3.42.92 \(\int \frac {60 x^3-20 x^4+144 x^5-48 x^6+4 x^7+(120 x^2-40 x^3+216 x^4-72 x^5+6 x^6) \log ^2(4)+(60 x-20 x^2+72 x^3-24 x^4+2 x^5) \log ^4(4)+e^{2 x} (72 x^3+48 x^4-22 x^5+2 x^6+(72 x^2+120 x^3-46 x^4+4 x^5) \log ^2(4)+(72 x^2-24 x^3+2 x^4) \log ^4(4))+e^x (60 x^2-20 x^3+216 x^4-18 x^6+2 x^7+(120 x-40 x^2+288 x^3+48 x^4-40 x^5+4 x^6) \log ^2(4)+(60-20 x+72 x^2+48 x^3-22 x^4+2 x^5) \log ^4(4))+(-60 x^2+20 x^3-216 x^4+72 x^5-6 x^6+(-120 x+40 x^2-288 x^3+96 x^4-8 x^5) \log ^2(4)+(-60+20 x-72 x^2+24 x^3-2 x^4) \log ^4(4)+e^x (-144 x^3-24 x^4+20 x^5-2 x^6+(-144 x^2-96 x^3+44 x^4-4 x^5) \log ^2(4)+(-72 x^2+24 x^3-2 x^4) \log ^4(4))) \log (2 e^{-\frac {5}{-6 x+x^2}})+(72 x^3-24 x^4+2 x^5+(72 x^2-24 x^3+2 x^4) \log ^2(4)) \log ^2(2 e^{-\frac {5}{-6 x+x^2}})}{36 x^2-12 x^3+x^4} \, dx\)

Optimal. Leaf size=35 \[ \left (x+\log ^2(4)\right )^2 \left (-e^x-x+\log \left (2 e^{-\frac {5}{(-6+x) x}}\right )\right )^2 \]

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Rubi [F]  time = 29.97, 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 {60 x^3-20 x^4+144 x^5-48 x^6+4 x^7+\left (120 x^2-40 x^3+216 x^4-72 x^5+6 x^6\right ) \log ^2(4)+\left (60 x-20 x^2+72 x^3-24 x^4+2 x^5\right ) \log ^4(4)+e^{2 x} \left (72 x^3+48 x^4-22 x^5+2 x^6+\left (72 x^2+120 x^3-46 x^4+4 x^5\right ) \log ^2(4)+\left (72 x^2-24 x^3+2 x^4\right ) \log ^4(4)\right )+e^x \left (60 x^2-20 x^3+216 x^4-18 x^6+2 x^7+\left (120 x-40 x^2+288 x^3+48 x^4-40 x^5+4 x^6\right ) \log ^2(4)+\left (60-20 x+72 x^2+48 x^3-22 x^4+2 x^5\right ) \log ^4(4)\right )+\left (-60 x^2+20 x^3-216 x^4+72 x^5-6 x^6+\left (-120 x+40 x^2-288 x^3+96 x^4-8 x^5\right ) \log ^2(4)+\left (-60+20 x-72 x^2+24 x^3-2 x^4\right ) \log ^4(4)+e^x \left (-144 x^3-24 x^4+20 x^5-2 x^6+\left (-144 x^2-96 x^3+44 x^4-4 x^5\right ) \log ^2(4)+\left (-72 x^2+24 x^3-2 x^4\right ) \log ^4(4)\right )\right ) \log \left (2 e^{-\frac {5}{-6 x+x^2}}\right )+\left (72 x^3-24 x^4+2 x^5+\left (72 x^2-24 x^3+2 x^4\right ) \log ^2(4)\right ) \log ^2\left (2 e^{-\frac {5}{-6 x+x^2}}\right )}{36 x^2-12 x^3+x^4} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(60*x^3 - 20*x^4 + 144*x^5 - 48*x^6 + 4*x^7 + (120*x^2 - 40*x^3 + 216*x^4 - 72*x^5 + 6*x^6)*Log[4]^2 + (60
