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

Optimal. Leaf size=37 \[ x+\frac {1}{20} e^{2 x} x \left (-x+\log \left (\frac {(3-x) \left (-e^x+5 x\right )}{x}\right )\right )^2 \]

________________________________________________________________________________________

Rubi [F]  time = 53.69, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \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 \end {gather*}

Verification is not applicable to the result.

[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 {gather*} \begin {aligned} \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\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [A]  time = 0.12, size = 62, normalized size = 1.68 \begin {gather*} \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 ) \end {gather*}

Antiderivative was successfully verified.

[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

________________________________________________________________________________________

fricas [B]  time = 0.88, size = 73, normalized size = 1.97 \begin {gather*} \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 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

________________________________________________________________________________________

giac [B]  time = 1.18, size = 77, normalized size = 2.08 \begin {gather*} \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 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

________________________________________________________________________________________

maple [C]  time = 0.40, size = 2157, normalized size = 58.30

method	result	size
risch	\(\text {Expression too large to display}\)	\(2157\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((2*x^2-5*x-3)*exp(x)^3+(-10*x^3+25*x^2+15*x)*exp(x)^2)*ln(((x-3)*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(((x-3)*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,metho
d=_RETURNVERBOSE)

[Out]

x+1/20*exp(2*x)*x^3-1/20*Pi^2*x*csgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x))/x)^5*exp(2*x)+1/10*Pi^2*x*csgn(I*(-
x^2-(-1/5*exp(x)-3)*x-3/5*exp(x))/x)^2*exp(2*x)-1/10*I*Pi*x^2*exp(2*x)-1/80*Pi^2*x*csgn(I*(-x^2-(-1/5*exp(x)-3
)*x-3/5*exp(x))/x)^6*exp(2*x)-1/10*ln(5)*x*exp(2*x)*ln(x)+1/20*Pi^2*x*csgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x
))/x)^3*exp(2*x)-1/20*Pi^2*x*csgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x))/x)^4*exp(2*x)+1/20*I*Pi*x*csgn(I*(-x^2
-(-1/5*exp(x)-3)*x-3/5*exp(x)))*csgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x))/x)^2*exp(2*x)*ln(x)+1/20*I*Pi*ln(5)
*x*csgn(I/x)*csgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x))/x)^2*exp(2*x)-1/20*I*Pi*x*csgn(I/x)*csgn(I*(-x^2-(-1/5
*exp(x)-3)*x-3/5*exp(x))/x)^2*exp(2*x)*ln(x)+1/20*Pi^2*x*csgn(I/x)*csgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x))/
x)^4*exp(2*x)+1/20*I*Pi*x^2*csgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x))/x)^3*exp(2*x)-1/80*Pi^2*x*csgn(I*(-x^2-
(-1/5*exp(x)-3)*x-3/5*exp(x)))^2*csgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x))/x)^4*exp(2*x)+(-1/10*x*exp(2*x)*ln
(x)-1/20*I*Pi*x*csgn(I/x)*csgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x)))*csgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x
))/x)*exp(2*x)+1/20*I*Pi*x*csgn(I/x)*csgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x))/x)^2*exp(2*x)-1/10*I*Pi*x*csgn
(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x))/x)^2*exp(2*x)-1/20*I*Pi*x*csgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x)))*c
sgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x))/x)^2*exp(2*x)-1/20*I*Pi*x*csgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x))
/x)^3*exp(2*x)+1/10*I*Pi*x*exp(2*x)+1/10*x*ln(5)*exp(2*x)-1/10*exp(2*x)*x^2)*ln(x^2+(-1/5*exp(x)-3)*x+3/5*exp(
x))-1/10*I*Pi*x*exp(2*x)*ln(x)-1/20*Pi^2*x*csgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x)))*csgn(I*(-x^2-(-1/5*exp(
x)-3)*x-3/5*exp(x))/x)^4*exp(2*x)-1/20*Pi^2*x*csgn(I/x)*csgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x)))*csgn(I*(-x
^2-(-1/5*exp(x)-3)*x-3/5*exp(x))/x)^3*exp(2*x)+1/20*I*Pi*x*csgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x))/x)^3*exp
