\(\int \frac {e^{x^2} (16 x^2-8 x^3+x^4)+(-225+195 x-85 x^2+15 x^3) \log (-\frac {4}{-3+x})+e^{x^2} (360-306 x+110 x^2+74 x^3-78 x^4+22 x^5-2 x^6) \log (-\frac {4}{-3+x}) \log (5 \log (-\frac {4}{-3+x}))+e^{2 x^2} (-144+120 x-33 x^2+3 x^3) \log (-\frac {4}{-3+x}) \log ^2(5 \log (-\frac {4}{-3+x}))}{(-225+75 x) \log (-\frac {4}{-3+x})+e^{x^2} (360-210 x+30 x^2) \log (-\frac {4}{-3+x}) \log (5 \log (-\frac {4}{-3+x}))+e^{2 x^2} (-144+120 x-33 x^2+3 x^3) \log (-\frac {4}{-3+x}) \log ^2(5 \log (-\frac {4}{-3+x}))} \, dx\) [9751]

Optimal result

Integrand size = 241, antiderivative size = 38 \[ \int \frac {e^{x^2} \left (16 x^2-8 x^3+x^4\right )+\left (-225+195 x-85 x^2+15 x^3\right ) \log \left (-\frac {4}{-3+x}\right )+e^{x^2} \left (360-306 x+110 x^2+74 x^3-78 x^4+22 x^5-2 x^6\right ) \log \left (-\frac {4}{-3+x}\right ) \log \left (5 \log \left (-\frac {4}{-3+x}\right )\right )+e^{2 x^2} \left (-144+120 x-33 x^2+3 x^3\right ) \log \left (-\frac {4}{-3+x}\right ) \log ^2\left (5 \log \left (-\frac {4}{-3+x}\right )\right )}{(-225+75 x) \log \left (-\frac {4}{-3+x}\right )+e^{x^2} \left (360-210 x+30 x^2\right ) \log \left (-\frac {4}{-3+x}\right ) \log \left (5 \log \left (-\frac {4}{-3+x}\right )\right )+e^{2 x^2} \left (-144+120 x-33 x^2+3 x^3\right ) \log \left (-\frac {4}{-3+x}\right ) \log ^2\left (5 \log \left (-\frac {4}{-3+x}\right )\right )} \, dx=x+\frac {x^2}{3 \left (\frac {5}{-4+x}+e^{x^2} \log \left (5 \log \left (\frac {4}{3-x}\right )\right )\right )} \]

[Out]

x^2/(3*ln(5*ln(4/(-x+3)))*exp(x^2)+15/(x-4))+x

Rubi [F]

\[ \int \frac {e^{x^2} \left (16 x^2-8 x^3+x^4\right )+\left (-225+195 x-85 x^2+15 x^3\right ) \log \left (-\frac {4}{-3+x}\right )+e^{x^2} \left (360-306 x+110 x^2+74 x^3-78 x^4+22 x^5-2 x^6\right ) \log \left (-\frac {4}{-3+x}\right ) \log \left (5 \log \left (-\frac {4}{-3+x}\right )\right )+e^{2 x^2} \left (-144+120 x-33 x^2+3 x^3\right ) \log \left (-\frac {4}{-3+x}\right ) \log ^2\left (5 \log \left (-\frac {4}{-3+x}\right )\right )}{(-225+75 x) \log \left (-\frac {4}{-3+x}\right )+e^{x^2} \left (360-210 x+30 x^2\right ) \log \left (-\frac {4}{-3+x}\right ) \log \left (5 \log \left (-\frac {4}{-3+x}\right )\right )+e^{2 x^2} \left (-144+120 x-33 x^2+3 x^3\right ) \log \left (-\frac {4}{-3+x}\right ) \log ^2\left (5 \log \left (-\frac {4}{-3+x}\right )\right )} \, dx=\int \frac {e^{x^2} \left (16 x^2-8 x^3+x^4\right )+\left (-225+195 x-85 x^2+15 x^3\right ) \log \left (-\frac {4}{-3+x}\right )+e^{x^2} \left (360-306 x+110 x^2+74 x^3-78 x^4+22 x^5-2 x^6\right ) \log \left (-\frac {4}{-3+x}\right ) \log \left (5 \log \left (-\frac {4}{-3+x}\right )\right )+e^{2 x^2} \left (-144+120 x-33 x^2+3 x^3\right ) \log \left (-\frac {4}{-3+x}\right ) \log ^2\left (5 \log \left (-\frac {4}{-3+x}\right )\right )}{(-225+75 x) \log \left (-\frac {4}{-3+x}\right )+e^{x^2} \left (360-210 x+30 x^2\right ) \log \left (-\frac {4}{-3+x}\right ) \log \left (5 \log \left (-\frac {4}{-3+x}\right )\right )+e^{2 x^2} \left (-144+120 x-33 x^2+3 x^3\right ) \log \left (-\frac {4}{-3+x}\right ) \log ^2\left (5 \log \left (-\frac {4}{-3+x}\right )\right )} \, dx \]