*x - 20*x^2 + 72*x^3 - 24*x^4 + 2*x^5)*Log[4]^4 + E^(2*x)*(72*x^3 + 48*x^4 - 22*x^5 + 2*x^6 + (72*x^2 + 120*x^
3 - 46*x^4 + 4*x^5)*Log[4]^2 + (72*x^2 - 24*x^3 + 2*x^4)*Log[4]^4) + E^x*(60*x^2 - 20*x^3 + 216*x^4 - 18*x^6 +
2*x^7 + (120*x - 40*x^2 + 288*x^3 + 48*x^4 - 40*x^5 + 4*x^6)*Log[4]^2 + (60 - 20*x + 72*x^2 + 48*x^3 - 22*x^4
+ 2*x^5)*Log[4]^4) + (-60*x^2 + 20*x^3 - 216*x^4 + 72*x^5 - 6*x^6 + (-120*x + 40*x^2 - 288*x^3 + 96*x^4 - 8*x
^5)*Log[4]^2 + (-60 + 20*x - 72*x^2 + 24*x^3 - 2*x^4)*Log[4]^4 + E^x*(-144*x^3 - 24*x^4 + 20*x^5 - 2*x^6 + (-1
44*x^2 - 96*x^3 + 44*x^4 - 4*x^5)*Log[4]^2 + (-72*x^2 + 24*x^3 - 2*x^4)*Log[4]^4))*Log[2/E^(5/(-6*x + x^2))] +
(72*x^3 - 24*x^4 + 2*x^5 + (72*x^2 - 24*x^3 + 2*x^4)*Log[4]^2)*Log[2/E^(5/(-6*x + x^2))]^2)/(36*x^2 - 12*x^3
+ x^4),x]

[Out]

-12*E^x + E^(2*x)/2 + 240/(6 - x) + 20*x + 12*E^x*x - E^(2*x)*x - 6*E^x*x^2 + E^(2*x)*x^2 + 2*E^x*x^3 + x^4 +
22*E^x*Log[4]^2 - 22*E^x*x*Log[4]^2 - (10*ExpIntegralEi[x]*Log[4]^2)/3 - (25*Log[4]^4)/(108*(6 - x)) - (25*Log
[4]^4)/(36*x^2) - 4*E^x*(3 - Log[4])*(3 + Log[4]) + 4*E^x*x*(3 - Log[4])*(3 + Log[4]) - 2*E^x*x^2*(3 - Log[4])
*(3 + Log[4]) - (10*(5 - 18*Log[4]^2))/(3*(6 - x)) - 4*x*(5 - 18*Log[4]^2) - 4*E^6*ExpIntegralEi[-6 + x]*(5 -
18*Log[4]^2) - (25*Log[4]^2*(3 - Log[4]^2))/(54*(6 - x)) + (25*Log[4]^2*(3 - Log[4]^2))/(54*x) - (5*E^6*ExpInt
egralEi[-6 + x]*Log[4]^2*(3 - Log[4]^2))/9 + (5*ExpIntegralEi[x]*Log[4]^2*(3 - Log[4]^2))/9 + (120*(6 - Log[4]
^2))/(6 - x) + 12*x^2*(6 - Log[4]^2) - (30*(24 - Log[4]^2))/(6 - x) - (2*x^3*(24 - Log[4]^2))/3 + E^(2*x)*Log[
4]^2*(1 + Log[4]^2) - (25*Log[4]^2*(3 + Log[4]^2))/(54*(6 - x)) + (25*Log[4]^2*(3 + Log[4]^2))/(54*x) - (5*E^6
*ExpIntegralEi[-6 + x]*Log[4]^2*(3 + Log[4]^2))/9 + (5*ExpIntegralEi[x]*Log[4]^2*(3 + Log[4]^2))/9 + (30*(4 +
Log[4]^2))/(6 - x) + (360*(6 + Log[4]^2))/(6 - x)^2 + (5184*(6 + Log[4]^2))/(6 - x) + (2592*E^x*(6 + Log[4]^2)
)/(6 - x) + (120*(6 + Log[4]^2))/x + (7786*E^6*ExpIntegralEi[-6 + x]*(6 + Log[4]^2))/3 + (25*Log[4]^2*(6 + Log
[4]^2))/(36*(6 - x)^2) + (10*Log[4]^2*(6 + Log[4]^2))/(6 - x) - (2371*E^x*Log[4]^2*(6 + Log[4]^2))/(3*(6 - x))
+ (25*Log[4]^2*(6 + Log[4]^2))/(108*x) - (2371*E^6*ExpIntegralEi[-6 + x]*Log[4]^2*(6 + Log[4]^2))/3 - (432*E^
x*(3 - Log[4])*(3 + Log[4])*(6 + Log[4]^2))/(6 - x) - 432*E^6*ExpIntegralEi[-6 + x]*(3 - Log[4])*(3 + Log[4])*
