3.26.24 \(\int \frac {625000 x-625000 x^4+e^{13} (4-2 x+8 x^3-4 x^4)+e^5 (-2500+1250 x-5000 x^3+2500 x^4+e^3 (-1000 x+1000 x^4))+(-875000 x+875000 x^4+e^5 (2000-1000 x+4000 x^3-2000 x^4+e^3 (600 x-600 x^4))) \log (-2+x)+(525000 x-525000 x^4+e^5 (-600+300 x-1200 x^3+600 x^4+e^3 (-120 x+120 x^4))) \log ^2(-2+x)+(-175000 x+175000 x^4+e^5 (80-40 x+160 x^3-80 x^4+e^3 (8 x-8 x^4))) \log ^3(-2+x)+(35000 x-35000 x^4+e^5 (-4+2 x-8 x^3+4 x^4)) \log ^4(-2+x)+(-4200 x+4200 x^4) \log ^5(-2+x)+(280 x-280 x^4) \log ^6(-2+x)+(-8 x+8 x^4) \log ^7(-2+x)+(e^5 (1000 x-1000 x^4)+e^{10} (-4+2 x-8 x^3+4 x^4)+e^5 (-600 x+600 x^4) \log (-2+x)+e^5 (120 x-120 x^4) \log ^2(-2+x)+e^5 (-8 x+8 x^4) \log ^3(-2+x)) \log (\frac {-1+x^3}{x})}{e^{10} (2 x-x^2-2 x^4+x^5)} \, dx\)

Optimal. Leaf size=32 \[ \left (-e^3+\frac {(5-\log (-2+x))^4}{e^5}+\log \left (-\frac {1}{x}+x^2\right )\right )^2 \]

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Rubi [A]  time = 0.61, antiderivative size = 58, normalized size of antiderivative = 1.81, number of steps used = 4, number of rules used = 3, integrand size = 407, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.007, Rules used = {12, 6688, 6686} \begin {gather*} \frac {\left (e^5 \log \left (-\frac {1-x^3}{x}\right )+\log ^4(x-2)-20 \log ^3(x-2)+150 \log ^2(x-2)-500 \log (x-2)-e^8+625\right )^2}{e^{10}} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(625000*x - 625000*x^4 + E^13*(4 - 2*x + 8*x^3 - 4*x^4) + E^5*(-2500 + 1250*x - 5000*x^3 + 2500*x^4 + E^3*
(-1000*x + 1000*x^4)) + (-875000*x + 875000*x^4 + E^5*(2000 - 1000*x + 4000*x^3 - 2000*x^4 + E^3*(600*x - 600*
x^4)))*Log[-2 + x] + (525000*x - 525000*x^4 + E^5*(-600 + 300*x - 1200*x^3 + 600*x^4 + E^3*(-120*x + 120*x^4))
)*Log[-2 + x]^2 + (-175000*x + 175000*x^4 + E^5*(80 - 40*x + 160*x^3 - 80*x^4 + E^3*(8*x - 8*x^4)))*Log[-2 + x
]^3 + (35000*x - 35000*x^4 + E^5*(-4 + 2*x - 8*x^3 + 4*x^4))*Log[-2 + x]^4 + (-4200*x + 4200*x^4)*Log[-2 + x]^
5 + (280*x - 280*x^4)*Log[-2 + x]^6 + (-8*x + 8*x^4)*Log[-2 + x]^7 + (E^5*(1000*x - 1000*x^4) + E^10*(-4 + 2*x
- 8*x^3 + 4*x^4) + E^5*(-600*x + 600*x^4)*Log[-2 + x] + E^5*(120*x - 120*x^4)*Log[-2 + x]^2 + E^5*(-8*x + 8*x
^4)*Log[-2 + x]^3)*Log[(-1 + x^3)/x])/(E^10*(2*x - x^2 - 2*x^4 + x^5)),x]

[Out]

