3.66.0 ∫ 9796900−175000e5x+17500e6x−1000e7x+25e8x+31285x+e2x(10945000+7500x−7500x2)+e4x(1093800+50x−100x2)+e3x(−4376000−1000x+1500x2)+ex(−15650000−25000x+12500x2)+(18780−15000ex+4500e2x−600e3x+30e4x+30x) log(x)+9 log2(x) 9796900−15650000ex+10945000e2x−4376000e3x+1093800e4x−175000e5x+17500e6x−1000e7x+25e8x+(18780−15000ex+4500e2x−600e3x+30e4x) log(x)+9 log2(x) dx [6583]

Integrand size = 231, antiderivative size = 28 \[ \int \frac {9796900-175000 e^{5 x}+17500 e^{6 x}-1000 e^{7 x}+25 e^{8 x}+31285 x+e^{2 x} \left (10945000+7500 x-7500 x^2\right )+e^{4 x} \left (1093800+50 x-100 x^2\right )+e^{3 x} \left (-4376000-1000 x+1500 x^2\right )+e^x \left (-15650000-25000 x+12500 x^2\right )+\left (18780-15000 e^x+4500 e^{2 x}-600 e^{3 x}+30 e^{4 x}+30 x\right ) \log (x)+9 \log ^2(x)}{9796900-15650000 e^x+10945000 e^{2 x}-4376000 e^{3 x}+1093800 e^{4 x}-175000 e^{5 x}+17500 e^{6 x}-1000 e^{7 x}+25 e^{8 x}+\left (18780-15000 e^x+4500 e^{2 x}-600 e^{3 x}+30 e^{4 x}\right ) \log (x)+9 \log ^2(x)} \, dx=x+\frac {x^2}{\left (5-e^x\right )^4+\frac {1}{5} (5+3 \log (x))} \]

Rubi [F]

\[ \int \frac {9796900-175000 e^{5 x}+17500 e^{6 x}-1000 e^{7 x}+25 e^{8 x}+31285 x+e^{2 x} \left (10945000+7500 x-7500 x^2\right )+e^{4 x} \left (1093800+50 x-100 x^2\right )+e^{3 x} \left (-4376000-1000 x+1500 x^2\right )+e^x \left (-15650000-25000 x+12500 x^2\right )+\left (18780-15000 e^x+4500 e^{2 x}-600 e^{3 x}+30 e^{4 x}+30 x\right ) \log (x)+9 \log ^2(x)}{9796900-15650000 e^x+10945000 e^{2 x}-4376000 e^{3 x}+1093800 e^{4 x}-175000 e^{5 x}+17500 e^{6 x}-1000 e^{7 x}+25 e^{8 x}+\left (18780-15000 e^x+4500 e^{2 x}-600 e^{3 x}+30 e^{4 x}\right ) \log (x)+9 \log ^2(x)} \, dx=\int \frac {9796900-175000 e^{5 x}+17500 e^{6 x}-1000 e^{7 x}+25 e^{8 x}+31285 x+e^{2 x} \left (10945000+7500 x-7500 x^2\right )+e^{4 x} \left (1093800+50 x-100 x^2\right )+e^{3 x} \left (-4376000-1000 x+1500 x^2\right )+e^x \left (-15650000-25000 x+12500 x^2\right )+\left (18780-15000 e^x+4500 e^{2 x}-600 e^{3 x}+30 e^{4 x}+30 x\right ) \log (x)+9 \log ^2(x)}{9796900-15650000 e^x+10945000 e^{2 x}-4376000 e^{3 x}+1093800 e^{4 x}-175000 e^{5 x}+17500 e^{6 x}-1000 e^{7 x}+25 e^{8 x}+\left (18780-15000 e^x+4500 e^{2 x}-600 e^{3 x}+30 e^{4 x}\right ) \log (x)+9 \log ^2(x)} \, dx \]

Int[(9796900 - 175000*E^(5*x) + 17500*E^(6*x) - 1000*E^(7*x) + 25*E^(8*x) + 31285*x + E^(2*x)*(10945000 + 7500

*x - 7500*x^2) + E^(4*x)*(1093800 + 50*x - 100*x^2) + E^(3*x)*(-4376000 - 1000*x + 1500*x^2) + E^x*(-15650000

- 25000*x + 12500*x^2) + (18780 - 15000*E^x + 4500*E^(2*x) - 600*E^(3*x) + 30*E^(4*x) + 30*x)*Log[x] + 9*Log[x

]^2)/(9796900 - 15650000*E^x + 10945000*E^(2*x) - 4376000*E^(3*x) + 1093800*E^(4*x) - 175000*E^(5*x) + 17500*E