(6 + Log[4]^2) - (5*(5 - 18*Log[4]^2)*(6 + Log[4]^2))/(3*(6 - x)^2) - (24*(5 - 18*Log[4]^2)*(6 + Log[4]^2))/(6
- x) - (4*E^x*(5 - 18*Log[4]^2)*(6 + Log[4]^2))/(6 - x) - (5*(5 - 18*Log[4]^2)*(6 + Log[4]^2))/(9*x) - 4*E^6*
ExpIntegralEi[-6 + x]*(5 - 18*Log[4]^2)*(6 + Log[4]^2) + (25*(3 - Log[4]^2)*(6 + Log[4]^2))/(18*(6 - x)^2) + (
20*(3 - Log[4]^2)*(6 + Log[4]^2))/(6 - x) + (10*E^x*(3 - Log[4]^2)*(6 + Log[4]^2))/(3*(6 - x)) + (25*(3 - Log[
4]^2)*(6 + Log[4]^2))/(54*x) + (10*E^6*ExpIntegralEi[-6 + x]*(3 - Log[4]^2)*(6 + Log[4]^2))/3 - (30*(24 - Log[
4]^2)*(6 + Log[4]^2))/(6 - x)^2 - (432*(24 - Log[4]^2)*(6 + Log[4]^2))/(6 - x) - (10*(24 - Log[4]^2)*(6 + Log[
4]^2))/x + (5*E^x*(6 + Log[4]^2)^2)/(3*(6 - x)) + (5*E^6*ExpIntegralEi[-6 + x]*(6 + Log[4]^2)^2)/3 + 216*E^x*(
8 + Log[4]^2) + (360*(8 + Log[4]^2))/(6 - x) + 432*x*(8 + Log[4]^2) - 216*E^6*ExpIntegralEi[-6 + x]*(3 - Log[4
])*(3 + Log[4])*(8 + Log[4]^2) - 24*E^x*(9 + Log[4]^2) + (240*(9 + Log[4]^2))/(6 - x) + 24*E^x*x*(9 + Log[4]^2
) + 24*x^2*(9 + Log[4]^2) - 264*E^6*ExpIntegralEi[-6 + x]*Log[4]^2*(9 + Log[4]^2) - (20*(24 - Log[4]^2)*(9 + L
og[4]^2))/(6 - x) - 24*x*(24 - Log[4]^2)*(9 + Log[4]^2) + 4*E^x*(12 + Log[4]^2) + (60*(12 + Log[4]^2))/(6 - x)
- 4*E^x*x*(12 + Log[4]^2) + 2*E^x*x^2*(12 + Log[4]^2) + (4*x^3*(12 + Log[4]^2))/3 - 22*E^x*Log[4]^2*(12 + Log
[4]^2) + 2*E^x*(3 - Log[4])*(3 + Log[4])*(12 + Log[4]^2) - 2*E^x*x*(3 - Log[4])*(3 + Log[4])*(12 + Log[4]^2) +
(20*(6 - Log[4]^2)*(12 + Log[4]^2))/(6 - x) + 24*x*(6 - Log[4]^2)*(12 + Log[4]^2) - (10*(24 - Log[4]^2)*(12 +
Log[4]^2))/(6 - x) - x^2*(24 - Log[4]^2)*(12 + Log[4]^2) - (E^(2*x)*(1 + 2*Log[4]^2))/2 + E^(2*x)*x*(1 + 2*Lo
g[4]^2) + 24*E^x*(9 + 2*Log[4]^2) + (144*E^x*(6 + Log[4]^2)*(9 + 2*Log[4]^2))/(6 - x) + 144*E^6*ExpIntegralEi[
-6 + x]*(6 + Log[4]^2)*(9 + 2*Log[4]^2) + 24*E^6*ExpIntegralEi[-6 + x]*(12 + Log[4]^2)*(9 + 2*Log[4]^2) + 864*
E^6*ExpIntegralEi[-6 + x]*(15 + 2*Log[4]^2) + (60*(36 - Log[4]^4))/(6 - x)^2 + (864*(36 - Log[4]^4))/(6 - x) +
(20*(36 - Log[4]^4))/x - 24*E^x*(81 - Log[4]^4) - 4*E^x*Log[2*E^(5/((6 - x)*x))] + 4*E^x*x*Log[2*E^(5/((6 - x
)*x))] - 2*E^x*x^2*Log[2*E^(5/((6 - x)*x))] - 2*x^3*Log[2*E^(5/((6 - x)*x))] - x^2*Log[4]^2*Log[2*E^(5/((6 - x