[In]

Int[(E^x^2*(16*x^2 - 8*x^3 + x^4) + (-225 + 195*x - 85*x^2 + 15*x^3)*Log[-4/(-3 + x)] + E^x^2*(360 - 306*x + 1
10*x^2 + 74*x^3 - 78*x^4 + 22*x^5 - 2*x^6)*Log[-4/(-3 + x)]*Log[5*Log[-4/(-3 + x)]] + E^(2*x^2)*(-144 + 120*x
- 33*x^2 + 3*x^3)*Log[-4/(-3 + x)]*Log[5*Log[-4/(-3 + x)]]^2)/((-225 + 75*x)*Log[-4/(-3 + x)] + E^x^2*(360 - 2
10*x + 30*x^2)*Log[-4/(-3 + x)]*Log[5*Log[-4/(-3 + x)]] + E^(2*x^2)*(-144 + 120*x - 33*x^2 + 3*x^3)*Log[-4/(-3
+ x)]*Log[5*Log[-4/(-3 + x)]]^2),x]

[Out]

x + (5*Defer[Int][x^2/(5 + E^x^2*(-4 + x)*Log[5*Log[-4/(-3 + x)]])^2, x])/3 - (40*Defer[Int][x^3/(5 + E^x^2*(-
4 + x)*Log[5*Log[-4/(-3 + x)]])^2, x])/3 + (10*Defer[Int][x^4/(5 + E^x^2*(-4 + x)*Log[5*Log[-4/(-3 + x)]])^2,
x])/3 + 5*Defer[Int][1/(Log[-4/(-3 + x)]*Log[5*Log[-4/(-3 + x)]]*(5 + E^x^2*(-4 + x)*Log[5*Log[-4/(-3 + x)]])^
2), x] + 15*Defer[Int][1/((-3 + x)*Log[-4/(-3 + x)]*Log[5*Log[-4/(-3 + x)]]*(5 + E^x^2*(-4 + x)*Log[5*Log[-4/(
-3 + x)]])^2), x] + (5*Defer[Int][x/(Log[-4/(-3 + x)]*Log[5*Log[-4/(-3 + x)]]*(5 + E^x^2*(-4 + x)*Log[5*Log[-4
/(-3 + x)]])^2), x])/3 - (5*Defer[Int][x^2/(Log[-4/(-3 + x)]*Log[5*Log[-4/(-3 + x)]]*(5 + E^x^2*(-4 + x)*Log[5
*Log[-4/(-3 + x)]])^2), x])/3 - (8*Defer[Int][x/(5 + E^x^2*(-4 + x)*Log[5*Log[-4/(-3 + x)]]), x])/3 + (2*Defer
[Int][x^2/(5 + E^x^2*(-4 + x)*Log[5*Log[-4/(-3 + x)]]), x])/3 + (8*Defer[Int][x^3/(5 + E^x^2*(-4 + x)*Log[5*Lo
g[-4/(-3 + x)]]), x])/3 - (2*Defer[Int][x^4/(5 + E^x^2*(-4 + x)*Log[5*Log[-4/(-3 + x)]]), x])/3 - Defer[Int][1
/(Log[-4/(-3 + x)]*Log[5*Log[-4/(-3 + x)]]*(5 + E^x^2*(-4 + x)*Log[5*Log[-4/(-3 + x)]])), x] - 3*Defer[Int][1/
((-3 + x)*Log[-4/(-3 + x)]*Log[5*Log[-4/(-3 + x)]]*(5 + E^x^2*(-4 + x)*Log[5*Log[-4/(-3 + x)]])), x] - Defer[I
nt][x/(Log[-4/(-3 + x)]*Log[5*Log[-4/(-3 + x)]]*(5 + E^x^2*(-4 + x)*Log[5*Log[-4/(-3 + x)]])), x]/3 + Defer[In
t][x^2/(Log[-4/(-3 + x)]*Log[5*Log[-4/(-3 + x)]]*(5 + E^x^2*(-4 + x)*Log[5*Log[-4/(-3 + x)]])), x]/3

