac {25}{2} \int \frac {(-1+x) x^3 \left (x-\log \left (\frac {\left (e^x-5 x\right ) (-3+x)}{x}\right )\right )}{e^x-5 x} \, dx \\ & = x+\frac {5 x^4}{8}-\frac {x^5}{2}+\frac {1}{20} \int \frac {e^{2 x} \left (-x \left (-6-3 x-5 x^2+2 x^3\right )-\left (6+6 x+10 x^2-4 x^3\right ) \log \left (\frac {\left (e^x-5 x\right ) (-3+x)}{x}\right )-\left (-3-5 x+2 x^2\right ) \log ^2\left (\frac {\left (e^x-5 x\right ) (-3+x)}{x}\right )\right )}{3-x} \, dx-\frac {1}{2} \int \left (e^x (-1+x) x^2-e^x (-1+x) x \log \left (\frac {\left (e^x-5 x\right ) (-3+x)}{x}\right )\right ) \, dx-\frac {5}{2} \int x^2 \log \left (\frac {\left (e^x-5 x\right ) (-3+x)}{x}\right ) \, dx+\frac {5}{2} \int x^3 \log \left (\frac {\left (e^x-5 x\right ) (-3+x)}{x}\right ) \, dx-\frac {25}{2} \int \left (-\frac {x^3 \left (x-\log \left (\frac {\left (e^x-5 x\right ) (-3+x)}{x}\right )\right )}{e^x-5 x}+\frac {x^4 \left (x-\log \left (\frac {\left (e^x-5 x\right ) (-3+x)}{x}\right )\right )}{e^x-5 x}\right ) \, dx \\ & = x+\frac {5 x^4}{8}-\frac {x^5}{2}-\frac {5}{6} x^3 \log \left (-\frac {\left (e^x-5 x\right ) (3-x)}{x}\right )+\frac {5}{8} x^4 \log \left (-\frac {\left (e^x-5 x\right ) (3-x)}{x}\right )+\frac {1}{20} \int \left (\frac {e^{2 x} x \left (-6-3 x-5 x^2+2 x^3\right )}{-3+x}-\frac {2 e^{2 x} \left (-3-3 x-5 x^2+2 x^3\right ) \log \left (\frac {\left (e^x-5 x\right ) (-3+x)}{x}\right )}{-3+x}+e^{2 x} (1+2 x) \log ^2\left (\frac {\left (e^x-5 x\right ) (-3+x)}{x}\right )\right ) \, dx-\frac {1}{2} \int e^x (-1+x) x^2 \, dx+\frac {1}{2} \int e^x (-1+x) x \log \left (\frac {\left (e^x-5 x\right ) (-3+x)}{x}\right ) \, dx-\frac {5}{8} \int \frac {5 x^5-e^x x^3 \left (3-3 x+x^2\right )}{\left (e^x-5 x\right ) (3-x)} \, dx+\frac {5}{6} \int \frac {5 x^4-e^x x^2 \left (3-3 x+x^2\right )}{\left (e^x-5 x\right ) (3-x)} \, dx+\frac {25}{2} \int \frac {x^3 \left (x-\log \left (\frac {\left (e^x-5 x\right ) (-3+x)}{x}\right )\right )}{e^x-5 x} \, dx-\frac {25}{2} \int \frac {x^4 \left (x-\log \left (\frac {\left (e^x-5 x\right ) (-3+x)}{x}\right )\right )}{e^x-5 x} \, dx \\ & = x+\frac {5 x^4}{8}-\frac {x^5}{2}+\frac {3}{2} e^x \log \left (-\frac {\left (e^x-5 x\right ) (3-x)}{x}\right )-\frac {3}{2} e^x x \log \left (-\frac {\left (e^x-5 x\right ) (3-x)}{x}\right )+\frac {1}{2} e^x x^2 \log \left (-\frac {\left (e^x-5 x\right ) (3-x)}{x}\right )-\frac {5}{6} x^3 \log \left (-\frac {\left (e^x-5 x\right ) (3-x)}{x}\right )+\frac {5}{8} x^4 \log \left (-\frac {\left (e^x-5 x\right ) (3-x)}{x}\right )+\frac {1}{20} \int \frac {e^{2 x} x \left (-6-3 x-5 x^2+2 x^3\right )}{-3+x} \, dx+\frac {1}{20} \int e^{2 x} (1+2 x) \log ^2\left (\frac {\left (e^x-5 x\right ) (-3+x)}{x}\right ) \, dx-\frac {1}{10} \int \frac {e^{2 x} \left (-3-3 x-5 x^2+2 x^3\right ) \log \left (\frac {\left (e^x-5 x\right ) (-3+x)}{x}\right )}{-3+x} \, dx-\frac {1}{2} \int \left (-e^x x^2+e^x x^3\right ) \, dx-\frac {1}{2} \int \frac {e^x \left (3-3 x+x^2\right ) \left (5 x^2-e^x \left (3-3 x+x^2\right )\right )}{\left (e^x-5 x\right ) (3-x) x} \, dx-\frac {5}{8} \int \left (\frac {5 (-1+x) x^4}{e^x-5 x}+\frac {x^3 \left (3-3 x+x^2\right )}{-3+x}\right ) \, dx+\frac {5}{6} \int \left (\frac {5 (-1+x) x^3}{e^x-5 x}+\frac {x^2 \left (3-3 x+x^2\right )}{-3+x}\right ) \, dx+\frac {25}{2} \int \left (\frac {x^4}{e^x-5 x}-\frac {x^3 \log \left (\frac {\left (e^x-5 x\right ) (-3+x)}{x}\right )}{e^x-5 x}\right ) \, dx-\frac {25}{2} \int \left (\frac {x^5}{e^x-5 x}-\frac {x^4 \log \left (\frac {\left (e^x-5 x\right ) (-3+x)}{x}\right )}{e^x-5 x}\right ) \, dx \\ & = x+\frac {5 x^4}{8}-\frac {x^5}{2}+\frac {3}{2} e^x \log \left (-\frac {\left (e^x-5 x\right ) (3-x)}{x}\right )-\frac {1}{40} e^{2 x} \log \left (-\frac {\left (e^x-5 x\right ) (3-x)}{x}\right )-\frac {3}{2} e^x x \log \left (-\frac {\left (e^x-5 x\right ) (3-x)}{x}\right )+\frac {1}{20} e^{2 x} x \log \left (-\frac {\left (e^x-5 x\right ) (3-x)}{x}\right )+\frac {1}{2} e^x x^2 \log \left (-\frac {\left (e^x-5 x\right ) (3-x)}{x}\right )-\frac {1}{10} e^{2 x} x^2 \log \left (-\frac {\left (e^x-5 x\right ) (3-x)}{x}\right )-\frac {5}{6} x^3 \log \left (-\frac {\left (e^x-5 x\right ) (3-x)}{x}\right )+\frac {5}{8} x^4 \log \left (-\frac {\left (e^x-5 x\right ) (3-x)}{x}\right )+\frac {3}{10} e^6 \text {Ei}(-2 (3-x)) \log \left (-\frac {\left (e^x-5 x\right ) (3-x)}{x}\right )+\frac {1}{20} \int \left (-6 e^{2 x}-\frac {18 e^{2 x}}{-3+x}+e^{2 x} x^2+2 e^{2 x} x^3\right ) \, dx+\frac {1}{20} \int \left (e^{2 x} \log ^2\left (\frac {\left (e^x-5 x\right ) (-3+x)}{x}\right )+2 e^{2 x} x \log ^2\left (\frac {\left (e^x-5 x\right ) (-3+x)}{x}\right )\right ) \, dx+\frac {1}{10} \int \frac {\left (5 x^2-e^x \left (3-3 x+x^2\right )\right ) \left (e^{2 x} \left (1-2 x+4 x^2\right )-12 e^6 \text {Ei}(-6+2 x)\right )}{4 \left (e^x-5 x\right ) (3-x) x} \, dx+\frac {1}{2} \int e^x x^2 \, dx-\frac {1}{2} \int e^x x^3 \, dx-\frac {1}{2} \int \left (\frac {e^x \left (3-3 x+x^2\right )^2}{(-3+x) x}+\frac {5 e^x \left (-3+6 x-4 x^2+x^3\right )}{e^x-5 x}\right ) \, dx-\frac {5}{8} \int \frac {x^3 \left (3-3 x+x^2\right )}{-3+x} \, dx+\frac {5}{6} \int \frac {x^2 \left (3-3 x+x^2\right )}{-3+x} \, dx-\frac {25}{8} \int \frac {(-1+x) x^4}{e^x-5 x} \, dx+\frac {25}{6} \int \frac {(-1+x) x^3}{e^x-5 x} \, dx+\frac {25}{2} \int \frac {x^4}{e^x-5 x} \, dx-\frac {25}{2} \int \frac {x^5}{e^x-5 x} \, dx-\frac {25}{2} \int \frac {x^3 \log \left (\frac {\left (e^x-5 x\right ) (-3+x)}{x}\right )}{e^x-5 x} \, dx+\frac {25}{2} \int \frac {x^4 \log \left (\frac {\left (e^x-5 x\right ) (-3+x)}{x}\right )}{e^x-5 x} \, dx \\ & = x+\frac {e^x x^2}{2}-\frac {e^x x^3}{2}+\frac {5 x^4}{8}-\frac {x^5}{2}+\frac {3}{2} e^x \log \left (-\frac {\left (e^x-5 x\right ) (3-x)}{x}\right )-\frac {1}{40} e^{2 x} \log \left (-\frac {\left (e^x-5 x\right ) (3-x)}{x}\right )-\frac {3}{2} e^x x \log \left (-\frac {\left (e^x-5 x\right ) (3-x)}{x}\right )+\frac {1}{20} e^{2 x} x \log \left (-\frac {\left (e^x-5 x\right ) (3-x)}{x}\right )+\frac {1}{2} e^x x^2 \log \left (-\frac {\left (e^x-5 x\right ) (3-x)}{x}\right )-\frac {1}{10} e^{2 x} x^2 \log \left (-\frac {\left (e^x-5 x\right ) (3-x)}{x}\right )-\frac {5}{6} x^3 \log \left (-\frac {\left (e^x-5 x\right ) (3-x)}{x}\right )+\frac {5}{8} x^4 \log \left (-\frac {\left (e^x-5 x\right ) (3-x)}{x}\right )+\frac {3}{10} e^6 \text {Ei}(-2 (3-x)) \log \left (-\frac {\left (e^x-5 x\right ) (3-x)}{x}\right )+\frac {1}{40} \int \frac {\left (5 x^2-e^x \left (3-3 x+x^2\right )\right ) \left (e^{2 x} \left (1-2 x+4 x^2\right )-12 e^6 \text {Ei}(-6+2 x)\right )}{\left (e^x-5 x\right ) (3-x) x} \, dx+\frac {1}{20} \int e^{2 x} x^2 \, dx+\frac {1}{20} \int e^{2 x} \log ^2\left (\frac {\left (e^x-5 x\right ) (-3+x)}{x}\right ) \, dx+\frac {1}{10} \int e^{2 x} x^3 \, dx+\frac {1}{10} \int e^{2 x} x \log ^2\left (\frac {\left (e^x-5 x\right ) (-3+x)}{x}\right ) \, dx-\frac {3}{10} \int e^{2 x} \, dx-\frac {1}{2} \int \frac {e^x \left (3-3 x+x^2\right )^2}{(-3+x) x} \, dx-\frac {5}{8} \int \left (27+\frac {81}{-3+x}+9 x+3 x^2+x^4\right ) \, dx+\frac {5}{6} \int \left (9+\frac {27}{-3+x}+3 x+x^3\right ) \, dx-\frac {9}{10} \int \frac {e^{2 x}}{-3+x} \, dx+\frac {3}{2} \int e^x x^2 \, dx-\frac {5}{2} \int \frac {e^x \left (-3+6 x-4 x^2+x^3\right )}{e^x-5 x} \, dx-\frac {25}{8} \int \left (-\frac {x^4}{e^x-5 x}+\frac {x^5}{e^x-5 