)*x))] + (5*Log[4]^4*Log[2*E^(5/((6 - x)*x))])/(3*x) - 24*x*(6 - Log[4]^2)*Log[2*E^(5/((6 - x)*x))] + x^2*(24
- Log[4]^2)*Log[2*E^(5/((6 - x)*x))] + 4*E^x*(1 + Log[4]^2)*Log[2*E^(5/((6 - x)*x))] - 4*E^x*x*(1 + Log[4]^2)*
Log[2*E^(5/((6 - x)*x))] - 2*E^x*Log[4]^2*(2 + Log[4]^2)*Log[2*E^(5/((6 - x)*x))] - (864*(6 + Log[4]^2)*Log[2*
E^(5/((6 - x)*x))])/(6 - x) - (5*Log[4]^2*(6 + Log[4]^2)*Log[2*E^(5/((6 - x)*x))])/(3*(6 - x)) + (4*(5 - 18*Lo
g[4]^2)*(6 + Log[4]^2)*Log[2*E^(5/((6 - x)*x))])/(6 - x) - (10*(3 - Log[4]^2)*(6 + Log[4]^2)*Log[2*E^(5/((6 -
x)*x))])/(3*(6 - x)) + (72*(24 - Log[4]^2)*(6 + Log[4]^2)*Log[2*E^(5/((6 - x)*x))])/(6 - x) - 48*x*(9 + Log[4]
^2)*Log[2*E^(5/((6 - x)*x))] - 2*x^2*(12 + Log[4]^2)*Log[2*E^(5/((6 - x)*x))] + 2*x*(24 - Log[4]^2)*(12 + Log[
4]^2)*Log[2*E^(5/((6 - x)*x))] - (144*(36 - Log[4]^4)*Log[2*E^(5/((6 - x)*x))])/(6 - x) + 120*Log[6 - x] - (10
55*Log[4]^4*Log[6 - x])/648 + (5*(5 - 18*Log[4]^2)*Log[6 - x])/9 + 20*(3 - Log[4]^2)*Log[6 - x] + (25*Log[4]^2
*(3 - Log[4]^2)*Log[6 - x])/162 + 20*(6 - Log[4]^2)*Log[6 - x] - 10*(24 - Log[4]^2)*Log[6 - x] + (25*Log[4]^2*
(3 + Log[4]^2)*Log[6 - x])/162 + 30*(6 + Log[4]^2)*Log[6 - x] + (25*Log[4]^2*(6 + Log[4]^2)*Log[6 - x])/648 -
(5*(5 - 18*Log[4]^2)*(6 + Log[4]^2)*Log[6 - x])/54 + (25*(3 - Log[4]^2)*(6 + Log[4]^2)*Log[6 - x])/324 - (5*(2
4 - Log[4]^2)*(6 + Log[4]^2)*Log[6 - x])/3 - 60*(8 + Log[4]^2)*Log[6 - x] - 216*(24 - Log[4]^2)*(8 + Log[4]^2)
*Log[6 - x] + 40*(9 + Log[4]^2)*Log[6 - x] + 288*(6 - Log[4]^2)*(9 + Log[4]^2)*Log[6 - x] + (10*(24 - Log[4]^2
)*(9 + Log[4]^2)*Log[6 - x])/3 + 20*(12 + Log[4]^2)*Log[6 - x] - 4*(5 - 18*Log[4]^2)*(12 + Log[4]^2)*Log[6 - x
] - (10*(6 - Log[4]^2)*(12 + Log[4]^2)*Log[6 - x])/3 - (5*(24 - Log[4]^2)*(12 + Log[4]^2)*Log[6 - x])/3 + 1728
*(15 + 2*Log[4]^2)*Log[6 - x] + (10*(36 - Log[4]^4)*Log[6 - x])/3 - (10*(5 - 18*Log[4]^2)*Log[-6 + x])/(3*(6 -
x)) - (10*(5 - 18*Log[4]^2)*Log[-6 + x])/(3*x) - (25*Log[4]^2*(3 - Log[4]^2)*Log[-6 + x])/(54*(6 - x)) - (25*
Log[4]^2*(3 - Log[4]^2)*Log[-6 + x])/(54*x) - (25*Log[4]^2*(3 + Log[4]^2)*Log[-6 + x])/(54*(6 - x)) - (25*Log[
4]^2*(3 + Log[4]^2)*Log[-6 + x])/(54*x) + (360*(8 + Log[4]^2)*Log[-6 + x])/(6 - x) + (360*(8 + Log[4]^2)*Log[-
6 + x])/x - (20*(24 - Log[4]^2)*(9 + Log[4]^2)*Log[-6 + x])/(6 - x) - (20*(24 - Log[4]^2)*(9 + Log[4]^2)*Log[-