Rubi steps \begin{align*} \text {integral}& = \int \frac {-e^{x^2} (-4+x)^2 x^2+(-3+x) \log \left (-\frac {4}{-3+x}\right ) \left (-5 \left (15-8 x+3 x^2\right )+2 e^{x^2} \left (60-31 x+8 x^2+15 x^3-8 x^4+x^5\right ) \log \left (5 \log \left (-\frac {4}{-3+x}\right )\right )-3 e^{2 x^2} (-4+x)^2 \log ^2\left (5 \log \left (-\frac {4}{-3+x}\right )\right )\right )}{3 (3-x) \log \left (-\frac {4}{-3+x}\right ) \left (5+e^{x^2} (-4+x) \log \left (5 \log \left (-\frac {4}{-3+x}\right )\right )\right )^2} \, dx \\ & = \frac {1}{3} \int \frac {-e^{x^2} (-4+x)^2 x^2+(-3+x) \log \left (-\frac {4}{-3+x}\right ) \left (-5 \left (15-8 x+3 x^2\right )+2 e^{x^2} \left (60-31 x+8 x^2+15 x^3-8 x^4+x^5\right ) \log \left (5 \log \left (-\frac {4}{-3+x}\right )\right )-3 e^{2 x^2} (-4+x)^2 \log ^2\left (5 \log \left (-\frac {4}{-3+x}\right )\right )\right )}{(3-x) \log \left (-\frac {4}{-3+x}\right ) \left (5+e^{x^2} (-4+x) \log \left (5 \log \left (-\frac {4}{-3+x}\right )\right )\right )^2} \, dx \\ & = \frac {1}{3} \int \left (3+\frac {5 x^2 \left (4-x-3 \log \left (-\frac {4}{-3+x}\right ) \log \left (5 \log \left (-\frac {4}{-3+x}\right )\right )+25 x \log \left (-\frac {4}{-3+x}\right ) \log \left (5 \log \left (-\frac {4}{-3+x}\right )\right )-14 x^2 \log \left (-\frac {4}{-3+x}\right ) \log \left (5 \log \left (-\frac {4}{-3+x}\right )\right )+2 x^3 \log \left (-\frac {4}{-3+x}\right ) \log \left (5 \log \left (-\frac {4}{-3+x}\right )\right )\right )}{(-3+x) \log \left (-\frac {4}{-3+x}\right ) \log \left (5 \log \left (-\frac {4}{-3+x}\right )\right ) \left (5-4 e^{x^2} \log \left (5 \log \left (-\frac {4}{-3+x}\right )\right )+e^{x^2} x \log \left (5 \log \left (-\frac {4}{-3+x}\right )\right )\right )^2}-\frac {(-4+x) x \left (-x+6 \log \left (-\frac {4}{-3+x}\right ) \log \left (5 \log \left (-\frac {4}{-3+x}\right )\right )-2 x \log \left (-\frac {4}{-3+x}\right ) \log \left (5 \log \left (-\frac {4}{-3+x}\right )\right )-6 x^2 \log \left (-\frac {4}{-3+x}\right ) \log \left (5 \log \left (-\frac {4}{-3+x}\right )\right )+2 x^3 \log \left (-\frac {4}{-3+x}\right ) \log \left (5 \log \left (-\frac {4}{-3+x}\right )\right )\right )}{(-3+x) \log \left (-\frac {4}{-3+x}\right ) \log \left (5 \log \left (-\frac {4}{-3+x}\right )\right ) \left (5-4 e^{x^2} \log \left (5 \log \left (-\frac {4}{-3+x}\right )\right )+e^{x^2} x \log \left (5 \log \left (-\frac {4}{-3+x}\right )\right )\right )}\right ) \, dx \\ & = x-\frac {1}{3} \int \frac {(-4+x) x \left (-x+6 \log \left (-\frac {4}{-3+x}\right ) \log \left (5 \log \left (-\frac {4}{-3+x}\right )\right )-2 x \log \left (-\frac {4}{-3+x}\right ) \log \left (5 \log \left (-\frac {4}{-3+x}\right )\right )-6 x^2 \log \left (-\frac {4}{-3+x}\right ) \log \left (5 \log \left (-\frac {4}{-3+x}\right )\right )+2 x^3 \log \left (-\frac {4}{-3+x}\right ) \log \left (5 \log \left (-\frac {4}{-3+x}\right )\right )\right )}{(-3+x) \log \left (-\frac {4}{-3+x}\right ) \log \left (5 \log \left (-\frac {4}{-3+x}\right )\right ) \left (5-4 e^{x^2} \log \left (5 \log \left (-\frac {4}{-3+x}\right )\right )+e^{x^2} x \log \left (5 \log \left (-\frac {4}{-3+x}\right )\right )\right )} \, dx+\frac {5}{3} \int \frac {x^2 \left (4-x-3 \log \left (-\frac {4}{-3+x}\right ) \log \left (5 \log \left (-\frac {4}{-3+x}\right )\right )+25 x \log \left (-\frac {4}{-3+x}\right ) \log \left (5 \log \left (-\frac {4}{-3+x}\right )\right )-14 x^2 \log \left (-\frac {4}{-3+x}\right ) \log \left (5 \log \left (-\frac {4}{-3+x}\right )\right )+2 x^3 \log \left (-\frac {4}{-3+x}\right ) \log \left (5 \log \left (-\frac {4}{-3+x}\right )\right )\right )}{(-3+x) \log \left (-\frac {4}{-3+x}\right ) \log \left (5 \log \left (-\frac {4}{-3+x}\right )\right ) \left (5-4 e^{x^2} \log \left (5 \log \left (-\frac {4}{-3+x}\right )\right )+e^{x^2} x \log \left (5 \log \left (-\frac {4}{-3+x}\right )\right )\right )^2} \, dx \\ & = x-\frac {1}{3} \int \frac {(4-x) x \left (-x+2 \left (3-x-3 x^2+x^3\right ) \log \left (-\frac {4}{-3+x}\right ) \log \left (5 \log \left (-\frac {4}{-3+x}\right )\right )\right )}{(3-x) \log \left (-\frac {4}{-3+x}\right ) \log \left (5 \log \left (-\frac {4}{-3+x}\right )\right ) \left (5+e^{x^2} (-4+x) \log \left (5 \log \left (-\frac {4}{-3+x}\right )\right )\right )} \, dx+\frac {5}{3} \int \frac {x^2 \left (-4+x-\left (-3+25 x-14 x^2+2 x^3\right ) \log \left (-\frac {4}{-3+x}\right ) \log \left (5 \log \left (-\frac {4}{-3+x}\right )\right )\right )}{(3-x) \log \left (-\frac {4}{-3+x}\right ) \log \left (5 \log \left (-\frac {4}{-3+x}\right )\right ) \left (5+e^{x^2} (-4+x) \log \left (5 \log \left (-\frac {4}{-3+x}\right )\right )\right )^2} \, dx \\ & = \text {Too large to display} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.27 (sec) , antiderivative size = 41, normalized size of antiderivative = 1.08 \[ \int \frac {e^{x^2} \left (16 x^2-8 x^3+x^4\right )+\left (-225+195 x-85 x^2+15 x^3\right ) \log \left (-\frac {4}{-3+x}\right )+e^{x^2} \left (360-306 x+110 x^2+74 x^3-78 x^4+22 x^5-2 x^6\right ) \log \left (-\frac {4}{-3+x}\right ) \log \left (5 \log \left (-\frac {4}{-3+x}\right )\right )+e^{2 x^2} \left (-144+120 x-33 x^2+3 x^3\right ) \log \left (-\frac {4}{-3+x}\right ) \log ^2\left (5 \log \left (-\frac {4}{-3+x}\right )\right )}{(-225+75 x) \log \left (-\frac {4}{-3+x}\right )+e^{x^2} \left (360-210 x+30 x^2\right ) \log \left (-\frac {4}{-3+x}\right ) \log \left (5 \log \left (-\frac {4}{-3+x}\right )\right )+e^{2 x^2} \left (-144+120 x-33 x^2+3 x^3\right ) \log \left (-\frac {4}{-3+x}\right ) \log ^2\left (5 \log \left (-\frac {4}{-3+x}\right )\right )} \, dx=\frac {1}{3} \left (3 (-3+x)+\frac {(-4+x) x^2}{5+e^{x^2} (-4+x) \log \left (5 \log \left (-\frac {4}{-3+x}\right )\right )}\right ) \]