(625 - E^8 - 500*Log[-2 + x] + 150*Log[-2 + x]^2 - 20*Log[-2 + x]^3 + Log[-2 + x]^4 + E^5*Log[-((1 - x^3)/x)])
^2/E^10

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

Rule 6686

Int[(u_)*(y_)^(m_.), x_Symbol] :> With[{q = DerivativeDivides[y, u, x]}, Simp[(q*y^(m + 1))/(m + 1), x] /;  !F
alseQ[q]] /; FreeQ[m, x] && NeQ[m, -1]

Rule 6688

Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; SimplerIntegrandQ[v, u, x]]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \frac {625000 x-625000 x^4+e^{13} \left (4-2 x+8 x^3-4 x^4\right )+e^5 \left (-2500+1250 x-5000 x^3+2500 x^4+e^3 \left (-1000 x+1000 x^4\right )\right )+\left (-875000 x+875000 x^4+e^5 \left (2000-1000 x+4000 x^3-2000 x^4+e^3 \left (600 x-600 x^4\right )\right )\right ) \log (-2+x)+\left (525000 x-525000 x^4+e^5 \left (-600+300 x-1200 x^3+600 x^4+e^3 \left (-120 x+120 x^4\right )\right )\right ) \log ^2(-2+x)+\left (-175000 x+175000 x^4+e^5 \left (80-40 x+160 x^3-80 x^4+e^3 \left (8 x-8 x^4\right )\right )\right ) \log ^3(-2+x)+\left (35000 x-35000 x^4+e^5 \left (-4+2 x-8 x^3+4 x^4\right )\right ) \log ^4(-2+x)+\left (-4200 x+4200 x^4\right ) \log ^5(-2+x)+\left (280 x-280 x^4\right ) \log ^6(-2+x)+\left (-8 x+8 x^4\right ) \log ^7(-2+x)+\left (e^5 \left (1000 x-1000 x^4\right )+e^{10} \left (-4+2 x-8 x^3+4 x^4\right )+e^5 \left (-600 x+600 x^4\right ) \log (-2+x)+e^5 \left (120 x-120 x^4\right ) \log ^2(-2+x)+e^5 \left (-8 x+8 x^4\right ) \log ^3(-2+x)\right ) \log \left (\frac {-1+x^3}{x}\right )}{2 x-x^2-2 x^4+x^5} \, dx}{e^{10}}\\ &=\frac {\int \frac {2 \left (500 x \left (-1+x^3\right )-e^5 \left (-2+x-4 x^3+2 x^4\right )-300 x \left (-1+x^3\right ) \log (-2+x)+60 x \left (-1+x^3\right ) \log ^2(-2+x)-4 x \left (-1+x^3\right ) \log ^3(-2+x)\right ) \left (-625 \left (1-\frac {e^8}{625}\right )+500 \log (-2+x)-150 \log ^2(-2+x)+20 \log ^3(-2+x)-\log ^4(-2+x)-e^5 \log \left (\frac {-1+x^3}{x}\right )\right )}{x \left (2-x-2 x^3+x^4\right )} \, dx}{e^{10}}\\ &=\frac {2 \int \frac {\left (500 x \left (-1+x^3\right )-e^5 \left (-2+x-4 x^3+2 x^4\right )-300 x \left (-1+x^3\right ) \log (-2+x)+60 x \left (-1+x^3\right ) \log ^2(-2+x)-4 x \left (-1+x^3\right ) \log ^3(-2+x)\right ) \left (-625 \left (1-\frac {e^8}{625}\right )+500 \log (-2+x)-150 \log ^2(-2+x)+20 \log ^3(-2+x)-\log ^4(-2+x)-e^5 \log \left (\frac {-1+x^3}{x}\right )\right )}{x \left (2-x-2 x^3+x^4\right )} \, dx}{e^{10}}\\ &=\frac {\left (625-e^8-500 \log (-2+x)+150 \log ^2(-2+x)-20 \log ^3(-2+x)+\log ^4(-2+x)+e^5 \log \left (-\frac {1-x^3}{x}\right )\right )^2}{e^{10}}\\ \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.23, size = 182, normalized size = 5.69 \begin {gather*} -\frac {2 \left (-500 \left (-625+e^8\right ) \log (2-x)+50 \left (-4375+3 e^8\right ) \log ^2(-2+x)-20 \left (-4375+e^8\right ) \log ^3(-2+x)+\left (-21875+e^8\right ) \log ^4(-2+x)+3500 \log ^5(-2+x)-350 \log ^6(-2+x)+20 \log ^7(-2+x)-\frac {1}{2} \log ^8(-2+x)-e^5 \left (-625+e^8\right ) \log (x)+e^5 \left (-625+e^8\right ) \log \left (1-x^3\right )-e^5 \log (-2+x) \left (-500+150 \log (-2+x)-20 \log ^2(-2+x)+\log ^3(-2+x)\right ) \log \left (\frac {-1+x^3}{x}\right )-\frac {1}{2} e^{10} \log ^2\left (\frac {-1+x^3}{x}\right )\right )}{e^{10}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(625000*x - 625000*x^4 + E^13*(4 - 2*x + 8*x^3 - 4*x^4) + E^5*(-2500 + 1250*x - 5000*x^3 + 2500*x^4
+ E^3*(-1000*x + 1000*x^4)) + (-875000*x + 875000*x^4 + E^5*(2000 - 1000*x + 4000*x^3 - 2000*x^4 + E^3*(600*x
- 600*x^4)))*Log[-2 + x] + (525000*x - 525000*x^4 + E^5*(-600 + 300*x - 1200*x^3 + 600*x^4 + E^3*(-120*x + 120
*x^4)))*Log[-2 + x]^2 + (-175000*x + 175000*x^4 + E^5*(80 - 40*x + 160*x^3 - 80*x^4 + E^3*(8*x - 8*x^4)))*Log[
-2 + x]^3 + (35000*x - 35000*x^4 + E^5*(-4 + 2*x - 8*x^3 + 4*x^4))*Log[-2 + x]^4 + (-4200*x + 4200*x^4)*Log[-2
+ x]^5 + (280*x - 280*x^4)*Log[-2 + x]^6 + (-8*x + 8*x^4)*Log[-2 + x]^7 + (E^5*(1000*x - 1000*x^4) + E^10*(-4
+ 2*x - 8*x^3 + 4*x^4) + E^5*(-600*x + 600*x^4)*Log[-2 + x] + E^5*(120*x - 120*x^4)*Log[-2 + x]^2 + E^5*(-8*x
+ 8*x^4)*Log[-2 + x]^3)*Log[(-1 + x^3)/x])/(E^10*(2*x - x^2 - 2*x^4 + x^5)),x]

