3.73.30 \(\int \frac {e^{\frac {(2500+250 x-400 x^2+50 x^3) \log ^2(x)}{-5-x+(1875-750 x+75 x^2) \log ^2(x)}} ((-50000-15000 x+7000 x^2+600 x^3-200 x^4) \log (x)+(2500 x+8000 x^2-700 x^3-200 x^4) \log ^2(x)+(4687500 x-3750000 x^2+1125000 x^3-150000 x^4+7500 x^5) \log ^4(x))}{25 x+10 x^2+x^3+(-18750 x+3750 x^2+750 x^3-150 x^4) \log ^2(x)+(3515625 x-2812500 x^2+843750 x^3-112500 x^4+5625 x^5) \log ^4(x)} \, dx\)

Optimal. Leaf size=32 \[ 2 e^{\frac {4+2 x}{3-\frac {5+x}{25 (5-x)^2 \log ^2(x)}}} \]

________________________________________________________________________________________

Rubi [F]  time = 89.53, 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 {\exp \left (\frac {\left (2500+250 x-400 x^2+50 x^3\right ) \log ^2(x)}{-5-x+\left (1875-750 x+75 x^2\right ) \log ^2(x)}\right ) \left (\left (-50000-15000 x+7000 x^2+600 x^3-200 x^4\right ) \log (x)+\left (2500 x+8000 x^2-700 x^3-200 x^4\right ) \log ^2(x)+\left (4687500 x-3750000 x^2+1125000 x^3-150000 x^4+7500 x^5\right ) \log ^4(x)\right )}{25 x+10 x^2+x^3+\left (-18750 x+3750 x^2+750 x^3-150 x^4\right ) \log ^2(x)+\left (3515625 x-2812500 x^2+843750 x^3-112500 x^4+5625 x^5\right ) \log ^4(x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^(((2500 + 250*x - 400*x^2 + 50*x^3)*Log[x]^2)/(-5 - x + (1875 - 750*x + 75*x^2)*Log[x]^2))*((-50000 - 1
5000*x + 7000*x^2 + 600*x^3 - 200*x^4)*Log[x] + (2500*x + 8000*x^2 - 700*x^3 - 200*x^4)*Log[x]^2 + (4687500*x
- 3750000*x^2 + 1125000*x^3 - 150000*x^4 + 7500*x^5)*Log[x]^4))/(25*x + 10*x^2 + x^3 + (-18750*x + 3750*x^2 +
750*x^3 - 150*x^4)*Log[x]^2 + (3515625*x - 2812500*x^2 + 843750*x^3 - 112500*x^4 + 5625*x^5)*Log[x]^4),x]

[Out]

