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

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

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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 = {} $$\begin{array}{c}\int \frac{\exp \left(\frac{(2500+250x-400x^2+50x^3){\log }^2(x)}{-5-x+(1875-750x+75x^2){\log }^2(x)}\right)((-50000-15000x+7000x^2+600x^3-200x^4)\log (x)+(2500x+8000x^2-700x^3-200x^4){\log }^2(x)+(4687500x-3750000x^2+1125000x^3-150000x^4+7500x^5){\log }^4(x))}{25x+10x^2+x^3+(-18750x+3750x^2+750x^3-150x^4){\log }^2(x)+(3515625x-2812500x^2+843750x^3-112500x^4+5625x^5){\log }^4(x)}dx\end{array}$$

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

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

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))

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

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))

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

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))

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

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)

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

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)

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

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))

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

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))

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