[Out]

(-2*(-500*(-625 + E^8)*Log[2 - x] + 50*(-4375 + 3*E^8)*Log[-2 + x]^2 - 20*(-4375 + E^8)*Log[-2 + x]^3 + (-2187
5 + E^8)*Log[-2 + x]^4 + 3500*Log[-2 + x]^5 - 350*Log[-2 + x]^6 + 20*Log[-2 + x]^7 - Log[-2 + x]^8/2 - E^5*(-6
25 + E^8)*Log[x] + E^5*(-625 + E^8)*Log[1 - x^3] - E^5*Log[-2 + x]*(-500 + 150*Log[-2 + x] - 20*Log[-2 + x]^2
+ Log[-2 + x]^3)*Log[(-1 + x^3)/x] - (E^10*Log[(-1 + x^3)/x]^2)/2))/E^10

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fricas [B]  time = 0.63, size = 155, normalized size = 4.84 \begin {gather*} {\left (\log \left (x - 2\right )^{8} - 40 \, \log \left (x - 2\right )^{7} + 700 \, \log \left (x - 2\right )^{6} - 2 \, {\left (e^{8} - 21875\right )} \log \left (x - 2\right )^{4} - 7000 \, \log \left (x - 2\right )^{5} + 40 \, {\left (e^{8} - 4375\right )} \log \left (x - 2\right )^{3} - 100 \, {\left (3 \, e^{8} - 4375\right )} \log \left (x - 2\right )^{2} + e^{10} \log \left (\frac {x^{3} - 1}{x}\right )^{2} + 1000 \, {\left (e^{8} - 625\right )} \log \left (x - 2\right ) + 2 \, {\left (e^{5} \log \left (x - 2\right )^{4} - 20 \, e^{5} \log \left (x - 2\right )^{3} + 150 \, e^{5} \log \left (x - 2\right )^{2} - 500 \, e^{5} \log \left (x - 2\right ) - e^{13} + 625 \, e^{5}\right )} \log \left (\frac {x^{3} - 1}{x}\right )\right )} e^{\left (-10\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((8*x^4-8*x)*exp(5)*log(x-2)^3+(-120*x^4+120*x)*exp(5)*log(x-2)^2+(600*x^4-600*x)*exp(5)*log(x-2)+(
4*x^4-8*x^3+2*x-4)*exp(5)^2+(-1000*x^4+1000*x)*exp(5))*log((x^3-1)/x)+(8*x^4-8*x)*log(x-2)^7+(-280*x^4+280*x)*
log(x-2)^6+(4200*x^4-4200*x)*log(x-2)^5+((4*x^4-8*x^3+2*x-4)*exp(5)-35000*x^4+35000*x)*log(x-2)^4+(((-8*x^4+8*
x)*exp(3)-80*x^4+160*x^3-40*x+80)*exp(5)+175000*x^4-175000*x)*log(x-2)^3+(((120*x^4-120*x)*exp(3)+600*x^4-1200
*x^3+300*x-600)*exp(5)-525000*x^4+525000*x)*log(x-2)^2+(((-600*x^4+600*x)*exp(3)-2000*x^4+4000*x^3-1000*x+2000
)*exp(5)+875000*x^4-875000*x)*log(x-2)+(-4*x^4+8*x^3-2*x+4)*exp(3)*exp(5)^2+((1000*x^4-1000*x)*exp(3)+2500*x^4
-5000*x^3+1250*x-2500)*exp(5)-625000*x^4+625000*x)/(x^5-2*x^4-x^2+2*x)/exp(5)^2,x, algorithm="fricas")

[Out]

(log(x - 2)^8 - 40*log(x - 2)^7 + 700*log(x - 2)^6 - 2*(e^8 - 21875)*log(x - 2)^4 - 7000*log(x - 2)^5 + 40*(e^
8 - 4375)*log(x - 2)^3 - 100*(3*e^8 - 4375)*log(x - 2)^2 + e^10*log((x^3 - 1)/x)^2 + 1000*(e^8 - 625)*log(x -
2) + 2*(e^5*log(x - 2)^4 - 20*e^5*log(x - 2)^3 + 150*e^5*log(x - 2)^2 - 500*e^5*log(x - 2) - e^13 + 625*e^5)*l
og((x^3 - 1)/x))*e^(-10)

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giac [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((8*x^4-8*x)*exp(5)*log(x-2)^3+(-120*x^4+120*x)*exp(5)*log(x-2)^2+(600*x^4-600*x)*exp(5)*log(x-2)+(
4*x^4-8*x^3+2*x-4)*exp(5)^2+(-1000*x^4+1000*x)*exp(5))*log((x^3-1)/x)+(8*x^4-8*x)*log(x-2)^7+(-280*x^4+280*x)*
log(x-2)^6+(4200*x^4-4200*x)*log(x-2)^5+((4*x^4-8*x^3+2*x-4)*exp(5)-35000*x^4+35000*x)*log(x-2)^4+(((-8*x^4+8*
x)*exp(3)-80*x^4+160*x^3-40*x+80)*exp(5)+175000*x^4-175000*x)*log(x-2)^3+(((120*x^4-120*x)*exp(3)+600*x^4-1200
*x^3+300*x-600)*exp(5)-525000*x^4+525000*x)*log(x-2)^2+(((-600*x^4+600*x)*exp(3)-2000*x^4+4000*x^3-1000*x+2000
)*exp(5)+875000*x^4-875000*x)*log(x-2)+(-4*x^4+8*x^3-2*x+4)*exp(3)*exp(5)^2+((1000*x^4-1000*x)*exp(3)+2500*x^4
-5000*x^3+1250*x-2500)*exp(5)-625000*x^4+625000*x)/(x^5-2*x^4-x^2+2*x)/exp(5)^2,x, algorithm="giac")