6 + x])/x + (20*(6 - Log[4]^2)*(12 + Log[4]^2)*Log[-6 + x])/(6 - x) + (20*(6 - Log[4]^2)*(12 + Log[4]^2)*Log[-
6 + x])/x + 4*(5 - 18*Log[4]^2)*Log[2*E^(5/((6 - x)*x))]*Log[-6 + x] + (5*Log[4]^2*(3 - Log[4]^2)*Log[2*E^(5/(
(6 - x)*x))]*Log[-6 + x])/9 + (5*Log[4]^2*(3 + Log[4]^2)*Log[2*E^(5/((6 - x)*x))]*Log[-6 + x])/9 - 432*(8 + Lo
g[4]^2)*Log[2*E^(5/((6 - x)*x))]*Log[-6 + x] + 24*(24 - Log[4]^2)*(9 + Log[4]^2)*Log[2*E^(5/((6 - x)*x))]*Log[
-6 + x] - 24*(6 - Log[4]^2)*(12 + Log[4]^2)*Log[2*E^(5/((6 - x)*x))]*Log[-6 + x] + (1055*Log[4]^4*Log[x])/648
- (5*(5 - 18*Log[4]^2)*Log[x])/9 - (25*Log[4]^2*(3 - Log[4]^2)*Log[x])/324 + (25*Log[4]^2*(3 - Log[4]^2)*Log[x
])/(54*x) + (25*x*Log[4]^2*(3 - Log[4]^2)*Log[x])/(324*(6 - x)) - 20*(6 - Log[4]^2)*Log[x] - (25*Log[4]^2*(3 +
Log[4]^2)*Log[x])/324 + (25*Log[4]^2*(3 + Log[4]^2)*Log[x])/(54*x) + (25*x*Log[4]^2*(3 + Log[4]^2)*Log[x])/(3
24*(6 - x)) - 20*(6 + Log[4]^2)*Log[x] - (25*Log[4]^2*(6 + Log[4]^2)*Log[x])/648 + (5*(5 - 18*Log[4]^2)*(6 + L
og[4]^2)*Log[x])/54 - (25*(3 - Log[4]^2)*(6 + Log[4]^2)*Log[x])/324 + (5*(24 - Log[4]^2)*(6 + Log[4]^2)*Log[x]
)/3 + 60*(8 + Log[4]^2)*Log[x] - 40*(9 + Log[4]^2)*Log[x] - (10*(24 - Log[4]^2)*(9 + Log[4]^2)*Log[x])/3 + (10
*(6 - Log[4]^2)*(12 + Log[4]^2)*Log[x])/3 + (5*(24 - Log[4]^2)*(12 + Log[4]^2)*Log[x])/3 - (10*(36 - Log[4]^4)
*Log[x])/3 - (5*Log[4]^2*(3 - Log[4]^2)*Log[2*E^(5/((6 - x)*x))]*Log[x])/9 - (5*Log[4]^2*(3 + Log[4]^2)*Log[2*
E^(5/((6 - x)*x))]*Log[x])/9 + 2*Log[4]^2*Defer[Int][Log[2/E^(5/((-6 + x)*x))]^2, x] + 2*Defer[Int][x*Log[2/E^
(5/((-6 + x)*x))]^2, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {60 x^3-20 x^4+144 x^5-48 x^6+4 x^7+\left (120 x^2-40 x^3+216 x^4-72 x^5+6 x^6\right ) \log ^2(4)+\left (60 x-20 x^2+72 x^3-24 x^4+2 x^5\right ) \log ^4(4)+e^{2 x} \left (72 x^3+48 x^4-22 x^5+2 x^6+\left (72 x^2+120 x^3-46 x^4+4 x^5\right ) \log ^2(4)+\left (72 x^2-24 x^3+2 x^4\right ) \log ^4(4)\right )+e^x \left (60 x^2-20 x^3+216 x^4-18 x^6+2 x^7+\left (120 x-40 x^2+288 x^3+48 x^4-40 x^5+4 x^6\right ) \log ^2(4)+\left (60-20 x+72 x^2+48 x^3-22 x^4+2 x^5\right ) \log ^4(4)\right )+\left (-60 x^2+20 x^3-216 x^4+72 x^5-6 x^6+\left (-120 x+40 x^2-288 x^3+96 x^4-8 x^5\right ) \log ^2(4)+\left (-60+20 x-72 