x}\right ) \, dx+\frac {25}{6} \int \left (-\frac {x^3}{e^x-5 x}+\frac {x^4}{e^x-5 x}\right ) \, dx+\frac {25}{2} \int \frac {x^4}{e^x-5 x} \, dx-\frac {25}{2} \int \frac {x^5}{e^x-5 x} \, dx+\frac {25}{2} \int \frac {\left (5 x^2-e^x \left (3-3 x+x^2\right )\right ) \int \frac {x^3}{e^x-5 x} \, dx}{\left (e^x-5 x\right ) (3-x) x} \, dx-\frac {25}{2} \int \frac {\left (5 x^2-e^x \left (3-3 x+x^2\right )\right ) \int \frac {x^4}{e^x-5 x} \, dx}{\left (e^x-5 x\right ) (3-x) x} \, dx-\frac {1}{2} \left (25 \log \left (\frac {\left (e^x-5 x\right ) (-3+x)}{x}\right )\right ) \int \frac {x^3}{e^x-5 x} \, dx+\frac {1}{2} \left (25 \log \left (\frac {\left (e^x-5 x\right ) (-3+x)}{x}\right )\right ) \int \frac {x^4}{e^x-5 x} \, dx-\int e^x x \, dx \\ & = -\frac {3 e^{2 x}}{20}-\frac {67 x}{8}-e^x x-\frac {25 x^2}{16}+2 e^x x^2+\frac {1}{40} e^{2 x} x^2-\frac {5 x^3}{8}-\frac {e^x x^3}{2}+\frac {1}{20} e^{2 x} x^3+\frac {5 x^4}{6}-\frac {5 x^5}{8}-\frac {9}{10} e^6 \text {Ei}(-2 (3-x))-\frac {225}{8} \log (3-x)+\frac {3}{2} e^x \log \left (-\frac {\left (e^x-5 x\right ) (3-x)}{x}\right )-\frac {1}{40} e^{2 x} \log \left (-\frac {\left (e^x-5 x\right ) (3-x)}{x}\right )-\frac {3}{2} e^x x \log \left (-\frac {\left (e^x-5 x\right ) (3-x)}{x}\right )+\frac {1}{20} e^{2 x} x \log \left (-\frac {\left (e^x-5 x\right ) (3-x)}{x}\right )+\frac {1}{2} e^x x^2 \log \left (-\frac {\left (e^x-5 x\right ) (3-x)}{x}\right )-\frac {1}{10} e^{2 x} x^2 \log \left (-\frac {\left (e^x-5 x\right ) (3-x)}{x}\right )-\frac {5}{6} x^3 \log \left (-\frac {\left (e^x-5 x\right ) (3-x)}{x}\right )+\frac {5}{8} x^4 \log \left (-\frac {\left (e^x-5 x\right ) (3-x)}{x}\right )+\frac {3}{10} e^6 \text {Ei}(-2 (3-x)) \log \left (-\frac {\left (e^x-5 x\right ) (3-x)}{x}\right )+\frac {1}{40} \int \left (5 e^x \left (-1+3 x-6 x^2+4 x^3\right )+\frac {e^{2 x} \left (3-9 x+19 x^2-14 x^3+4 x^4\right )}{(-3+x) x}+\frac {5 (-1+x) \left (25 x^2-50 x^3+100 x^4-12 e^6 \text {Ei}(-6+2 x)\right )}{e^x-5 x}+\frac {75 x^2-250 x^3+525 x^4-450 x^5+100 x^6-36 e^6 \text {Ei}(-6+2 x)+36 e^6 x \text {Ei}(-6+2 x)-12 e^6 x^2 \text {Ei}(-6+2 x)}{(-3+x) x}\right ) \, dx-\frac {1}{20} \int e^{2 x} x \, dx+\frac {1}{20} \int e^{2 x} \log ^2\left (\frac {\left (e^x-5 x\right ) (-3+x)}{x}\right ) \, dx+\frac {1}{10} \int e^{2 x} x \log ^2\left (\frac {\left (e^x-5 x\right ) (-3+x)}{x}\right ) \, dx-\frac {3}{20} \int e^{2 x} x^2 \, dx-\frac {1}{2} \int \left (6 