[Out]

Timed out

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maple [C]  time = 21.02, size = 218135, normalized size = 6816.72

method	result	size
risch	\(\text {Expression too large to display}\)	\(218135\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((8*x^4-8*x)*exp(5)*ln(x-2)^3+(-120*x^4+120*x)*exp(5)*ln(x-2)^2+(600*x^4-600*x)*exp(5)*ln(x-2)+(4*x^4-8*x
^3+2*x-4)*exp(5)^2+(-1000*x^4+1000*x)*exp(5))*ln((x^3-1)/x)+(8*x^4-8*x)*ln(x-2)^7+(-280*x^4+280*x)*ln(x-2)^6+(
4200*x^4-4200*x)*ln(x-2)^5+((4*x^4-8*x^3+2*x-4)*exp(5)-35000*x^4+35000*x)*ln(x-2)^4+(((-8*x^4+8*x)*exp(3)-80*x
^4+160*x^3-40*x+80)*exp(5)+175000*x^4-175000*x)*ln(x-2)^3+(((120*x^4-120*x)*exp(3)+600*x^4-1200*x^3+300*x-600)
*exp(5)-525000*x^4+525000*x)*ln(x-2)^2+(((-600*x^4+600*x)*exp(3)-2000*x^4+4000*x^3-1000*x+2000)*exp(5)+875000*
x^4-875000*x)*ln(x-2)+(-4*x^4+8*x^3-2*x+4)*exp(3)*exp(5)^2+((1000*x^4-1000*x)*exp(3)+2500*x^4-5000*x^3+1250*x-
2500)*exp(5)-625000*x^4+625000*x)/(x^5-2*x^4-x^2+2*x)/exp(5)^2,x,method=_RETURNVERBOSE)

[Out]