(4*Defer[Int][E^((-50*(-5 + x)^2*(2 + x)*Log[x]^2)/(5 + x - 75*(-5 + x)^2*Log[x]^2)), x])/3 - (1000*Defer[Int]
[1/(E^((50*(-5 + x)^2*(2 + x)*Log[x]^2)/(5 + x - 75*(-5 + x)^2*Log[x]^2))*(5 + x - 75*(-5 + x)^2*Log[x]^2)^2),
x])/3 - (5600*Defer[Int][1/(E^((50*(-5 + x)^2*(2 + x)*Log[x]^2)/(5 + x - 75*(-5 + x)^2*Log[x]^2))*(-5 + x)*(5
+ x - 75*(-5 + x)^2*Log[x]^2)^2), x])/3 - 36*Defer[Int][x/(E^((50*(-5 + x)^2*(2 + x)*Log[x]^2)/(5 + x - 75*(-
5 + x)^2*Log[x]^2))*(5 + x - 75*(-5 + x)^2*Log[x]^2)^2), x] - (4*Defer[Int][x^2/(E^((50*(-5 + x)^2*(2 + x)*Log
[x]^2)/(5 + x - 75*(-5 + x)^2*Log[x]^2))*(5 + x - 75*(-5 + x)^2*Log[x]^2)^2), x])/3 - 15000*Defer[Int][Log[x]/
(E^((50*(-5 + x)^2*(2 + x)*Log[x]^2)/(5 + x - 75*(-5 + x)^2*Log[x]^2))*(5 + x - 75*(-5 + x)^2*Log[x]^2)^2), x]
- 50000*Defer[Int][Log[x]/(E^((50*(-5 + x)^2*(2 + x)*Log[x]^2)/(5 + x - 75*(-5 + x)^2*Log[x]^2))*x*(5 + x - 7
5*(-5 + x)^2*Log[x]^2)^2), x] + 7000*Defer[Int][(x*Log[x])/(E^((50*(-5 + x)^2*(2 + x)*Log[x]^2)/(5 + x - 75*(-
5 + x)^2*Log[x]^2))*(5 + x - 75*(-5 + x)^2*Log[x]^2)^2), x] + 600*Defer[Int][(x^2*Log[x])/(E^((50*(-5 + x)^2*(
2 + x)*Log[x]^2)/(5 + x - 75*(-5 + x)^2*Log[x]^2))*(5 + x - 75*(-5 + x)^2*Log[x]^2)^2), x] - 200*Defer[Int][(x
^3*Log[x])/(E^((50*(-5 + x)^2*(2 + x)*Log[x]^2)/(5 + x - 75*(-5 + x)^2*Log[x]^2))*(5 + x - 75*(-5 + x)^2*Log[x
]^2)^2), x] - (560*Defer[Int][1/(E^((50*(-5 + x)^2*(2 + x)*Log[x]^2)/(5 + x - 75*(-5 + x)^2*Log[x]^2))*(5 - x)
*(5 + x - 75*(-5 + x)^2*Log[x]^2)), x])/3 - (68*Defer[Int][1/(E^((50*(-5 + x)^2*(2 + x)*Log[x]^2)/(5 + x - 75*
(-5 + x)^2*Log[x]^2))*(-5 - x + 75*(-5 + x)^2*Log[x]^2)), x])/3