e^x+\frac {3 e^x}{-3+x}-\frac {3 e^x}{x}-3 e^x x+e^x x^2\right ) \, dx-\frac {5}{2} \int \left (-\frac {3 e^x}{e^x-5 x}+\frac {6 e^x x}{e^x-5 x}-\frac {4 e^x x^2}{e^x-5 x}+\frac {e^x x^3}{e^x-5 x}\right ) \, dx-3 \int e^x x \, dx+\frac {25}{8} \int \frac {x^4}{e^x-5 x} \, dx-\frac {25}{8} \int \frac {x^5}{e^x-5 x} \, dx-\frac {25}{6} \int \frac {x^3}{e^x-5 x} \, dx+\frac {25}{6} \int \frac {x^4}{e^x-5 x} \, dx+\frac {25}{2} \int \frac {x^4}{e^x-5 x} \, dx-\frac {25}{2} \int \frac {x^5}{e^x-5 x} \, dx+\frac {25}{2} \int \left (\frac {5 (-1+x) \int \frac {x^3}{e^x-5 x} \, dx}{e^x-5 x}+\frac {\left (3-3 x+x^2\right ) \int \frac {x^3}{e^x-5 x} \, dx}{(-3+x) x}\right ) \, dx-\frac {25}{2} \int \left (\frac {5 (-1+x) \int \frac {x^4}{e^x-5 x} \, dx}{e^x-5 x}+\frac {\left (3-3 x+x^2\right ) \int \frac {x^4}{e^x-5 x} \, dx}{(-3+x) x}\right ) \, dx-\frac {1}{2} \left (25 \log \left (\frac {\left (e^x-5 x\right ) (-3+x)}{x}\right )\right ) \int \frac {x^3}{e^x-5 x} \, dx+\frac {1}{2} \left (25 \log \left (\frac {\left (e^x-5 x\right ) (-3+x)}{x}\right )\right ) \int \frac {x^4}{e^x-5 x} \, dx+\int e^x \, dx \\ & = e^x-\frac {3 e^{2 x}}{20}-\frac {67 x}{8}-4 e^x x-\frac {1}{40} e^{2 x} x-\frac {25 x^2}{16}+2 e^x x^2-\frac {1}{20} e^{2 x} x^2-\frac {5 x^3}{8}-\frac {e^x x^3}{2}+\frac {1}{20} e^{2 x} x^3+\frac {5 x^4}{6}-\frac {5 x^5}{8}-\frac {9}{10} e^6 \text {Ei}(-2 (3-x))-\frac {225}{8} \log (3-x)+\frac {3}{2} e^x \log \left (-\frac {\left (e^x-5 x\right ) (3-x)}{x}\right )-\frac {1}{40} e^{2 x} \log \left (-\frac {\left (e^x-5 x\right ) (3-x)}{x}\right )-\frac {3}{2} e^x x \log \left (-\frac {\left (e^x-5 x\right ) (3-x)}{x}\right )+\frac {1}{20} e^{2 x} x \log \left (-\frac {\left (e^x-5 x\right ) (3-x)}{x}\right )+\frac {1}{2} e^x x^2 \log \left (-\frac {\left (e^x-5 x\right ) (3-x)}{x}\right )-\frac {1}{10} e^{2 x} x^2 \log \left (-\frac {\left (e^x-5 x\right ) (3-x)}{x}\right )-\frac {5}{6} x^3 \log \left (-\frac {\left (e^x-5 x\right ) (3-x)}{x}\right )+\frac {5}{8} x^4 \log \left (-\frac {\left (e^x-5 x\right ) (3-x)}{x}\right )+\frac {3}{10} e^6 \text {Ei}(-2 (3-x)) \log \left (-\frac {\left (e^x-5 x\right ) (3-x)}{x}\right )+\frac {1}{40} \int e^{2 x} \, dx+\frac {1}{40} \int \frac {e^{2 x} \left (3-9 x+19 x^2-14 x^3+4 x^4\right )}{(-3+x) x} \, dx+\frac {1}{40} \int \frac {75 x^2-250 x^3+525 x^4-450 x^5+100 x^6-36 e^6 \text {Ei}(-6+2 x)+36 e^6 x \text {Ei}(-6+2 x)-12 e^6 x^2 \text {Ei}(-6+2 x)}{(-3+x) x} \, dx+\frac {1}{20} \int e^{2 x} \log ^2\left (\frac {\left (e^x-5 x\right ) (-3+x)}{x}\right ) \, dx+\frac {1}{10} \int e^{2 x} x \log ^2\left (\frac {\left (e^x-5 x\right ) (-3+x)}{x}\right ) \, dx+\frac {1}{8} \int e^x \left (-1+3 x-6 x^2+4 x^3\right ) \, dx+\frac {1}{8} \int \frac {(-1+x) \left (25 x^2-50 x^3+100 x^4-12 e^6 \text {Ei}(-6+2 x)\right )}{e^x-5 x} \, dx+\frac {3}{20} \int e^{2 x} x \, dx-\frac {1}{2} \int e^x x^2 \, dx-\frac {3}{2} \int \frac {e^x}{-3+x} \, dx+\frac {3}{2} \int \frac {e^x}{x} \, dx+\frac {3}{2} \int e^x x \, dx-\frac {5}{2} \int \frac {e^x x^3}{e^x-5 x} \, dx+\frac {25}{8} \int \frac {x^4}{e^x-5 x} \, dx-\frac {25}{8} \int \frac {x^5}{e^x-5 x} \, dx-\frac {25}{6} \int \frac {x^3}{e^x-5 x} \, dx+\frac {25}{6} \int \frac {x^4}{e^x-5 x} \, dx+\frac {15}{2} \int \frac {e^x}{e^x-5 x} \, dx+10 \int \frac {e^x x^2}{e^x-5 x} \, dx+\frac {25}{2} \int \frac {x^4}{e^x-5 x} \, dx-\frac {25}{2} \int \frac {x^5}{e^x-5 x} \, dx+\frac {25}{2} \int \frac {\left (3-3 x+x^2\right ) \int \frac {x^3}{e^x-5 x} \, dx}{(-3+x) x} \, dx-\frac {25}{2} \int \frac {\left (3-3 x+x^2\right ) \int \frac {x^4}{e^x-5 x} \, dx}{(-3+x) x} \, dx-15 \int \frac {e^x x}{e^x-5 x} \, dx+\frac {125}{2} \int \frac {(-1+x) \int \frac {x^3}{e^x-5 x} \, dx}{e^x-5 x} \, dx-\frac {125}{2} \int \frac {(-1+x) \int \frac {x^4}{e^x-5 x} \, dx}{e^x-5 x} \, dx-\frac {1}{2} \left (25 \log \left (\frac {\left (e^x-5 x\right ) (-3+x)}{x}\right )\right ) \int \frac {x^3}{e^x-5 x} \, dx+\frac {1}{2} \left (25 \log \left (\frac {\left (e^x-5 x\right ) (-3+x)}{x}\right )\right ) \int \frac {x^4}{e^x-5 x} \, dx \\ & = \text {Too large to display} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.13 (sec) , antiderivative size = 62, normalized size of antiderivative = 1.68 \[ \int \frac {300 x-100 x^2+e^x (-60+20 x)+e^{3 x} \left (-6 x-3 x^2-5 x^3+2 x^4\right )+e^{2 x} \left (55 x^3+15 x^4-10 x^5\right )+\left (e^{3 x} \left (6+6 x+10 x^2-4 x^3\right )+e^{2 x} \left (-70 x^2-40 x^3+20 x^4\right )\right ) \log \left (\frac {e^x (-3+x)+15 x-5 x^2}{x}\right )+\left (e^{3 x} \left (-3-5 x+2 x^2\right )+e^{2 x} \left (15 x+25 x^2-10 x^3\right )\right ) \log ^2\left (\frac {e^x (-3+x)+15 x-5 x^2}{x}\right )}{300 x-100 x^2+e^x (-60+20 x)} \, dx=\frac {1}{20} x \left (20+e^{2 x} x^2-2 e^{2 x} x \log \left (\frac {\left (e^x-5 x\right ) (-3+x)}{x}\right )+e^{2 x} \log ^2\left (\frac {\left (e^x-5 x\right ) (-3+x)}{x}\right )\right ) \]