result too large to display

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maxima [B]  time = 0.90, size = 392, normalized size = 12.25 \begin {gather*} \frac {1}{21} \, {\left (21 \, \log \left (x - 2\right )^{8} - 840 \, \log \left (x - 2\right )^{7} + 14700 \, \log \left (x - 2\right )^{6} - 42 \, {\left (e^{5} \log \relax (x) + e^{8} - 21875\right )} \log \left (x - 2\right )^{4} - 147000 \, \log \left (x - 2\right )^{5} + 840 \, {\left (e^{5} \log \relax (x) + e^{8} - 4375\right )} \log \left (x - 2\right )^{3} + 21 \, e^{10} \log \left (x^{2} + x + 1\right )^{2} + 21 \, e^{10} \log \left (x - 1\right )^{2} - 2100 \, {\left (3 \, e^{5} \log \relax (x) + 3 \, e^{8} - 4375\right )} \log \left (x - 2\right )^{2} + 21 \, e^{10} \log \relax (x)^{2} - 4 \, \sqrt {3} {\left (e^{13} - 625 \, e^{5}\right )} \arctan \left (\frac {1}{3} \, \sqrt {3} {\left (2 \, x + 1\right )}\right ) + 2 \, {\left (2 \, \sqrt {3} \arctan \left (\frac {1}{3} \, \sqrt {3} {\left (2 \, x + 1\right )}\right ) - 5 \, \log \left (x^{2} + x + 1\right ) - 14 \, \log \left (x - 1\right ) + 3 \, \log \left (x - 2\right ) + 21 \, \log \relax (x)\right )} e^{13} - 1250 \, {\left (2 \, \sqrt {3} \arctan \left (\frac {1}{3} \, \sqrt {3} {\left (2 \, x + 1\right )}\right ) - 5 \, \log \left (x^{2} + x + 1\right ) - 14 \, \log \left (x - 1\right ) + 3 \, \log \left (x - 2\right ) + 21 \, \log \relax (x)\right )} e^{5} + 2 \, {\left (21 \, e^{5} \log \left (x - 2\right )^{4} - 420 \, e^{5} \log \left (x - 2\right )^{3} + 3150 \, e^{5} \log \left (x - 2\right )^{2} + 21 \, e^{10} \log \left (x - 1\right ) - 10500 \, e^{5} \log \left (x - 2\right ) - 21 \, e^{10} \log \relax (x) - 16 \, e^{13} + 10000 \, e^{5}\right )} \log \left (x^{2} + x + 1\right ) + 14 \, {\left (3 \, e^{5} \log \left (x - 2\right )^{4} - 60 \, e^{5} \log \left (x - 2\right )^{3} + 450 \, e^{5} \log \left (x - 2\right )^{2} - 1500 \, e^{5} \log \left (x - 2\right ) - 3 \, e^{10} \log \relax (x) - e^{13} + 625 \, e^{5}\right )} \log \left (x - 1\right ) + 6 \, {\left (3500 \, e^{5} \log \relax (x) - e^{13} + 3500 \, e^{8} + 625 \, e^{5} - 2187500\right )} \log \left (x - 2\right )\right )} e^{\left (-10\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((8*x^4-8*x)*exp(5)*log(x-2)^3+(-120*x^4+120*x)*exp(5)*log(x-2)^2+(600*x^4-600*x)*exp(5)*log(x-2)+(
4*x^4-8*x^3+2*x-4)*exp(5)^2+(-1000*x^4+1000*x)*exp(5))*log((x^3-1)/x)+(8*x^4-8*x)*log(x-2)^7+(-280*x^4+280*x)*
log(x-2)^6+(4200*x^4-4200*x)*log(x-2)^5+((4*x^4-8*x^3+2*x-4)*exp(5)-35000*x^4+35000*x)*log(x-2)^4+(((-8*x^4+8*
x)*exp(3)-80*x^4+160*x^3-40*x+80)*exp(5)+175000*x^4-175000*x)*log(x-2)^3+(((120*x^4-120*x)*exp(3)+600*x^4-1200
*x^3+300*x-600)*exp(5)-525000*x^4+525000*x)*log(x-2)^2+(((-600*x^4+600*x)*exp(3)-2000*x^4+4000*x^3-1000*x+2000
)*exp(5)+875000*x^4-875000*x)*log(x-2)+(-4*x^4+8*x^3-2*x+4)*exp(3)*exp(5)^2+((1000*x^4-1000*x)*exp(3)+2500*x^4
-5000*x^3+1250*x-2500)*exp(5)-625000*x^4+625000*x)/(x^5-2*x^4-x^2+2*x)/exp(5)^2,x, algorithm="maxima")

[Out]