^(6*x) - 1000*E^(7*x) + 25*E^(8*x) + (18780 - 15000*E^x + 4500*E^(2*x) - 600*E^(3*x) + 30*E^(4*x))*Log[x] + 9*

x - 15*Defer[Int][x/(3130 - 2500*E^x + 750*E^(2*x) - 100*E^(3*x) + 5*E^(4*x) + 3*Log[x])^2, x] + 62600*Defer[I

nt][x^2/(3130 - 2500*E^x + 750*E^(2*x) - 100*E^(3*x) + 5*E^(4*x) + 3*Log[x])^2, x] - 37500*Defer[Int][(E^x*x^2

)/(3130 - 2500*E^x + 750*E^(2*x) - 100*E^(3*x) + 5*E^(4*x) + 3*Log[x])^2, x] + 7500*Defer[Int][(E^(2*x)*x^2)/(

3130 - 2500*E^x + 750*E^(2*x) - 100*E^(3*x) + 5*E^(4*x) + 3*Log[x])^2, x] - 500*Defer[Int][(E^(3*x)*x^2)/(3130

- 2500*E^x + 750*E^(2*x) - 100*E^(3*x) + 5*E^(4*x) + 3*Log[x])^2, x] + 60*Defer[Int][(x^2*Log[x])/(3130 - 250

0*E^x + 750*E^(2*x) - 100*E^(3*x) + 5*E^(4*x) + 3*Log[x])^2, x] + 10*Defer[Int][x/(3130 - 2500*E^x + 750*E^(2*

x) - 100*E^(3*x) + 5*E^(4*x) + 3*Log[x]), x] - 20*Defer[Int][x^2/(3130 - 2500*E^x + 750*E^(2*x) - 100*E^(3*x)

Rubi steps \begin{align*} \text {integral}& = \int \frac {5 \left (1959380-35000 e^{5 x}+3500 e^{6 x}-200 e^{7 x}+5 e^{8 x}+6257 x+10 e^{4 x} \left (21876+x-2 x^2\right )+2500 e^x \left (-1252-2 x+x^2\right )-500 e^{2 x} \left (-4378-3 x+3 x^2\right )+100 e^{3 x} \left (-8752-2 x+3 x^2\right )\right )+30 \left (626-500 e^x+150 e^{2 x}-20 e^{3 x}+e^{4 x}+x\right ) \log (x)+9 \log ^2(x)}{\left (5 \left (626-500 e^x+150 e^{2 x}-20 e^{3 x}+e^{4 x}\right )+3 \log (x)\right )^2} \, dx \\ & = \int \left (1-\frac {10 x (-1+2 x)}{3130-2500 e^x+750 e^{2 x}-100 e^{3 x}+5 e^{4 x}+3 \log (x)}-\frac {5 x \left (3-12520 x+7500 e^x x-1500 e^{2 x} x+100 e^{3 x} x-12 x \log (x)\right )}{\left (3130-2500 e^x+750 e^{2 x}-100 e^{3 x}+5 e^{4 x}+3 \log (x)\right )^2}\right ) \, dx \\ & = x-5 \int \frac {x \left (3-12520 x+7500 e^x x-1500 e^{2 x} x+100 e^{3 x} x-12 x \log (x)\right )}{\left (3130-2500 e^x+750 e^{2 x}-100 e^{3 x}+5 e^{4 x}+3 \log (x)\right )^2} \, dx-10 \int \frac {x (-1+2 x)}{3130-2500 e^x+750 e^{2 x}-100 e^{3 x}+5 e^{4 x}+3 \log (x)} \, dx \\ & = x-5 \int \left (\frac {3 x}{\left (3130-2500 e^x+750 e^{2 x}-100 e^{3 x}+5 e^{4 x}+3 \log (x)\right )^2}-\frac {12520 x^2}{\left (3130-2500 e^x+750 e^{2 x}-100 e^{3 x}+5 e^{4 x}+3 \log (x)\right )^2}+\frac {7500 e^x x^2}{\left (3130-2500 e^x+750 e^{2 x}-100 e^{3 x}+5 e^{4 x}+3 \log (x)\right )^2}-\frac {1500 e^{2 x} x^2}{\left (3130-2500 e^x+750 e^{2 x}-100 e^{3 x}+5 e^{4 x}+3 \log (x)\right )^2}+\frac {100 e^{3 x} x^2}{\left (3130-2500 e^x+750 e^{2 x}-100 e^{3 x}+5 e^{4 x}+3 \log (x)\right )^2}-\frac {12 x^2 \log (x)}{\left (3130-2500 e^x+750 e^{2 x}-100 e^{3 x}+5 e^{4 x}+3 \log (x)\right )^2}\right ) \, dx-10 \int \left (-\frac {x}{3130-2500 e^x+750 e^{2 x}-100 e^{3 x}+5 e^{4 x}+3 \log (x)}+\frac {2 x^2}{3130-2500 e^x+750 e^{2 x}-100 e^{3 x}+5 e^{4 x}+3 \log (x)}\right ) \, dx \\ & = x+10 \int \frac {x}{3130-2500 e^x+750 e^{2 x}-100 e^{3 x}+5 e^{4 x}+3 \log (x)} \, dx-15 \int \frac {x}{\left (3130-2500 e^x+750 e^{2 x}-100 e^{3 x}+5 e^{4 x}+3 \log (x)\right )^2} \, dx-20 \int \frac {x^2}{3130-2500 e^x+750 e^{2 x}-100 e^{3 x}+5 e^{4 x}+3 \log (x)} \, dx+60 \int \frac {x^2 \log (x)}{\left (3130-2500 e^x+750 e^{2 x}-100 e^{3 x}+5 e^{4 x}+3 \log (x)\right )^2} \, dx-500 \int \frac {e^{3 x} x^2}{\left (3130-2500 e^x+750 e^{2 x}-100 e^{3 x}+5 e^{4 x}+3 \log (x)\right )^2} \, dx+7500 \int \frac {e^{2 x} x^2}{\left (3130-2500 e^x+750 e^{2 x}-100 e^{3 x}+5 e^{4 x}+3 \log (x)\right )^2} \, dx-37500 \int \frac {e^x x^2}{\left (3130-2500 e^x+750 e^{2 x}-100 e^{3 x}+5 e^{4 x}+3 \log (x)\right )^2} \, dx+62600 \int \frac {x^2}{\left (3130-2500 e^x+750 e^{2 x}-100 e^{3 x}+5 e^{4 x}+3 \log (x)\right )^2} \, dx \\ \end{align*}