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {100 \exp \left (-\frac {50 (-5+x)^2 (2+x) \log ^2(x)}{5+x-75 (-5+x)^2 \log ^2(x)}\right ) (5-x) \log (x) \left (2 \left (-50-25 x+2 x^2+x^3\right )+x \left (5+17 x+2 x^2\right ) \log (x)-75 (-5+x)^3 x \log ^3(x)\right )}{x \left (5+x-75 (-5+x)^2 \log ^2(x)\right )^2} \, dx\\ &=100 \int \frac {\exp \left (-\frac {50 (-5+x)^2 (2+x) \log ^2(x)}{5+x-75 (-5+x)^2 \log ^2(x)}\right ) (5-x) \log (x) \left (2 \left (-50-25 x+2 x^2+x^3\right )+x \left (5+17 x+2 x^2\right ) \log (x)-75 (-5+x)^3 x \log ^3(x)\right )}{x \left (5+x-75 (-5+x)^2 \log ^2(x)\right )^2} \, dx\\ &=100 \int \left (\frac {1}{75} \exp \left (-\frac {50 (-5+x)^2 (2+x) \log ^2(x)}{5+x-75 (-5+x)^2 \log ^2(x)}\right )-\frac {\exp \left (-\frac {50 (-5+x)^2 (2+x) \log ^2(x)}{5+x-75 (-5+x)^2 \log ^2(x)}\right ) \left (10+7 x+x^2\right ) \left (15 x+x^2-18750 \log (x)+11250 x \log (x)-2250 x^2 \log (x)+150 x^3 \log (x)\right )}{75 (-5+x) x \left (-5-x+1875 \log ^2(x)-750 x \log ^2(x)+75 x^2 \log ^2(x)\right )^2}+\frac {\exp \left (-\frac {50 (-5+x)^2 (2+x) \log ^2(x)}{5+x-75 (-5+x)^2 \log ^2(x)}\right ) (-55-17 x)}{75 (-5+x) \left (-5-x+1875 \log ^2(x)-750 x \log ^2(x)+75 x^2 \log ^2(x)\right )}\right ) \, dx\\ &=\frac {4}{3} \int \exp \left (-\frac {50 (-5+x)^2 (2+x) \log ^2(x)}{5+x-75 (-5+x)^2 \log ^2(x)}\right ) \, dx-\frac {4}{3} \int \frac {\exp \left (-\frac {50 (-5+x)^2 (2+x) \log ^2(x)}{5+x-75 (-5+x)^2 \log ^2(x)}\right ) \left (10+7 x+x^2\right ) \left (15 x+x^2-18750 \log (x)+11250 x \log (x)-2250 x^2 \log (x)+150 x^3 \log (x)\right )}{(-5+x) x \left (-5-x+1875 \log ^2(x)-750 x \log ^2(x)+75 x^2 \log ^2(x)\right )^2} \, dx+\frac {4}{3} \int \frac {\exp \left (-\frac {50 (-5+x)^2 (2+x) \log ^2(x)}{5+x-75 (-5+x)^2 \log ^2(x)}\right ) (-55-17 x)}{(-5+x) \left (-5-x+1875 \log ^2(x)-750 x \log ^2(x)+75 x^2 \log ^2(x)\right )} \, dx\\ &=\frac {4}{3} \int \exp \left (-\frac {50 (-5+x)^2 (2+x) \log ^2(x)}{5+x-75 (-5+x)^2 \log ^2(x)}\right ) \, dx-\frac {4}{3} \int \frac {\exp \left (-\frac {50 (-5+x)^2 (2+x) \log ^2(x)}{5+x-75 (-5+x)^2 \log ^2(x)}\right ) \left (10+7 x+x^2\right ) \left (-x (15+x)-150 (-5+x)^3 \log (x)\right )}{(5-x) x \left (5+x-75 (-5+x)^2 \log ^2(x)\right )^2} \, dx+\frac {4}{3} \int \frac {\exp \left (-\frac {50 (-5+x)^2 (2+x) \log ^2(x)}{5+x-75 (-5+x)^2 \log ^2(x)}\right ) (-55-17 x)}{(5-x) \left (5+x-75 (-5+x)^2 \log ^2(x)\right )} \, dx\\ &=\frac {4}{3} \int \exp \left (-\frac {50 (-5+x)^2 (2+x) \log ^2(x)}{5+x-75 (-5+x)^2 \log ^2(x)}\right ) \, dx-\frac {4}{3} \int \left (\frac {\exp \left (-\frac {50 (-5+x)^2 (2+x) \log ^2(x)}{5+x-75 (-5+x)^2 \log ^2(x)}\right ) \left (15 x+x^2-18750 \log (x)+11250 x \log (x)-2250 x^2 \log (x)+150 x^3 \log (x)\right )}{\left (-5-x+1875 \log ^2(x)-750 x \log ^2(x)+75 x^2 \log ^2(x)\right )^2}+\frac {14 \exp \left (-\frac {50 (-5+x)^2 (2+x) \log ^2(x)}{5+x-75 (-5+x)^2 \log ^2(x)}\right ) \left (15 x+x^2-18750 \log (x)+11250 x \log (x)-2250 x^2 \log (x)+150 x^3 \log (x)\right )}{(-5+x) \left (-5-x+1875 \log ^2(x)-750 x \log ^2(x)+75 x^2 \log ^2(x)\right )^2}-\frac {2 \exp \left (-\frac {50 (-5+x)^2 (2+x) \log ^2(x)}{5+x-75 (-5+x)^2 \log ^2(x)}\right ) \left (15 x+x^2-18750 \log (x)+11250 x \log (x)-2250 x^2 \log (x)+150 x^3 \log (x)\right )}{x \left (-5-x+1875 \log ^2(x)-750 x \log ^2(x)+75 x^2 \log ^2(x)\right )^2}\right ) \, dx+\frac {4}{3} \int \left (-\frac {17 \exp \left (-\frac {50 (-5+x)^2 (2+x) \log ^2(x)}{5+x-75 (-5+x)^2 \log ^2(x)}\right )}{-5-x+1875 \log ^2(x)-750 x \log ^2(x)+75 x^2 \log ^2(x)}-\frac {140 \exp \left (-\frac {50 (-5+x)^2 (2+x) \log ^2(x)}{5+x-75 (-5+x)^2 \log ^2(x)}\right )}{(-5+x) \left (-5-x+1875 \log ^2(x)-750 x \log ^2(x)+75 x^2 \log ^2(x)\right )}\right ) \, dx\\ &=\frac {4}{3} \int \exp \left (-\frac {50 (-5+x)^2 (2+x) \log ^2(x)}{5+x-75 (-5+x)^2 \log ^2(x)}\right ) \, dx-\frac {4}{3} \int \frac {\exp \left (-\frac {50 (-5+x)^2 (2+x) \log ^2(x)}{5+x-75 (-5+x)^2 \log ^2(x)}\right ) \left (15 x+x^2-18750 \log (x)+11250 x \log (x)-2250 x^2 \log (x)+150 x^3 \log (x)\right )}{\left (-5-x+1875 \log ^2(x)-750 x \log ^2(x)+75 x^2 \log ^2(x)\right )^2} \, dx+\frac {8}{3} \int \frac {\exp \left (-\frac {50 (-5+x)^2 (2+x) \log ^2(x)}{5+x-75 (-5+x)^2 \log ^2(x)}\right ) \left (15 x+x^2-18750 \log (x)+11250 x \log (x)-2250 x^2 \log (x)+150 x^3 \log (x)\right )}{x \left (-5-x+1875 \log ^2(x)-750 x \log ^2(x)+75 x^2 \log ^2(x)\right )^2} \, dx-\frac {56}{3} \int \frac {\exp \left (-\frac {50 (-5+x)^2 (2+x) \log ^2(x)}{5+x-75 (-5+x)^2 \log ^2(x)}\right ) \left (15 x+x^2-18750 \log (x)+11250 x \log (x)-2250 x^2 \log (x)+150 x^3 \log (x)\right )}{(-5+x) \left (-5-x+1875 \log ^2(x)-750 x \log ^2(x)+75 x^2 \log ^2(x)\right )^2} \, dx-\frac {68}{3} \int \frac {\exp \left (-\frac {50 (-5+x)^2 (2+x) \log ^2(x)}{5+x-75 (-5+x)^2 \log ^2(x)}\right )}{-5-x+1875 \log ^2(x)-750 x \log ^2(x)+75 x^2 \log ^2(x)} \, dx-\frac {560}{3} \int \frac {\exp \left (-\frac {50 (-5+x)^2 (2+x) \log ^2(x)}{5+x-75 (-5+x)^2 \log ^2(x)}\right )}{(-5+x) \left (-5-x+1875 \log ^2(x)-750 x \log ^2(x)+75 x^2 \log ^2(x)\right )} \, dx\\ &=\frac {4}{3} \int \exp \left (-\frac {50 (-5+x)^2 (2+x) \log ^2(x)}{5+x-75 (-5+x)^2 \log ^2(x)}\right ) \, dx-\frac {4}{3} \int \frac {\exp \left (-\frac {50 (-5+x)^2 (2+x) \log ^2(x)}{5+x-75 (-5+x)^2 \log ^2(x)}\right ) \left (x (15+x)+150 (-5+x)^3 \log (x)\right )}{\left (5+x-75 (-5+x)^2 \log ^2(x)\right )^2} \, dx+\frac {8}{3} \int \frac {\exp \left (-\frac {50 (-5+x)^2 (2+x) \log ^2(x)}{5+x-75 (-5+x)^2 \log ^2(x)}\right ) \left (x (15+x)+150 (-5+x)^3 \log (x)\right )}{x \left (5+x-75 (-5+x)^2 \log ^2(x)\right )^2} \, dx-\frac {56}{3} \int \frac {\exp \left (-\frac {50 (-5+x)^2 (2+x) \log ^2(x)}{5+x-75 (-5+x)^2 \log ^2(x)}\right ) \left (-x (15+x)-150 (-5+x)^3 \log (x)\right )}{(5-x) \left (5+x-75 (-5+x)^2 \log ^2(x)\right )^2} \, dx-\frac {68}{3} \int \frac {\exp \left (-\frac {50 (-5+x)^2 (2+x) \log ^2(x)}{5+x-75 (-5+x)^2 \log ^2(x)}\right )}{-5-x+75 (-5+x)^2 \log ^2(x)} \, dx-\frac {560}{3} \int \frac {\exp \left (-\frac {50 (-5+x)^2 (2+x) \log ^2(x)}{5+x-75 (-5+x)^2 \log ^2(x)}\right )}{(5-x) \left (5+x-75 (-5+x)^2 \log ^2(x)\right )} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [A]  time = 0.20, size = 34, normalized size = 1.06 \begin {gather*} 2 e^{-\frac {50 (-5+x)^2 (2+x) \log ^2(x)}{5+x-75 (-5+x)^2 \log ^2(x)}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^(((2500 + 250*x - 400*x^2 + 50*x^3)*Log[x]^2)/(-5 - x + (1875 - 750*x + 75*x^2)*Log[x]^2))*((-500
00 - 15000*x + 7000*x^2 + 600*x^3 - 200*x^4)*Log[x] + (2500*x + 8000*x^2 - 700*x^3 - 200*x^4)*Log[x]^2 + (4687
500*x - 3750000*x^2 + 1125000*x^3 - 150000*x^4 + 7500*x^5)*Log[x]^4))/(25*x + 10*x^2 + x^3 + (-18750*x + 3750*
x^2 + 750*x^3 - 150*x^4)*Log[x]^2 + (3515625*x - 2812500*x^2 + 843750*x^3 - 112500*x^4 + 5625*x^5)*Log[x]^4),x
]