[In]

Integrate[(E^x^2*(16*x^2 - 8*x^3 + x^4) + (-225 + 195*x - 85*x^2 + 15*x^3)*Log[-4/(-3 + x)] + E^x^2*(360 - 306
*x + 110*x^2 + 74*x^3 - 78*x^4 + 22*x^5 - 2*x^6)*Log[-4/(-3 + x)]*Log[5*Log[-4/(-3 + x)]] + E^(2*x^2)*(-144 +
120*x - 33*x^2 + 3*x^3)*Log[-4/(-3 + x)]*Log[5*Log[-4/(-3 + x)]]^2)/((-225 + 75*x)*Log[-4/(-3 + x)] + E^x^2*(3
60 - 210*x + 30*x^2)*Log[-4/(-3 + x)]*Log[5*Log[-4/(-3 + x)]] + E^(2*x^2)*(-144 + 120*x - 33*x^2 + 3*x^3)*Log[
-4/(-3 + x)]*Log[5*Log[-4/(-3 + x)]]^2),x]

[Out]

(3*(-3 + x) + ((-4 + x)*x^2)/(5 + E^x^2*(-4 + x)*Log[5*Log[-4/(-3 + x)]]))/3

Maple [C] (warning: unable to verify)

Result contains higher order function than in optimal. Order 9 vs. order 3.