Mathematica [A] (veriﬁed)

Time = 0.19 (sec) , antiderivative size = 41, normalized size of antiderivative = 1.46 \[ \int \frac {9796900-175000 e^{5 x}+17500 e^{6 x}-1000 e^{7 x}+25 e^{8 x}+31285 x+e^{2 x} \left (10945000+7500 x-7500 x^2\right )+e^{4 x} \left (1093800+50 x-100 x^2\right )+e^{3 x} \left (-4376000-1000 x+1500 x^2\right )+e^x \left (-15650000-25000 x+12500 x^2\right )+\left (18780-15000 e^x+4500 e^{2 x}-600 e^{3 x}+30 e^{4 x}+30 x\right ) \log (x)+9 \log ^2(x)}{9796900-15650000 e^x+10945000 e^{2 x}-4376000 e^{3 x}+1093800 e^{4 x}-175000 e^{5 x}+17500 e^{6 x}-1000 e^{7 x}+25 e^{8 x}+\left (18780-15000 e^x+4500 e^{2 x}-600 e^{3 x}+30 e^{4 x}\right ) \log (x)+9 \log ^2(x)} \, dx=x+\frac {5 x^2}{3130-2500 e^x+750 e^{2 x}-100 e^{3 x}+5 e^{4 x}+3 \log (x)} \]

Integrate[(9796900 - 175000*E^(5*x) + 17500*E^(6*x) - 1000*E^(7*x) + 25*E^(8*x) + 31285*x + E^(2*x)*(10945000

+ 7500*x - 7500*x^2) + E^(4*x)*(1093800 + 50*x - 100*x^2) + E^(3*x)*(-4376000 - 1000*x + 1500*x^2) + E^x*(-156

50000 - 25000*x + 12500*x^2) + (18780 - 15000*E^x + 4500*E^(2*x) - 600*E^(3*x) + 30*E^(4*x) + 30*x)*Log[x] + 9

*Log[x]^2)/(9796900 - 15650000*E^x + 10945000*E^(2*x) - 4376000*E^(3*x) + 1093800*E^(4*x) - 175000*E^(5*x) + 1

7500*E^(6*x) - 1000*E^(7*x) + 25*E^(8*x) + (18780 - 15000*E^x + 4500*E^(2*x) - 600*E^(3*x) + 30*E^(4*x))*Log[x

Maple [A] (veriﬁed)

Time = 0.84 (sec) , antiderivative size = 38, normalized size of antiderivative = 1.36


method	result	size

risch	\(x +\frac {5 x^{2}}{5 \,{\mathrm e}^{4 x}-100 \,{\mathrm e}^{3 x}+750 \,{\mathrm e}^{2 x}+3 \ln \left (x \right )-2500 \,{\mathrm e}^{x}+3130}\)	\(38\)
parallelrisch	\(\frac {939000 x +225000 x \,{\mathrm e}^{2 x}-30000 x \,{\mathrm e}^{3 x}-750000 \,{\mathrm e}^{x} x +900 x \ln \left (x \right )+1500 x \,{\mathrm e}^{4 x}+1500 x^{2}}{1500 \,{\mathrm e}^{4 x}-30000 \,{\mathrm e}^{3 x}+225000 \,{\mathrm e}^{2 x}+900 \ln \left (x \right )-750000 \,{\mathrm e}^{x}+939000}\)	\(73\)

int((9*ln(x)^2+(30*exp(x)^4-600*exp(x)^3+4500*exp(x)^2-15000*exp(x)+30*x+18780)*ln(x)+25*exp(x)^8-1000*exp(x)^

7+17500*exp(x)^6-175000*exp(x)^5+(-100*x^2+50*x+1093800)*exp(x)^4+(1500*x^2-1000*x-4376000)*exp(x)^3+(-7500*x^

2+7500*x+10945000)*exp(x)^2+(12500*x^2-25000*x-15650000)*exp(x)+31285*x+9796900)/(9*ln(x)^2+(30*exp(x)^4-600*e

xp(x)^3+4500*exp(x)^2-15000*exp(x)+18780)*ln(x)+25*exp(x)^8-1000*exp(x)^7+17500*exp(x)^6-175000*exp(x)^5+10938

Fricas [B] (veriﬁcation not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 71 vs. \(2 (23) = 46\).