[Out]

2/E^((50*(-5 + x)^2*(2 + x)*Log[x]^2)/(5 + x - 75*(-5 + x)^2*Log[x]^2))

________________________________________________________________________________________

fricas [A]  time = 0.72, size = 43, normalized size = 1.34 \begin {gather*} 2 \, e^{\left (\frac {50 \, {\left (x^{3} - 8 \, x^{2} + 5 \, x + 50\right )} \log \relax (x)^{2}}{75 \, {\left (x^{2} - 10 \, x + 25\right )} \log \relax (x)^{2} - x - 5}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((7500*x^5-150000*x^4+1125000*x^3-3750000*x^2+4687500*x)*log(x)^4+(-200*x^4-700*x^3+8000*x^2+2500*x)
*log(x)^2+(-200*x^4+600*x^3+7000*x^2-15000*x-50000)*log(x))*exp((50*x^3-400*x^2+250*x+2500)*log(x)^2/((75*x^2-
750*x+1875)*log(x)^2-x-5))/((5625*x^5-112500*x^4+843750*x^3-2812500*x^2+3515625*x)*log(x)^4+(-150*x^4+750*x^3+
3750*x^2-18750*x)*log(x)^2+x^3+10*x^2+25*x),x, algorithm="fricas")

[Out]

2*e^(50*(x^3 - 8*x^2 + 5*x + 50)*log(x)^2/(75*(x^2 - 10*x + 25)*log(x)^2 - x - 5))

________________________________________________________________________________________

giac [B]  time = 0.63, size = 151, normalized size = 4.72 \begin {gather*} 2 \, e^{\left (\frac {50 \, x^{3} \log \relax (x)^{2}}{75 \, x^{2} \log \relax (x)^{2} - 750 \, x \log \relax (x)^{2} + 1875 \, \log \relax (x)^{2} - x - 5} - \frac {400 \, x^{2} \log \relax (x)^{2}}{75 \, x^{2} \log \relax (x)^{2} - 750 \, x \log \relax (x)^{2} + 1875 \, \log \relax (x)^{2} - x - 5} + \frac {250 \, x \log \relax (x)^{2}}{75 \, x^{2} \log \relax (x)^{2} - 750 \, x \log \relax (x)^{2} + 1875 \, \log \relax (x)^{2} - x - 5} + \frac {2500 \, \log \relax (x)^{2}}{75 \, x^{2} \log \relax (x)^{2} - 750 \, x \log \relax (x)^{2} + 1875 \, \log \relax (x)^{2} - x - 5}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((7500*x^5-150000*x^4+1125000*x^3-3750000*x^2+4687500*x)*log(x)^4+(-200*x^4-700*x^3+8000*x^2+2500*x)
*log(x)^2+(-200*x^4+600*x^3+7000*x^2-15000*x-50000)*log(x))*exp((50*x^3-400*x^2+250*x+2500)*log(x)^2/((75*x^2-
750*x+1875)*log(x)^2-x-5))/((5625*x^5-112500*x^4+843750*x^3-2812500*x^2+3515625*x)*log(x)^4+(-150*x^4+750*x^3+
3750*x^2-18750*x)*log(x)^2+x^3+10*x^2+25*x),x, algorithm="giac")