Time = 30.56 (sec) , antiderivative size = 111, normalized size of antiderivative = 2.92

method	result	size
risch	\(x +\frac {\left (x -4\right ) x^{2}}{3 x \,{\mathrm e}^{x^{2}} \ln \left (10 \ln \left (2\right )+5 i \pi -5 \ln \left (-3+x \right )+5 i \pi \operatorname {csgn}\left (\frac {i}{-3+x}\right )^{2} \left (\operatorname {csgn}\left (\frac {i}{-3+x}\right )-1\right )\right )-12 \,{\mathrm e}^{x^{2}} \ln \left (10 \ln \left (2\right )+5 i \pi -5 \ln \left (-3+x \right )+5 i \pi \operatorname {csgn}\left (\frac {i}{-3+x}\right )^{2} \left (\operatorname {csgn}\left (\frac {i}{-3+x}\right )-1\right )\right )+15}\)	\(111\)
parallelrisch	\(\frac {5400+990 x^{2} \ln \left (5 \ln \left (-\frac {4}{-3+x}\right )\right ) {\mathrm e}^{x^{2}}+330 x^{3}-2880 \,{\mathrm e}^{x^{2}} \ln \left (5 \ln \left (-\frac {4}{-3+x}\right )\right ) x -1320 x^{2}-4320 \,{\mathrm e}^{x^{2}} \ln \left (5 \ln \left (-\frac {4}{-3+x}\right )\right )+4950 x}{990 \,{\mathrm e}^{x^{2}} \ln \left (5 \ln \left (-\frac {4}{-3+x}\right )\right ) x -3960 \,{\mathrm e}^{x^{2}} \ln \left (5 \ln \left (-\frac {4}{-3+x}\right )\right )+4950}\)	\(111\)

[In]

int(((3*x^3-33*x^2+120*x-144)*exp(x^2)^2*ln(-4/(-3+x))*ln(5*ln(-4/(-3+x)))^2+(-2*x^6+22*x^5-78*x^4+74*x^3+110*
x^2-306*x+360)*exp(x^2)*ln(-4/(-3+x))*ln(5*ln(-4/(-3+x)))+(15*x^3-85*x^2+195*x-225)*ln(-4/(-3+x))+(x^4-8*x^3+1
6*x^2)*exp(x^2))/((3*x^3-33*x^2+120*x-144)*exp(x^2)^2*ln(-4/(-3+x))*ln(5*ln(-4/(-3+x)))^2+(30*x^2-210*x+360)*e
xp(x^2)*ln(-4/(-3+x))*ln(5*ln(-4/(-3+x)))+(75*x-225)*ln(-4/(-3+x))),x,method=_RETURNVERBOSE)

[Out]

x+1/3*(x-4)*x^2/(x*exp(x^2)*ln(10*ln(2)+5*I*Pi-5*ln(-3+x)+5*I*Pi*csgn(I/(-3+x))^2*(csgn(I/(-3+x))-1))-4*exp(x^
2)*ln(10*ln(2)+5*I*Pi-5*ln(-3+x)+5*I*Pi*csgn(I/(-3+x))^2*(csgn(I/(-3+x))-1))+5)

Fricas [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 61, normalized size of antiderivative = 1.61 \[ \int \frac {e^{x^2} \left (16 x^2-8 x^3+x^4\right )+\left (-225+195 x-85 x^2+15 x^3\right ) \log \left (-\frac {4}{-3+x}\right )+e^{x^2} \left (360-306 x+110 x^2+74 x^3-78 x^4+22 x^5-2 x^6\right ) \log \left (-\frac {4}{-3+x}\right ) \log \left (5 \log \left (-\frac {4}{-3+x}\right )\right )+e^{2 x^2} \left (-144+120 x-33 x^2+3 x^3\right ) \log \left (-\frac {4}{-3+x}\right ) \log ^2\left (5 \log \left (-\frac {4}{-3+x}\right )\right )}{(-225+75 x) \log \left (-\frac {4}{-3+x}\right )+e^{x^2} \left (360-210 x+30 x^2\right ) \log \left (-\frac {4}{-3+x}\right ) \log \left (5 \log \left (-\frac {4}{-3+x}\right )\right )+e^{2 x^2} \left (-144+120 x-33 x^2+3 x^3\right ) \log \left (-\frac {4}{-3+x}\right ) \log ^2\left (5 \log \left (-\frac {4}{-3+x}\right )\right )} \, dx=\frac {x^{3} + 3 \, {\left (x^{2} - 4 \, x\right )} e^{\left (x^{2}\right )} \log \left (5 \, \log \left (-\frac {4}{x - 3}\right )\right ) - 4 \, x^{2} + 15 \, x}{3 \, {\left ({\left (x - 4\right )} e^{\left (x^{2}\right )} \log \left (5 \, \log \left (-\frac {4}{x - 3}\right )\right ) + 5\right )}} \]