Time = 0.26 (sec) , antiderivative size = 71, normalized size of antiderivative = 2.54 \[ \int \frac {9796900-175000 e^{5 x}+17500 e^{6 x}-1000 e^{7 x}+25 e^{8 x}+31285 x+e^{2 x} \left (10945000+7500 x-7500 x^2\right )+e^{4 x} \left (1093800+50 x-100 x^2\right )+e^{3 x} \left (-4376000-1000 x+1500 x^2\right )+e^x \left (-15650000-25000 x+12500 x^2\right )+\left (18780-15000 e^x+4500 e^{2 x}-600 e^{3 x}+30 e^{4 x}+30 x\right ) \log (x)+9 \log ^2(x)}{9796900-15650000 e^x+10945000 e^{2 x}-4376000 e^{3 x}+1093800 e^{4 x}-175000 e^{5 x}+17500 e^{6 x}-1000 e^{7 x}+25 e^{8 x}+\left (18780-15000 e^x+4500 e^{2 x}-600 e^{3 x}+30 e^{4 x}\right ) \log (x)+9 \log ^2(x)} \, dx=\frac {5 \, x^{2} + 5 \, x e^{\left (4 \, x\right )} - 100 \, x e^{\left (3 \, x\right )} + 750 \, x e^{\left (2 \, x\right )} - 2500 \, x e^{x} + 3 \, x \log \left (x\right ) + 3130 \, x}{5 \, e^{\left (4 \, x\right )} - 100 \, e^{\left (3 \, x\right )} + 750 \, e^{\left (2 \, x\right )} - 2500 \, e^{x} + 3 \, \log \left (x\right ) + 3130} \]

integrate((9*log(x)^2+(30*exp(x)^4-600*exp(x)^3+4500*exp(x)^2-15000*exp(x)+30*x+18780)*log(x)+25*exp(x)^8-1000

*exp(x)^7+17500*exp(x)^6-175000*exp(x)^5+(-100*x^2+50*x+1093800)*exp(x)^4+(1500*x^2-1000*x-4376000)*exp(x)^3+(

-7500*x^2+7500*x+10945000)*exp(x)^2+(12500*x^2-25000*x-15650000)*exp(x)+31285*x+9796900)/(9*log(x)^2+(30*exp(x

)^4-600*exp(x)^3+4500*exp(x)^2-15000*exp(x)+18780)*log(x)+25*exp(x)^8-1000*exp(x)^7+17500*exp(x)^6-175000*exp(

x)^5+1093800*exp(x)^4-4376000*exp(x)^3+10945000*exp(x)^2-15650000*exp(x)+9796900),x, algorithm="fricas")

(5*x^2 + 5*x*e^(4*x) - 100*x*e^(3*x) + 750*x*e^(2*x) - 2500*x*e^x + 3*x*log(x) + 3130*x)/(5*e^(4*x) - 100*e^(3

Sympy [A] (veriﬁcation not implemented)

Time = 0.23 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.29 \[ \int \frac {9796900-175000 e^{5 x}+17500 e^{6 x}-1000 e^{7 x}+25 e^{8 x}+31285 x+e^{2 x} \left (10945000+7500 x-7500 x^2\right )+e^{4 x} \left (1093800+50 x-100 x^2\right )+e^{3 x} \left (-4376000-1000 x+1500 x^2\right )+e^x \left (-15650000-25000 x+12500 x^2\right )+\left (18780-15000 e^x+4500 e^{2 x}-600 e^{3 x}+30 e^{4 x}+30 x\right ) \log (x)+9 \log ^2(x)}{9796900-15650000 e^x+10945000 e^{2 x}-4376000 e^{3 x}+1093800 e^{4 x}-175000 e^{5 x}+17500 e^{6 x}-1000 e^{7 x}+25 e^{8 x}+\left (18780-15000 e^x+4500 e^{2 x}-600 e^{3 x}+30 e^{4 x}\right ) \log (x)+9 \log ^2(x)} \, dx=\frac {x^{2}}{e^{4 x} - 20 e^{3 x} + 150 e^{2 x} - 500 e^{x} + \frac {3 \log {\left (x \right )}}{5} + 626} + x \]

integrate((9*ln(x)**2+(30*exp(x)**4-600*exp(x)**3+4500*exp(x)**2-15000*exp(x)+30*x+18780)*ln(x)+25*exp(x)**8-1