(2*x)*ln(x)-1/20*I*Pi*ln(5)*x*csgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x))/x)^3*exp(2*x)+1/20*Pi^2*x*csgn(I/x)*c
sgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x)))*csgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x))/x)*exp(2*x)-1/80*Pi^2*x*
csgn(I/x)^2*csgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x)))^2*csgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x))/x)^2*exp(
2*x)+1/20*x*exp(2*x)*ln(x^2+(-1/5*exp(x)-3)*x+3/5*exp(x))^2-1/20*Pi^2*x*exp(2*x)+1/20*ln(5)^2*x*exp(2*x)+1/20*
x*exp(2*x)*ln(x)^2+1/10*x^2*exp(2*x)*ln(x)-1/10*x^2*ln(5)*exp(2*x)+1/10*I*Pi*ln(5)*x*exp(2*x)-1/40*Pi^2*x*csgn
(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x)))*csgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x))/x)^5*exp(2*x)+1/20*Pi^2*x*c
sgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x)))*csgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x))/x)^2*exp(2*x)+1/10*I*Pi*
x^2*csgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x))/x)^2*exp(2*x)-1/20*I*Pi*x^2*csgn(I/x)*csgn(I*(-x^2-(-1/5*exp(x)
-3)*x-3/5*exp(x))/x)^2*exp(2*x)-1/40*Pi^2*x*csgn(I/x)*csgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x)))^2*csgn(I*(-x
^2-(-1/5*exp(x)-3)*x-3/5*exp(x))/x)^3*exp(2*x)-1/20*Pi^2*x*csgn(I/x)*csgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x)
)/x)^2*exp(2*x)-1/80*Pi^2*x*csgn(I/x)^2*csgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x))/x)^4*exp(2*x)+1/20*I*Pi*x*c
sgn(I/x)*csgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x)))*csgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x))/x)*exp(2*x)*ln
(x)-1/20*I*Pi*ln(5)*x*csgn(I/x)*csgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x)))*csgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5
*exp(x))/x)*exp(2*x)+1/40*Pi^2*x*csgn(I/x)*csgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x))/x)^5*exp(2*x)+1/20*I*Pi*
x^2*csgn(I/x)*csgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x)))*csgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x))/x)*exp(2*
x)-1/20*I*Pi*ln(5)*x*csgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x)))*csgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x))/x)
^2*exp(2*x)+1/40*Pi^2*x*csgn(I/x)^2*csgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x)))*csgn(I*(-x^2-(-1/5*exp(x)-3)*x
-3/5*exp(x))/x)^3*exp(2*x)+1/20*I*Pi*x^2*csgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x)))*csgn(I*(-x^2-(-1/5*exp(x)
-3)*x-3/5*exp(x))/x)^2*exp(2*x)+1/10*I*Pi*x*csgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x))/x)^2*exp(2*x)*ln(x)-1/1
0*I*Pi*ln(5)*x*csgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x))/x)^2*exp(2*x)

________________________________________________________________________________________

maxima [B]  time = 0.75, size = 106, normalized size = 2.86 \begin {gather*} \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 \relax (x)\right )} e^{\left (2 \, x\right )} \log \left (x - 3\right ) + \frac {1}{20} \, {\left (x^{3} + 2 \, x^{2} \log \relax (x) + x \log \relax (x)^{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 \relax (x)\right )} e^{\left (2 \, x\right )}\right )} \log \left (-5 \, x + e^{x}\right ) + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

________________________________________________________________________________________

mupad [B]  time = 4.45, size = 69, normalized size = 1.86 \begin {gather*} 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} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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

________________________________________________________________________________________

sympy [F(-2)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: ShapeError} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2*x**2-5*x-3)*exp(x)**3+(-10*x**3+25*x**2+15*x)*exp(x)**2)*ln(((x-3)*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(((x-3)*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)

[Out]

Exception raised: ShapeError

________________________________________________________________________________________