[Out]

2*e^(50*x^3*log(x)^2/(75*x^2*log(x)^2 - 750*x*log(x)^2 + 1875*log(x)^2 - x - 5) - 400*x^2*log(x)^2/(75*x^2*log
(x)^2 - 750*x*log(x)^2 + 1875*log(x)^2 - x - 5) + 250*x*log(x)^2/(75*x^2*log(x)^2 - 750*x*log(x)^2 + 1875*log(
x)^2 - x - 5) + 2500*log(x)^2/(75*x^2*log(x)^2 - 750*x*log(x)^2 + 1875*log(x)^2 - x - 5))

________________________________________________________________________________________

maple [F]  time = 0.03, size = 0, normalized size = 0.00 \[\int \frac {\left (\left (7500 x^{5}-150000 x^{4}+1125000 x^{3}-3750000 x^{2}+4687500 x \right ) \ln \relax (x )^{4}+\left (-200 x^{4}-700 x^{3}+8000 x^{2}+2500 x \right ) \ln \relax (x )^{2}+\left (-200 x^{4}+600 x^{3}+7000 x^{2}-15000 x -50000\right ) \ln \relax (x )\right ) {\mathrm e}^{\frac {\left (50 x^{3}-400 x^{2}+250 x +2500\right ) \ln \relax (x )^{2}}{\left (75 x^{2}-750 x +1875\right ) \ln \relax (x )^{2}-x -5}}}{\left (5625 x^{5}-112500 x^{4}+843750 x^{3}-2812500 x^{2}+3515625 x \right ) \ln \relax (x )^{4}+\left (-150 x^{4}+750 x^{3}+3750 x^{2}-18750 x \right ) \ln \relax (x )^{2}+x^{3}+10 x^{2}+25 x}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((7500*x^5-150000*x^4+1125000*x^3-3750000*x^2+4687500*x)*ln(x)^4+(-200*x^4-700*x^3+8000*x^2+2500*x)*ln(x)^
2+(-200*x^4+600*x^3+7000*x^2-15000*x-50000)*ln(x))*exp((50*x^3-400*x^2+250*x+2500)*ln(x)^2/((75*x^2-750*x+1875
)*ln(x)^2-x-5))/((5625*x^5-112500*x^4+843750*x^3-2812500*x^2+3515625*x)*ln(x)^4+(-150*x^4+750*x^3+3750*x^2-187
50*x)*ln(x)^2+x^3+10*x^2+25*x),x)

[Out]

int(((7500*x^5-150000*x^4+1125000*x^3-3750000*x^2+4687500*x)*ln(x)^4+(-200*x^4-700*x^3+8000*x^2+2500*x)*ln(x)^
2+(-200*x^4+600*x^3+7000*x^2-15000*x-50000)*ln(x))*exp((50*x^3-400*x^2+250*x+2500)*ln(x)^2/((75*x^2-750*x+1875
)*ln(x)^2-x-5))/((5625*x^5-112500*x^4+843750*x^3-2812500*x^2+3515625*x)*ln(x)^4+(-150*x^4+750*x^3+3750*x^2-187
50*x)*ln(x)^2+x^3+10*x^2+25*x),x)

________________________________________________________________________________________

maxima [B]  time = 107.87, size = 118, normalized size = 3.69 \begin {gather*} 2 \, e^{\left (\frac {2}{3} \, x + \frac {2 \, x}{225 \, {\left (75 \, {\left (x^{2} - 10 \, x + 25\right )} \log \relax (x)^{4} - {\left (x + 5\right )} \log \relax (x)^{2}\right )}} + \frac {34 \, x}{3 \, {\left (75 \, {\left (x^{2} - 10 \, x + 25\right )} \log \relax (x)^{2} - x - 5\right )}} + \frac {2}{45 \, {\left (75 \, {\left (x^{2} - 10 \, x + 25\right )} \log \relax (x)^{4} - {\left (x + 5\right )} \log \relax (x)^{2}\right )}} - \frac {10}{75 \, {\left (x^{2} - 10 \, x + 25\right )} \log \relax (x)^{2} - x - 5} + \frac {2}{225 \, \log \relax (x)^{2}} + \frac {4}{3}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((7500*x^5-150000*x^4+1125000*x^3-3750000*x^2+4687500*x)*log(x)^4+(-200*x^4-700*x^3+8000*x^2+2500*x)
*log(x)^2+(-200*x^4+600*x^3+7000*x^2-15000*x-50000)*log(x))*exp((50*x^3-400*x^2+250*x+2500)*log(x)^2/((75*x^2-
750*x+1875)*log(x)^2-x-5))/((5625*x^5-112500*x^4+843750*x^3-2812500*x^2+3515625*x)*log(x)^4+(-150*x^4+750*x^3+
3750*x^2-18750*x)*log(x)^2+x^3+10*x^2+25*x),x, algorithm="maxima")