[In]

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) +
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]

[Out]

(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))/2
0

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(70\) vs. \(2(33)=66\).

Time = 1.46 (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	\(\text {Expression too large to display}\)	\(2157\)

[In]

int((((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)*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,met
hod=_RETURNVERBOSE)

[Out]

1/20*exp(x)^2*x^3-1/10*ln(((-3+x)*exp(x)-5*x^2+15*x)/x)*exp(x)^2*x^2+1/20*ln(((-3+x)*exp(x)-5*x^2+15*x)/x)^2*e
xp(x)^2*x+3/2+x

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 73 vs. \(2 (32) = 64\).

Time = 0.24 (sec) , antiderivative size = 73, normalized size of antiderivative = 1.97 \[ \int \frac {300 x-100 x^2+e^x (-60+20 x)+e^{3 x} \left (-6 x-3 x^2-5 x^3+2 x^4\right )+e^{2 x} \left (55 x^3+15 x^4-10 x^5\right )+\left (e^{3 x} \left (6+6 x+10 x^2-4 x^3\right )+e^{2 x} \left (-70 x^2-40 x^3+20 x^4\right )\right ) \log \left (\frac {e^x (-3+x)+15 x-5 x^2}{x}\right )+\left (e^{3 x} \left (-3-5 x+2 x^2\right )+e^{2 x} \left (15 x+25 x^2-10 x^3\right )\right ) \log ^2\left (\frac {e^x (-3+x)+15 x-5 x^2}{x}\right )}{300 x-100 x^2+e^x (-60+20 x)} \, dx=\frac {1}{20} \, x^{3} e^{\left (2 \, x\right )} - \frac {1}{10} \, x^{2} e^{\left (2 \, x\right )} \log \left (-\frac {5 \, x^{2} - {\left (x - 3\right )} e^{x} - 15 \, x}{x}\right ) + \frac {1}{20} \, x e^{\left (2 \, x\right )} \log \left (-\frac {5 \, x^{2} - {\left (x - 3\right )} e^{x} - 15 \, x}{x}\right )^{2} + x \]

[In]

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")

[Out]

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

Sympy [F(-1)]

Timed out. \[ \int \frac {300 x-100 x^2+e^x (-60+20 x)+e^{3 x} \left (-6 x-3 x^2-5 x^3+2 x^4\right )+e^{2 x} \left (55 x^3+15 x^4-10 x^5\right )+\left (e^{3 x} \left (6+6 x+10 x^2-4 x^3\right )+e^{2 x} \left (-70 x^2-40 x^3+20 x^4\right )\right ) \log \left (\frac {e^x (-3+x)+15 x-5 x^2}{x}\right )+\left (e^{3 x} \left (-3-5 x+2 x^2\right )+e^{2 x} \left (15 x+25 x^2-10 x^3\right )\right ) \log ^2\left (\frac {e^x (-3+x)+15 x-5 x^2}{x}\right )}{300 x-100 x^2+e^x (-60+20 x)} \, dx=\text {Timed out} \]

[In]

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-60)*exp(x)-100*x**2+300*x)/((20*x-6
0)*exp(x)-100*x**2+300*x),x)

[Out]

Timed out

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 106 vs. \(2 (32) = 64\).

Time = 0.24 (sec) , antiderivative size = 106, normalized size of antiderivative = 2.86 \[ \int \frac {300 x-100 x^2+e^x (-60+20 x)+e^{3 x} \left (-6 x-3 x^2-5 x^3+2 x^4\right )+e^{2 x} \left (55 x^3+15 x^4-10 x^5\right )+\left (e^{3 x} \left (6+6 x+10 x^2-4 x^3\right )+e^{2 x} \left (-70 x^2-40 x^3+20 x^4\right )\right ) \log \left (\frac {e^x (-3+x)+15 x-5 x^2}{x}\right )+\left (e^{3 x} \left (-3-5 x+2 x^2\right )+e^{2 x} \left (15 x+25 x^2-10 x^3\right )\right ) \log ^2\left (\frac {e^x (-3+x)+15 x-5 x^2}{x}\right )}{300 x-100 x^2+e^x (-60+20 x)} \, dx=\frac {1}{20} \, x e^{\left (2 \, x\right )} \log \left (x - 3\right )^{2} + \frac {1}{20} \, x e^{\left (2 \, x\right )} \log \left (-5 \, x + e^{x}\right )^{2} - \frac {1}{10} \, {\left (x^{2} + x \log \left (x\right )\right )} e^{\left (2 \, x\right )} \log \left (x - 3\right ) + \frac {1}{20} \, {\left (x^{3} + 2 \, x^{2} \log \left (x\right ) + x \log \left (x\right )^{2}\right )} e^{\left (2 \, x\right )} + \frac {1}{10} \, {\left (x e^{\left (2 \, x\right )} \log \left (x - 3\right ) - {\left (x^{2} + x \log \left (x\right )\right )} e^{\left (2 \, x\right )}\right )} \log \left (-5 \, x + e^{x}\right ) + x \]