[In]

integrate(((3*x^3-33*x^2+120*x-144)*exp(x^2)^2*log(-4/(-3+x))*log(5*log(-4/(-3+x)))^2+(-2*x^6+22*x^5-78*x^4+74
*x^3+110*x^2-306*x+360)*exp(x^2)*log(-4/(-3+x))*log(5*log(-4/(-3+x)))+(15*x^3-85*x^2+195*x-225)*log(-4/(-3+x))
+(x^4-8*x^3+16*x^2)*exp(x^2))/((3*x^3-33*x^2+120*x-144)*exp(x^2)^2*log(-4/(-3+x))*log(5*log(-4/(-3+x)))^2+(30*
x^2-210*x+360)*exp(x^2)*log(-4/(-3+x))*log(5*log(-4/(-3+x)))+(75*x-225)*log(-4/(-3+x))),x, algorithm="fricas")

[Out]

1/3*(x^3 + 3*(x^2 - 4*x)*e^(x^2)*log(5*log(-4/(x - 3))) - 4*x^2 + 15*x)/((x - 4)*e^(x^2)*log(5*log(-4/(x - 3))
) + 5)

Sympy [A] (verification not implemented)

Time = 0.43 (sec) , antiderivative size = 44, normalized size of antiderivative = 1.16 \[ \int \frac {e^{x^2} \left (16 x^2-8 x^3+x^4\right )+\left (-225+195 x-85 x^2+15 x^3\right ) \log \left (-\frac {4}{-3+x}\right )+e^{x^2} \left (360-306 x+110 x^2+74 x^3-78 x^4+22 x^5-2 x^6\right ) \log \left (-\frac {4}{-3+x}\right ) \log \left (5 \log \left (-\frac {4}{-3+x}\right )\right )+e^{2 x^2} \left (-144+120 x-33 x^2+3 x^3\right ) \log \left (-\frac {4}{-3+x}\right ) \log ^2\left (5 \log \left (-\frac {4}{-3+x}\right )\right )}{(-225+75 x) \log \left (-\frac {4}{-3+x}\right )+e^{x^2} \left (360-210 x+30 x^2\right ) \log \left (-\frac {4}{-3+x}\right ) \log \left (5 \log \left (-\frac {4}{-3+x}\right )\right )+e^{2 x^2} \left (-144+120 x-33 x^2+3 x^3\right ) \log \left (-\frac {4}{-3+x}\right ) \log ^2\left (5 \log \left (-\frac {4}{-3+x}\right )\right )} \, dx=x + \frac {x^{3} - 4 x^{2}}{\left (3 x \log {\left (5 \log {\left (- \frac {4}{x - 3} \right )} \right )} - 12 \log {\left (5 \log {\left (- \frac {4}{x - 3} \right )} \right )}\right ) e^{x^{2}} + 15} \]

[In]

integrate(((3*x**3-33*x**2+120*x-144)*exp(x**2)**2*ln(-4/(-3+x))*ln(5*ln(-4/(-3+x)))**2+(-2*x**6+22*x**5-78*x*
*4+74*x**3+110*x**2-306*x+360)*exp(x**2)*ln(-4/(-3+x))*ln(5*ln(-4/(-3+x)))+(15*x**3-85*x**2+195*x-225)*ln(-4/(
-3+x))+(x**4-8*x**3+16*x**2)*exp(x**2))/((3*x**3-33*x**2+120*x-144)*exp(x**2)**2*ln(-4/(-3+x))*ln(5*ln(-4/(-3+
x)))**2+(30*x**2-210*x+360)*exp(x**2)*ln(-4/(-3+x))*ln(5*ln(-4/(-3+x)))+(75*x-225)*ln(-4/(-3+x))),x)

[Out]

x + (x**3 - 4*x**2)/((3*x*log(5*log(-4/(x - 3))) - 12*log(5*log(-4/(x - 3))))*exp(x**2) + 15)

Maxima [C] (verification not implemented)

Result contains complex when optimal does not.