1/21*(21*log(x - 2)^8 - 840*log(x - 2)^7 + 14700*log(x - 2)^6 - 42*(e^5*log(x) + e^8 - 21875)*log(x - 2)^4 - 1
47000*log(x - 2)^5 + 840*(e^5*log(x) + e^8 - 4375)*log(x - 2)^3 + 21*e^10*log(x^2 + x + 1)^2 + 21*e^10*log(x -
1)^2 - 2100*(3*e^5*log(x) + 3*e^8 - 4375)*log(x - 2)^2 + 21*e^10*log(x)^2 - 4*sqrt(3)*(e^13 - 625*e^5)*arctan
(1/3*sqrt(3)*(2*x + 1)) + 2*(2*sqrt(3)*arctan(1/3*sqrt(3)*(2*x + 1)) - 5*log(x^2 + x + 1) - 14*log(x - 1) + 3*
log(x - 2) + 21*log(x))*e^13 - 1250*(2*sqrt(3)*arctan(1/3*sqrt(3)*(2*x + 1)) - 5*log(x^2 + x + 1) - 14*log(x -
1) + 3*log(x - 2) + 21*log(x))*e^5 + 2*(21*e^5*log(x - 2)^4 - 420*e^5*log(x - 2)^3 + 3150*e^5*log(x - 2)^2 +
21*e^10*log(x - 1) - 10500*e^5*log(x - 2) - 21*e^10*log(x) - 16*e^13 + 10000*e^5)*log(x^2 + x + 1) + 14*(3*e^5
*log(x - 2)^4 - 60*e^5*log(x - 2)^3 + 450*e^5*log(x - 2)^2 - 1500*e^5*log(x - 2) - 3*e^10*log(x) - e^13 + 625*
e^5)*log(x - 1) + 6*(3500*e^5*log(x) - e^13 + 3500*e^8 + 625*e^5 - 2187500)*log(x - 2))*e^(-10)

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mupad [B]  time = 3.36, size = 238, normalized size = 7.44 \begin {gather*} 1000\,\ln \left (x-2\right )\,{\mathrm {e}}^{-2}-625000\,\ln \left (x-2\right )\,{\mathrm {e}}^{-10}+{\ln \left (\frac {x^3-1}{x}\right )}^2-300\,{\ln \left (x-2\right )}^2\,{\mathrm {e}}^{-2}-2\,{\mathrm {e}}^3\,\ln \left (x^3-1\right )+40\,{\ln \left (x-2\right )}^3\,{\mathrm {e}}^{-2}-2\,{\ln \left (x-2\right )}^4\,{\mathrm {e}}^{-2}+1250\,{\mathrm {e}}^{-5}\,\ln \left (x^3-1\right )+437500\,{\ln \left (x-2\right )}^2\,{\mathrm {e}}^{-10}-175000\,{\ln \left (x-2\right )}^3\,{\mathrm {e}}^{-10}+43750\,{\ln \left (x-2\right )}^4\,{\mathrm {e}}^{-10}-7000\,{\ln \left (x-2\right )}^5\,{\mathrm {e}}^{-10}+700\,{\ln \left (x-2\right )}^6\,{\mathrm {e}}^{-10}-40\,{\ln \left (x-2\right )}^7\,{\mathrm {e}}^{-10}+{\ln \left (x-2\right )}^8\,{\mathrm {e}}^{-10}+2\,{\mathrm {e}}^3\,\ln \relax (x)-1250\,{\mathrm {e}}^{-5}\,\ln \relax (x)+300\,{\ln \left (x-2\right )}^2\,{\mathrm {e}}^{-5}\,\ln \left (\frac {x^3-1}{x}\right )-40\,{\ln \left (x-2\right )}^3\,{\mathrm {e}}^{-5}\,\ln \left (\frac {x^3-1}{x}\right )+2\,{\ln \left (x-2\right )}^4\,{\mathrm {e}}^{-5}\,\ln \left (\frac {x^3-1}{x}\right )-1000\,\ln \left (x-2\right )\,{\mathrm {e}}^{-5}\,\ln \left (\frac {x^3-1}{x}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(-10)*(625000*x + log(x - 2)^3*(exp(5)*(exp(3)*(8*x - 8*x^4) - 40*x + 160*x^3 - 80*x^4 + 80) - 175000*
x + 175000*x^4) - log(x - 2)^2*(exp(5)*(exp(3)*(120*x - 120*x^4) - 300*x + 1200*x^3 - 600*x^4 + 600) - 525000*
x + 525000*x^4) + log((x^3 - 1)/x)*(exp(5)*(1000*x - 1000*x^4) + exp(10)*(2*x - 8*x^3 + 4*x^4 - 4) - log(x - 2
)*exp(5)*(600*x - 600*x^4) - log(x - 2)^3*exp(5)*(8*x - 8*x^4) + log(x - 2)^2*exp(5)*(120*x - 120*x^4)) - exp(
13)*(2*x - 8*x^3 + 4*x^4 - 4) - log(x - 2)^7*(8*x - 8*x^4) + log(x - 2)^6*(280*x - 280*x^4) - log(x - 2)^5*(42
00*x - 4200*x^4) - exp(5)*(exp(3)*(1000*x - 1000*x^4) - 1250*x + 5000*x^3 - 2500*x^4 + 2500) + log(x - 2)*(exp
(5)*(exp(3)*(600*x - 600*x^4) - 1000*x + 4000*x^3 - 2000*x^4 + 2000) - 875000*x + 875000*x^4) - 625000*x^4 + l
og(x - 2)^4*(35000*x + exp(5)*(2*x - 8*x^3 + 4*x^4 - 4) - 35000*x^4)))/(2*x - x^2 - 2*x^4 + x^5),x)