[In]

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")

[Out]

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

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 77 vs. \(2 (32) = 64\).

Time = 0.84 (sec) , antiderivative size = 77, normalized size of antiderivative = 2.08 \[ \int \frac {300 x-100 x^2+e^x (-60+20 x)+e^{3 x} \left (-6 x-3 x^2-5 x^3+2 x^4\right )+e^{2 x} \left (55 x^3+15 x^4-10 x^5\right )+\left (e^{3 x} \left (6+6 x+10 x^2-4 x^3\right )+e^{2 x} \left (-70 x^2-40 x^3+20 x^4\right )\right ) \log \left (\frac {e^x (-3+x)+15 x-5 x^2}{x}\right )+\left (e^{3 x} \left (-3-5 x+2 x^2\right )+e^{2 x} \left (15 x+25 x^2-10 x^3\right )\right ) \log ^2\left (\frac {e^x (-3+x)+15 x-5 x^2}{x}\right )}{300 x-100 x^2+e^x (-60+20 x)} \, dx=\frac {1}{20} \, x^{3} e^{\left (2 \, x\right )} - \frac {1}{10} \, x^{2} e^{\left (2 \, x\right )} \log \left (-\frac {5 \, x^{2} - x e^{x} - 15 \, x + 3 \, e^{x}}{x}\right ) + \frac {1}{20} \, x e^{\left (2 \, x\right )} \log \left (-\frac {5 \, x^{2} - x e^{x} - 15 \, x + 3 \, e^{x}}{x}\right )^{2} + x \]

[In]

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")

[Out]

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

Mupad [B] (verification not implemented)

Time = 13.28 (sec) , antiderivative size = 69, normalized size of antiderivative = 1.86 \[ \int \frac {300 x-100 x^2+e^x (-60+20 x)+e^{3 x} \left (-6 x-3 x^2-5 x^3+2 x^4\right )+e^{2 x} \left (55 x^3+15 x^4-10 x^5\right )+\left (e^{3 x} \left (6+6 x+10 x^2-4 x^3\right )+e^{2 x} \left (-70 x^2-40 x^3+20 x^4\right )\right ) \log \left (\frac {e^x (-3+x)+15 x-5 x^2}{x}\right )+\left (e^{3 x} \left (-3-5 x+2 x^2\right )+e^{2 x} \left (15 x+25 x^2-10 x^3\right )\right ) \log ^2\left (\frac {e^x (-3+x)+15 x-5 x^2}{x}\right )}{300 x-100 x^2+e^x (-60+20 x)} \, dx=x+\frac {x^3\,{\mathrm {e}}^{2\,x}}{20}+\frac {x\,{\ln \left (\frac {15\,x+{\mathrm {e}}^x\,\left (x-3\right )-5\,x^2}{x}\right )}^2\,{\mathrm {e}}^{2\,x}}{20}-\frac {x^2\,\ln \left (\frac {15\,x+{\mathrm {e}}^x\,\left (x-3\right )-5\,x^2}{x}\right )\,{\mathrm {e}}^{2\,x}}{10} \]

[In]

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) - exp(2*x)*(15*x + 25*x^2 - 10*x^3)) + exp(2*x)*(55*x^3 + 15*x^4 - 10*x^5) +
log((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)

[Out]

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