Time = 0.48 (sec) , antiderivative size = 112, normalized size of antiderivative = 2.95 \[ \int \frac {e^{x^2} \left (16 x^2-8 x^3+x^4\right )+\left (-225+195 x-85 x^2+15 x^3\right ) \log \left (-\frac {4}{-3+x}\right )+e^{x^2} \left (360-306 x+110 x^2+74 x^3-78 x^4+22 x^5-2 x^6\right ) \log \left (-\frac {4}{-3+x}\right ) \log \left (5 \log \left (-\frac {4}{-3+x}\right )\right )+e^{2 x^2} \left (-144+120 x-33 x^2+3 x^3\right ) \log \left (-\frac {4}{-3+x}\right ) \log ^2\left (5 \log \left (-\frac {4}{-3+x}\right )\right )}{(-225+75 x) \log \left (-\frac {4}{-3+x}\right )+e^{x^2} \left (360-210 x+30 x^2\right ) \log \left (-\frac {4}{-3+x}\right ) \log \left (5 \log \left (-\frac {4}{-3+x}\right )\right )+e^{2 x^2} \left (-144+120 x-33 x^2+3 x^3\right ) \log \left (-\frac {4}{-3+x}\right ) \log ^2\left (5 \log \left (-\frac {4}{-3+x}\right )\right )} \, dx=\frac {x^{3} + 3 \, {\left (x^{2} - 4 \, x\right )} e^{\left (x^{2}\right )} \log \left (-2 \, \log \left (2\right ) + \log \left (-x + 3\right )\right ) - 4 \, x^{2} - 3 \, {\left ({\left (-i \, \pi - \log \left (5\right )\right )} x^{2} + 4 \, {\left (i \, \pi + \log \left (5\right )\right )} x\right )} e^{\left (x^{2}\right )} + 15 \, x}{3 \, {\left ({\left (x - 4\right )} e^{\left (x^{2}\right )} \log \left (-2 \, \log \left (2\right ) + \log \left (-x + 3\right )\right ) + {\left (-4 i \, \pi + {\left (i \, \pi + \log \left (5\right )\right )} x - 4 \, \log \left (5\right )\right )} e^{\left (x^{2}\right )} + 5\right )}} \]

[In]

integrate(((3*x^3-33*x^2+120*x-144)*exp(x^2)^2*log(-4/(-3+x))*log(5*log(-4/(-3+x)))^2+(-2*x^6+22*x^5-78*x^4+74
*x^3+110*x^2-306*x+360)*exp(x^2)*log(-4/(-3+x))*log(5*log(-4/(-3+x)))+(15*x^3-85*x^2+195*x-225)*log(-4/(-3+x))
+(x^4-8*x^3+16*x^2)*exp(x^2))/((3*x^3-33*x^2+120*x-144)*exp(x^2)^2*log(-4/(-3+x))*log(5*log(-4/(-3+x)))^2+(30*
x^2-210*x+360)*exp(x^2)*log(-4/(-3+x))*log(5*log(-4/(-3+x)))+(75*x-225)*log(-4/(-3+x))),x, algorithm="maxima")

[Out]

1/3*(x^3 + 3*(x^2 - 4*x)*e^(x^2)*log(-2*log(2) + log(-x + 3)) - 4*x^2 - 3*((-I*pi - log(5))*x^2 + 4*(I*pi + lo
g(5))*x)*e^(x^2) + 15*x)/((x - 4)*e^(x^2)*log(-2*log(2) + log(-x + 3)) + (-4*I*pi + (I*pi + log(5))*x - 4*log(
5))*e^(x^2) + 5)

Giac [F(-1)]

Timed out. \[ \int \frac {e^{x^2} \left (16 x^2-8 x^3+x^4\right )+\left (-225+195 x-85 x^2+15 x^3\right ) \log \left (-\frac {4}{-3+x}\right )+e^{x^2} \left (360-306 x+110 x^2+74 x^3-78 x^4+22 x^5-2 x^6\right ) \log \left (-\frac {4}{-3+x}\right ) \log \left (5 \log \left (-\frac {4}{-3+x}\right )\right )+e^{2 x^2} \left (-144+120 x-33 x^2+3 x^3\right ) \log \left (-\frac {4}{-3+x}\right ) \log ^2\left (5 \log \left (-\frac {4}{-3+x}\right )\right )}{(-225+75 x) \log \left (-\frac {4}{-3+x}\right )+e^{x^2} \left (360-210 x+30 x^2\right ) \log \left (-\frac {4}{-3+x}\right ) \log \left (5 \log \left (-\frac {4}{-3+x}\right )\right )+e^{2 x^2} \left (-144+120 x-33 x^2+3 x^3\right ) \log \left (-\frac {4}{-3+x}\right ) \log ^2\left (5 \log \left (-\frac {4}{-3+x}\right )\right )} \, dx=\text {Timed out} \]

[In]

integrate(((3*x^3-33*x^2+120*x-144)*exp(x^2)^2*log(-4/(-3+x))*log(5*log(-4/(-3+x)))^2+(-2*x^6+22*x^5-78*x^4+74
*x^3+110*x^2-306*x+360)*exp(x^2)*log(-4/(-3+x))*log(5*log(-4/(-3+x)))+(15*x^3-85*x^2+195*x-225)*log(-4/(-3+x))
+(x^4-8*x^3+16*x^2)*exp(x^2))/((3*x^3-33*x^2+120*x-144)*exp(x^2)^2*log(-4/(-3+x))*log(5*log(-4/(-3+x)))^2+(30*
x^2-210*x+360)*exp(x^2)*log(-4/(-3+x))*log(5*log(-4/(-3+x)))+(75*x-225)*log(-4/(-3+x))),x, algorithm="giac")