000*exp(x)**7+17500*exp(x)**6-175000*exp(x)**5+(-100*x**2+50*x+1093800)*exp(x)**4+(1500*x**2-1000*x-4376000)*e

xp(x)**3+(-7500*x**2+7500*x+10945000)*exp(x)**2+(12500*x**2-25000*x-15650000)*exp(x)+31285*x+9796900)/(9*ln(x)

**2+(30*exp(x)**4-600*exp(x)**3+4500*exp(x)**2-15000*exp(x)+18780)*ln(x)+25*exp(x)**8-1000*exp(x)**7+17500*exp

(x)**6-175000*exp(x)**5+1093800*exp(x)**4-4376000*exp(x)**3+10945000*exp(x)**2-15650000*exp(x)+9796900),x)

Maxima [B] (veriﬁcation not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 71 vs. \(2 (23) = 46\).

Time = 0.37 (sec) , antiderivative size = 71, normalized size of antiderivative = 2.54 \[ \int \frac {9796900-175000 e^{5 x}+17500 e^{6 x}-1000 e^{7 x}+25 e^{8 x}+31285 x+e^{2 x} \left (10945000+7500 x-7500 x^2\right )+e^{4 x} \left (1093800+50 x-100 x^2\right )+e^{3 x} \left (-4376000-1000 x+1500 x^2\right )+e^x \left (-15650000-25000 x+12500 x^2\right )+\left (18780-15000 e^x+4500 e^{2 x}-600 e^{3 x}+30 e^{4 x}+30 x\right ) \log (x)+9 \log ^2(x)}{9796900-15650000 e^x+10945000 e^{2 x}-4376000 e^{3 x}+1093800 e^{4 x}-175000 e^{5 x}+17500 e^{6 x}-1000 e^{7 x}+25 e^{8 x}+\left (18780-15000 e^x+4500 e^{2 x}-600 e^{3 x}+30 e^{4 x}\right ) \log (x)+9 \log ^2(x)} \, dx=\frac {5 \, x^{2} + 5 \, x e^{\left (4 \, x\right )} - 100 \, x e^{\left (3 \, x\right )} + 750 \, x e^{\left (2 \, x\right )} - 2500 \, x e^{x} + 3 \, x \log \left (x\right ) + 3130 \, x}{5 \, e^{\left (4 \, x\right )} - 100 \, e^{\left (3 \, x\right )} + 750 \, e^{\left (2 \, x\right )} - 2500 \, e^{x} + 3 \, \log \left (x\right ) + 3130} \]

integrate((9*log(x)^2+(30*exp(x)^4-600*exp(x)^3+4500*exp(x)^2-15000*exp(x)+30*x+18780)*log(x)+25*exp(x)^8-1000

*exp(x)^7+17500*exp(x)^6-175000*exp(x)^5+(-100*x^2+50*x+1093800)*exp(x)^4+(1500*x^2-1000*x-4376000)*exp(x)^3+(

-7500*x^2+7500*x+10945000)*exp(x)^2+(12500*x^2-25000*x-15650000)*exp(x)+31285*x+9796900)/(9*log(x)^2+(30*exp(x

)^4-600*exp(x)^3+4500*exp(x)^2-15000*exp(x)+18780)*log(x)+25*exp(x)^8-1000*exp(x)^7+17500*exp(x)^6-175000*exp(

x)^5+1093800*exp(x)^4-4376000*exp(x)^3+10945000*exp(x)^2-15650000*exp(x)+9796900),x, algorithm="maxima")

(5*x^2 + 5*x*e^(4*x) - 100*x*e^(3*x) + 750*x*e^(2*x) - 2500*x*e^x + 3*x*log(x) + 3130*x)/(5*e^(4*x) - 100*e^(3

Giac [B] (veriﬁcation not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 1712 vs. \(2 (23) = 46\).

Time = 25.33 (sec) , antiderivative size = 1712, normalized size of antiderivative = 61.14 \[ \int \frac {9796900-175000 e^{5 x}+17500 e^{6 x}-1000 e^{7 x}+25 e^{8 x}+31285 x+e^{2 x} \left (10945000+7500 x-7500 x^2\right )+e^{4 x} \left (1093800+50 x-100 x^2\right )+e^{3 x} \left (-4376000-1000 x+1500 x^2\right )+e^x \left (-15650000-25000 x+12500 x^2\right )+\left (18780-15000 e^x+4500 e^{2 x}-600 e^{3 x}+30 e^{4 x}+30 x\right ) \log (x)+9 \log ^2(x)}{9796900-15650000 e^x+10945000 e^{2 x}-4376000 e^{3 x}+1093800 e^{4 x}-175000 e^{5 x}+17500 e^{6 x}-1000 e^{7 x}+25 e^{8 x}+\left (18780-15000 e^x+4500 e^{2 x}-600 e^{3 x}+30 e^{4 x}\right ) \log (x)+9 \log ^2(x)} \, dx=\text {Too large to display} \]

integrate((9*log(x)^2+(30*exp(x)^4-600*exp(x)^3+4500*exp(x)^2-15000*exp(x)+30*x+18780)*log(x)+25*exp(x)^8-1000