[Out]

1000*log(x - 2)*exp(-2) - 625000*log(x - 2)*exp(-10) + log((x^3 - 1)/x)^2 - 300*log(x - 2)^2*exp(-2) - 2*exp(3
)*log(x^3 - 1) + 40*log(x - 2)^3*exp(-2) - 2*log(x - 2)^4*exp(-2) + 1250*exp(-5)*log(x^3 - 1) + 437500*log(x -
2)^2*exp(-10) - 175000*log(x - 2)^3*exp(-10) + 43750*log(x - 2)^4*exp(-10) - 7000*log(x - 2)^5*exp(-10) + 700
*log(x - 2)^6*exp(-10) - 40*log(x - 2)^7*exp(-10) + log(x - 2)^8*exp(-10) + 2*exp(3)*log(x) - 1250*exp(-5)*log
(x) + 300*log(x - 2)^2*exp(-5)*log((x^3 - 1)/x) - 40*log(x - 2)^3*exp(-5)*log((x^3 - 1)/x) + 2*log(x - 2)^4*ex
p(-5)*log((x^3 - 1)/x) - 1000*log(x - 2)*exp(-5)*log((x^3 - 1)/x)

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sympy [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((8*x**4-8*x)*exp(5)*ln(x-2)**3+(-120*x**4+120*x)*exp(5)*ln(x-2)**2+(600*x**4-600*x)*exp(5)*ln(x-2)
+(4*x**4-8*x**3+2*x-4)*exp(5)**2+(-1000*x**4+1000*x)*exp(5))*ln((x**3-1)/x)+(8*x**4-8*x)*ln(x-2)**7+(-280*x**4
+280*x)*ln(x-2)**6+(4200*x**4-4200*x)*ln(x-2)**5+((4*x**4-8*x**3+2*x-4)*exp(5)-35000*x**4+35000*x)*ln(x-2)**4+
(((-8*x**4+8*x)*exp(3)-80*x**4+160*x**3-40*x+80)*exp(5)+175000*x**4-175000*x)*ln(x-2)**3+(((120*x**4-120*x)*ex
p(3)+600*x**4-1200*x**3+300*x-600)*exp(5)-525000*x**4+525000*x)*ln(x-2)**2+(((-600*x**4+600*x)*exp(3)-2000*x**
4+4000*x**3-1000*x+2000)*exp(5)+875000*x**4-875000*x)*ln(x-2)+(-4*x**4+8*x**3-2*x+4)*exp(3)*exp(5)**2+((1000*x
**4-1000*x)*exp(3)+2500*x**4-5000*x**3+1250*x-2500)*exp(5)-625000*x**4+625000*x)/(x**5-2*x**4-x**2+2*x)/exp(5)
**2,x)

[Out]

Timed out

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