[Out]

2*e^(2/3*x + 2/225*x/(75*(x^2 - 10*x + 25)*log(x)^4 - (x + 5)*log(x)^2) + 34/3*x/(75*(x^2 - 10*x + 25)*log(x)^
2 - x - 5) + 2/45/(75*(x^2 - 10*x + 25)*log(x)^4 - (x + 5)*log(x)^2) - 10/(75*(x^2 - 10*x + 25)*log(x)^2 - x -
5) + 2/225/log(x)^2 + 4/3)

________________________________________________________________________________________

mupad [B]  time = 4.95, size = 64, normalized size = 2.00 \begin {gather*} 2\,{\mathrm {e}}^{-\frac {50\,x^3\,{\ln \relax (x)}^2-400\,x^2\,{\ln \relax (x)}^2+250\,x\,{\ln \relax (x)}^2+2500\,{\ln \relax (x)}^2}{-75\,x^2\,{\ln \relax (x)}^2+750\,x\,{\ln \relax (x)}^2+x-1875\,{\ln \relax (x)}^2+5}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(-(log(x)^2*(250*x - 400*x^2 + 50*x^3 + 2500))/(x - log(x)^2*(75*x^2 - 750*x + 1875) + 5))*(log(x)^2*(
2500*x + 8000*x^2 - 700*x^3 - 200*x^4) - log(x)*(15000*x - 7000*x^2 - 600*x^3 + 200*x^4 + 50000) + log(x)^4*(4
687500*x - 3750000*x^2 + 1125000*x^3 - 150000*x^4 + 7500*x^5)))/(25*x - log(x)^2*(18750*x - 3750*x^2 - 750*x^3
+ 150*x^4) + log(x)^4*(3515625*x - 2812500*x^2 + 843750*x^3 - 112500*x^4 + 5625*x^5) + 10*x^2 + x^3),x)

[Out]

2*exp(-(250*x*log(x)^2 + 2500*log(x)^2 - 400*x^2*log(x)^2 + 50*x^3*log(x)^2)/(x + 750*x*log(x)^2 - 1875*log(x)
^2 - 75*x^2*log(x)^2 + 5))

________________________________________________________________________________________

sympy [A]  time = 2.01, size = 41, normalized size = 1.28 \begin {gather*} 2 e^{\frac {\left (50 x^{3} - 400 x^{2} + 250 x + 2500\right ) \log {\relax (x )}^{2}}{- x + \left (75 x^{2} - 750 x + 1875\right ) \log {\relax (x )}^{2} - 5}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((7500*x**5-150000*x**4+1125000*x**3-3750000*x**2+4687500*x)*ln(x)**4+(-200*x**4-700*x**3+8000*x**2+
2500*x)*ln(x)**2+(-200*x**4+600*x**3+7000*x**2-15000*x-50000)*ln(x))*exp((50*x**3-400*x**2+250*x+2500)*ln(x)**
2/((75*x**2-750*x+1875)*ln(x)**2-x-5))/((5625*x**5-112500*x**4+843750*x**3-2812500*x**2+3515625*x)*ln(x)**4+(-
150*x**4+750*x**3+3750*x**2-18750*x)*ln(x)**2+x**3+10*x**2+25*x),x)

[Out]

2*exp((50*x**3 - 400*x**2 + 250*x + 2500)*log(x)**2/(-x + (75*x**2 - 750*x + 1875)*log(x)**2 - 5))

________________________________________________________________________________________