*exp(x)^7+17500*exp(x)^6-175000*exp(x)^5+(-100*x^2+50*x+1093800)*exp(x)^4+(1500*x^2-1000*x-4376000)*exp(x)^3+(

-7500*x^2+7500*x+10945000)*exp(x)^2+(12500*x^2-25000*x-15650000)*exp(x)+31285*x+9796900)/(9*log(x)^2+(30*exp(x

)^4-600*exp(x)^3+4500*exp(x)^2-15000*exp(x)+18780)*log(x)+25*exp(x)^8-1000*exp(x)^7+17500*exp(x)^6-175000*exp(

x)^5+1093800*exp(x)^4-4376000*exp(x)^3+10945000*exp(x)^2-15650000*exp(x)+9796900),x, algorithm="giac")

(103680*x^6*log(x)^4 + 103680*x^5*e^(4*x)*log(x)^4 - 2073600*x^5*e^(3*x)*log(x)^4 + 15552000*x^5*e^(2*x)*log(x

)^4 - 51840000*x^5*e^x*log(x)^4 + 62208*x^5*log(x)^5 + 108691200*x^6*log(x)^3 + 108691200*x^5*e^(4*x)*log(x)^3

- 2173392000*x^5*e^(3*x)*log(x)^3 + 16295040000*x^5*e^(2*x)*log(x)^3 - 54280800000*x^5*e^x*log(x)^3 + 1301702

40*x^5*log(x)^4 + 129600*x^4*e^(3*x)*log(x)^4 - 2592000*x^4*e^(2*x)*log(x)^4 + 19440000*x^4*e^x*log(x)^4 + 155

52*x^4*log(x)^5 + 541728000*x^6*log(x)^2 + 541728000*x^5*e^(4*x)*log(x)^2 - 10382616000*x^5*e^(3*x)*log(x)^2 +

72220320000*x^5*e^(2*x)*log(x)^2 - 203072400000*x^5*e^x*log(x)^2 + 68257944000*x^5*log(x)^3 - 103680*x^4*e^(4

*x)*log(x)^3 + 272937600*x^4*e^(3*x)*log(x)^3 - 5432832000*x^4*e^(2*x)*log(x)^3 + 40681440000*x^4*e^x*log(x)^3

- 16132608*x^4*log(x)^4 + 901920000*x^6*log(x) + 901920000*x^5*e^(4*x)*log(x) - 16535520000*x^5*e^(3*x)*log(x

) + 105230400000*x^5*e^(2*x)*log(x) - 225528000000*x^5*e^x*log(x) + 170454096000*x^5*log(x)^2 - 518400*x^4*e^(

4*x)*log(x)^2 + 141987312000*x^4*e^(3*x)*log(x)^2 - 2839617180000*x^4*e^(2*x)*log(x)^2 + 21296811600000*x^4*e^

x*log(x)^2 - 84547821600*x^4*log(x)^3 - 64800*x^3*e^(3*x)*log(x)^3 + 1134000*x^3*e^(2*x)*log(x)^3 - 6480000*x^

3*e^x*log(x)^3 - 11664*x^3*log(x)^4 + 500800000*x^6 + 500800000*x^5*e^(4*x) - 8764600000*x^5*e^(3*x) + 5009200

0000*x^5*e^(2*x) - 62690000000*x^5*e^x + 1772280000*x^5*log(x) - 864000*x^4*e^(4*x)*log(x) + 470794068000*x^4*

e^(3*x)*log(x) - 9416229390000*x^4*e^(2*x)*log(x) + 70628230800000*x^4*e^x*log(x) - 53156844452880*x^4*log(x)^

2 + 38880*x^3*e^(4*x)*log(x)^2 - 136101600*x^3*e^(3*x)*log(x)^2 + 2374002000*x^3*e^(2*x)*log(x)^2 - 1355184000

0*x^3*e^x*log(x)^2 - 12204432*x^3*log(x)^3 - 155524400000*x^5 - 480000*x^4*e^(4*x) + 391510180000*x^4*e^(3*x)

- 7831022150000*x^4*e^(2*x) + 58744098000000*x^4*e^x - 176443048431600*x^4*log(x) + 129600*x^3*e^(4*x)*log(x)

- 70765605000*x^3*e^(3*x)*log(x) + 1238372235000*x^3*e^(2*x)*log(x) - 7076366775000*x^3*e^x*log(x) + 126197319

60*x^3*log(x)^2 + 8100*x^2*e^(3*x)*log(x)^2 - 121500*x^2*e^(2*x)*log(x)^2 + 607500*x^2*e^x*log(x)^2 + 2916*x^2