[Out]

Timed out

Mupad [F(-1)]

Timed out. \[ \int \frac {e^{x^2} \left (16 x^2-8 x^3+x^4\right )+\left (-225+195 x-85 x^2+15 x^3\right ) \log \left (-\frac {4}{-3+x}\right )+e^{x^2} \left (360-306 x+110 x^2+74 x^3-78 x^4+22 x^5-2 x^6\right ) \log \left (-\frac {4}{-3+x}\right ) \log \left (5 \log \left (-\frac {4}{-3+x}\right )\right )+e^{2 x^2} \left (-144+120 x-33 x^2+3 x^3\right ) \log \left (-\frac {4}{-3+x}\right ) \log ^2\left (5 \log \left (-\frac {4}{-3+x}\right )\right )}{(-225+75 x) \log \left (-\frac {4}{-3+x}\right )+e^{x^2} \left (360-210 x+30 x^2\right ) \log \left (-\frac {4}{-3+x}\right ) \log \left (5 \log \left (-\frac {4}{-3+x}\right )\right )+e^{2 x^2} \left (-144+120 x-33 x^2+3 x^3\right ) \log \left (-\frac {4}{-3+x}\right ) \log ^2\left (5 \log \left (-\frac {4}{-3+x}\right )\right )} \, dx=\int \frac {\ln \left (-\frac {4}{x-3}\right )\,{\mathrm {e}}^{2\,x^2}\,\left (3\,x^3-33\,x^2+120\,x-144\right )\,{\ln \left (5\,\ln \left (-\frac {4}{x-3}\right )\right )}^2+\ln \left (-\frac {4}{x-3}\right )\,{\mathrm {e}}^{x^2}\,\left (-2\,x^6+22\,x^5-78\,x^4+74\,x^3+110\,x^2-306\,x+360\right )\,\ln \left (5\,\ln \left (-\frac {4}{x-3}\right )\right )+\ln \left (-\frac {4}{x-3}\right )\,\left (15\,x^3-85\,x^2+195\,x-225\right )+{\mathrm {e}}^{x^2}\,\left (x^4-8\,x^3+16\,x^2\right )}{\ln \left (-\frac {4}{x-3}\right )\,{\mathrm {e}}^{2\,x^2}\,\left (3\,x^3-33\,x^2+120\,x-144\right )\,{\ln \left (5\,\ln \left (-\frac {4}{x-3}\right )\right )}^2+\ln \left (-\frac {4}{x-3}\right )\,{\mathrm {e}}^{x^2}\,\left (30\,x^2-210\,x+360\right )\,\ln \left (5\,\ln \left (-\frac {4}{x-3}\right )\right )+\ln \left (-\frac {4}{x-3}\right )\,\left (75\,x-225\right )} \,d x \]

[In]

int((log(-4/(x - 3))*(195*x - 85*x^2 + 15*x^3 - 225) + exp(x^2)*(16*x^2 - 8*x^3 + x^4) + log(-4/(x - 3))*exp(x
^2)*log(5*log(-4/(x - 3)))*(110*x^2 - 306*x + 74*x^3 - 78*x^4 + 22*x^5 - 2*x^6 + 360) + log(-4/(x - 3))*exp(2*
x^2)*log(5*log(-4/(x - 3)))^2*(120*x - 33*x^2 + 3*x^3 - 144))/(log(-4/(x - 3))*(75*x - 225) + log(-4/(x - 3))*
exp(2*x^2)*log(5*log(-4/(x - 3)))^2*(120*x - 33*x^2 + 3*x^3 - 144) + log(-4/(x - 3))*exp(x^2)*log(5*log(-4/(x
- 3)))*(30*x^2 - 210*x + 360)),x)

[Out]

int((log(-4/(x - 3))*(195*x - 85*x^2 + 15*x^3 - 225) + exp(x^2)*(16*x^2 - 8*x^3 + x^4) + log(-4/(x - 3))*exp(x
^2)*log(5*log(-4/(x - 3)))*(110*x^2 - 306*x + 74*x^3 - 78*x^4 + 22*x^5 - 2*x^6 + 360) + log(-4/(x - 3))*exp(2*
x^2)*log(5*log(-4/(x - 3)))^2*(120*x - 33*x^2 + 3*x^3 - 144))/(log(-4/(x - 3))*(75*x - 225) + log(-4/(x - 3))*
exp(2*x^2)*log(5*log(-4/(x - 3)))^2*(120*x - 33*x^2 + 3*x^3 - 144) + log(-4/(x - 3))*exp(x^2)*log(5*log(-4/(x
- 3)))*(30*x^2 - 210*x + 360)), x)