*log(x)^3 - 146805146548000*x^4 + 108000*x^3*e^(4*x) - 117536803500*x^3*e^(3*x) + 2056942852500*x^3*e^(2*x) -

11754222262500*x^3*e^x + 13225767749460*x^3*log(x) - 6480*x^2*e^(4*x)*log(x) + 17031600*x^2*e^(3*x)*log(x) - 2

54502000*x^2*e^(2*x)*log(x) + 1270890000*x^2*e^x*log(x) + 5073192*x^2*log(x)^2 + 22004321088600*x^3 - 10800*x^

2*e^(4*x) + 8817426000*x^2*e^(3*x) - 132259770000*x^2*e^(2*x) + 661296150000*x^2*e^x + 1067523030*x^2*log(x) -

243*x*log(x)^2 - 1096868529090*x^2 + 405*x*e^(4*x) - 8100*x*e^(3*x) + 60750*x*e^(2*x) - 202500*x*e^x - 506817

*x*log(x) - 264262770*x)/(103680*x^4*e^(4*x)*log(x)^4 - 2073600*x^4*e^(3*x)*log(x)^4 + 15552000*x^4*e^(2*x)*lo

g(x)^4 - 51840000*x^4*e^x*log(x)^4 + 62208*x^4*log(x)^5 + 108691200*x^4*e^(4*x)*log(x)^3 - 2173824000*x^4*e^(3

*x)*log(x)^3 + 16303680000*x^4*e^(2*x)*log(x)^3 - 54345600000*x^4*e^x*log(x)^3 + 130118400*x^4*log(x)^4 + 5417

28000*x^4*e^(4*x)*log(x)^2 - 10834560000*x^4*e^(3*x)*log(x)^2 + 81259200000*x^4*e^(2*x)*log(x)^2 - 27086400000

0*x^4*e^x*log(x)^2 + 68365728000*x^4*log(x)^3 - 103680*x^3*e^(4*x)*log(x)^3 + 2073600*x^3*e^(3*x)*log(x)^3 - 1

5552000*x^3*e^(2*x)*log(x)^3 + 51840000*x^3*e^x*log(x)^3 - 62208*x^3*log(x)^4 + 901920000*x^4*e^(4*x)*log(x) -

18038400000*x^4*e^(3*x)*log(x) + 135288000000*x^4*e^(2*x)*log(x) - 450960000000*x^4*e^x*log(x) + 339662880000

*x^4*log(x)^2 - 518400*x^3*e^(4*x)*log(x)^2 + 10368000*x^3*e^(3*x)*log(x)^2 - 77760000*x^3*e^(2*x)*log(x)^2 +

259200000*x^3*e^x*log(x)^2 - 65214720*x^3*log(x)^3 + 500800000*x^4*e^(4*x) - 10016000000*x^4*e^(3*x) + 7512000

0000*x^4*e^(2*x) - 250400000000*x^4*e^x + 564902400000*x^4*log(x) - 864000*x^3*e^(4*x)*log(x) + 17280000*x^3*e

^(3*x)*log(x) - 129600000*x^3*e^(2*x)*log(x) + 432000000*x^3*e^x*log(x) - 325036800*x^3*log(x)^2 + 38880*x^2*e

^(4*x)*log(x)^2 - 777600*x^2*e^(3*x)*log(x)^2 + 5832000*x^2*e^(2*x)*log(x)^2 - 19440000*x^2*e^x*log(x)^2 + 233

28*x^2*log(x)^3 + 313500800000*x^4 - 480000*x^3*e^(4*x) + 9600000*x^3*e^(3*x) - 72000000*x^3*e^(2*x) + 2400000

00*x^3*e^x - 541152000*x^3*log(x) + 129600*x^2*e^(4*x)*log(x) - 2592000*x^2*e^(3*x)*log(x) + 19440000*x^2*e^(2

*x)*log(x) - 64800000*x^2*e^x*log(x) + 24416640*x^2*log(x)^2 - 300480000*x^3 + 108000*x^2*e^(4*x) - 2160000*x^

2*e^(3*x) + 16200000*x^2*e^(2*x) - 54000000*x^2*e^x + 81194400*x^2*log(x) - 6480*x*e^(4*x)*log(x) + 129600*x*e

^(3*x)*log(x) - 972000*x*e^(2*x)*log(x) + 3240000*x*e^x*log(x) - 3888*x*log(x)^2 + 67608000*x^2 - 10800*x*e^(4

*x) + 216000*x*e^(3*x) - 1620000*x*e^(2*x) + 5400000*x*e^x - 4062960*x*log(x) - 6760800*x + 405*e^(4*x) - 8100

Mupad [F(-1)]

Timed out. \[ \int \frac {9796900-175000 e^{5 x}+17500 e^{6 x}-1000 e^{7 x}+25 e^{8 x}+31285 x+e^{2 x} \left (10945000+7500 x-7500 x^2\right )+e^{4 x} \left (1093800+50 x-100 x^2\right )+e^{3 x} \left (-4376000-1000 x+1500 x^2\right )+e^x \left (-15650000-25000 x+12500 x^2\right )+\left (18780-15000 e^x+4500 e^{2 x}-600 e^{3 x}+30 e^{4 x}+30 x\right ) \log (x)+9 \log ^2(x)}{9796900-15650000 e^x+10945000 e^{2 x}-4376000 e^{3 x}+1093800 e^{4 x}-175000 e^{5 x}+17500 e^{6 x}-1000 e^{7 x}+25 e^{8 x}+\left (18780-15000 e^x+4500 e^{2 x}-600 e^{3 x}+30 e^{4 x}\right ) \log (x)+9 \log ^2(x)} \, dx=\int \frac {9\,{\ln \left (x\right )}^2+\left (30\,x+4500\,{\mathrm {e}}^{2\,x}-600\,{\mathrm {e}}^{3\,x}+30\,{\mathrm {e}}^{4\,x}-15000\,{\mathrm {e}}^x+18780\right )\,\ln \left (x\right )+31285\,x-175000\,{\mathrm {e}}^{5\,x}+17500\,{\mathrm {e}}^{6\,x}-1000\,{\mathrm {e}}^{7\,x}+25\,{\mathrm {e}}^{8\,x}+{\mathrm {e}}^{4\,x}\,\left (-100\,x^2+50\,x+1093800\right )-{\mathrm {e}}^{3\,x}\,\left (-1500\,x^2+1000\,x+4376000\right )+{\mathrm {e}}^{2\,x}\,\left (-7500\,x^2+7500\,x+10945000\right )-{\mathrm {e}}^x\,\left (-12500\,x^2+25000\,x+15650000\right )+9796900}{9\,{\ln \left (x\right )}^2+\left (4500\,{\mathrm {e}}^{2\,x}-600\,{\mathrm {e}}^{3\,x}+30\,{\mathrm {e}}^{4\,x}-15000\,{\mathrm {e}}^x+18780\right )\,\ln \left (x\right )+10945000\,{\mathrm {e}}^{2\,x}-4376000\,{\mathrm {e}}^{3\,x}+1093800\,{\mathrm {e}}^{4\,x}-175000\,{\mathrm {e}}^{5\,x}+17500\,{\mathrm {e}}^{6\,x}-1000\,{\mathrm {e}}^{7\,x}+25\,{\mathrm {e}}^{8\,x}-15650000\,{\mathrm {e}}^x+9796900} \,d x \]

int((31285*x - 175000*exp(5*x) + 17500*exp(6*x) - 1000*exp(7*x) + 25*exp(8*x) + exp(4*x)*(50*x - 100*x^2 + 109

3800) - exp(3*x)*(1000*x - 1500*x^2 + 4376000) + exp(2*x)*(7500*x - 7500*x^2 + 10945000) + 9*log(x)^2 + log(x)

*(30*x + 4500*exp(2*x) - 600*exp(3*x) + 30*exp(4*x) - 15000*exp(x) + 18780) - exp(x)*(25000*x - 12500*x^2 + 15

650000) + 9796900)/(10945000*exp(2*x) - 4376000*exp(3*x) + 1093800*exp(4*x) - 175000*exp(5*x) + 17500*exp(6*x)

- 1000*exp(7*x) + 25*exp(8*x) - 15650000*exp(x) + 9*log(x)^2 + log(x)*(4500*exp(2*x) - 600*exp(3*x) + 30*exp(

int((31285*x - 175000*exp(5*x) + 17500*exp(6*x) - 1000*exp(7*x) + 25*exp(8*x) + exp(4*x)*(50*x - 100*x^2 + 109

3800) - exp(3*x)*(1000*x - 1500*x^2 + 4376000) + exp(2*x)*(7500*x - 7500*x^2 + 10945000) + 9*log(x)^2 + log(x)

*(30*x + 4500*exp(2*x) - 600*exp(3*x) + 30*exp(4*x) - 15000*exp(x) + 18780) - exp(x)*(25000*x - 12500*x^2 + 15

650000) + 9796900)/(10945000*exp(2*x) - 4376000*exp(3*x) + 1093800*exp(4*x) - 175000*exp(5*x) + 17500*exp(6*x)

- 1000*exp(7*x) + 25*exp(8*x) - 15650000*exp(x) + 9*log(x)^2 + log(x)*(4500*exp(2*x) - 600*exp(3*x) + 30*exp(

Optimal result

Rubi [F]

Mathematica [A] (veriﬁed)

Maple [A] (veriﬁed)

Fricas [B] (veriﬁcation not implemented)

Sympy [A] (veriﬁcation not implemented)

Maxima [B] (veriﬁcation not implemented)

Giac [B] (veriﬁcation not implemented)

Mupad [F(-1)]