x^2+24 x^3-2 x^4\right ) \log ^4(4)+e^x \left (-144 x^3-24 x^4+20 x^5-2 x^6+\left (-144 x^2-96 x^3+44 x^4-4 x^5\right ) \log ^2(4)+\left (-72 x^2+24 x^3-2 x^4\right ) \log ^4(4)\right )\right ) \log \left (2 e^{-\frac {5}{-6 x+x^2}}\right )+\left (72 x^3-24 x^4+2 x^5+\left (72 x^2-24 x^3+2 x^4\right ) \log ^2(4)\right ) \log ^2\left (2 e^{-\frac {5}{-6 x+x^2}}\right )}{x^2 \left (36-12 x+x^2\right )} \, dx\\ &=\int \frac {60 x^3-20 x^4+144 x^5-48 x^6+4 x^7+\left (120 x^2-40 x^3+216 x^4-72 x^5+6 x^6\right ) \log ^2(4)+\left (60 x-20 x^2+72 x^3-24 x^4+2 x^5\right ) \log ^4(4)+e^{2 x} \left (72 x^3+48 x^4-22 x^5+2 x^6+\left (72 x^2+120 x^3-46 x^4+4 x^5\right ) \log ^2(4)+\left (72 x^2-24 x^3+2 x^4\right ) \log ^4(4)\right )+e^x \left (60 x^2-20 x^3+216 x^4-18 x^6+2 x^7+\left (120 x-40 x^2+288 x^3+48 x^4-40 x^5+4 x^6\right ) \log ^2(4)+\left (60-20 x+72 x^2+48 x^3-22 x^4+2 x^5\right ) \log ^4(4)\right )+\left (-60 x^2+20 x^3-216 x^4+72 x^5-6 x^6+\left (-120 x+40 x^2-288 x^3+96 x^4-8 x^5\right ) \log ^2(4)+\left (-60+20 x-72 x^2+24 x^3-2 x^4\right ) \log ^4(4)+e^x \left (-144 x^3-24 x^4+20 x^5-2 x^6+\left (-144 x^2-96 x^3+44 x^4-4 x^5\right ) \log ^2(4)+\left (-72 x^2+24 x^3-2 x^4\right ) \log ^4(4)\right )\right ) \log \left (2 e^{-\frac {5}{-6 x+x^2}}\right )+\left (72 x^3-24 x^4+2 x^5+\left (72 x^2-24 x^3+2 x^4\right ) \log ^2(4)\right ) \log ^2\left (2 e^{-\frac {5}{-6 x+x^2}}\right )}{(-6+x)^2 x^2} \, dx\\ &=\int \frac {2 \left (x+\log ^2(4)\right ) \left (e^x+x-\log \left (2 e^{-\frac {5}{(-6+x) x}}\right )\right ) \left (\left (2+e^x\right ) x^5+30 \log ^2(4)-10 x \left (-3+\log ^2(4)\right )+x^4 \left (-24+\log ^2(4)+e^x \left (-11+\log ^2(4)\right )\right )-12 x^3 \left (-6+\log ^2(4)+e^x \left (-2+\log ^2(4)\right )\right )+2 x^2 \left (-5+18 \log ^2(4)+18 e^x \left (1+\log ^2(4)\right )\right )-(-6+x)^2 x^2 \log \left (2 e^{-\frac {5}{(-6+x) x}}\right )\right )}{(6-x)^2 x^2} \, dx\\ &=2 \int \frac {\left (x+\log ^2(4)\right ) \left (e^x+x-\log \left (2 e^{-\frac {5}{(-6+x) x}}\right )\right ) \left (\left (2+e^x\right ) x^5+30 \log ^2(4)-10 x \left (-3+\log ^2(4)\right )+x^4 \left (-24+\log ^2(4)+e^x \left (-11+\log ^2(4)\right )\right )-12 x^3 \left (-6+\log ^2(4)+e^x \left (-2+\log ^2(4)\right )\right )+2 x^2 \left (-5+18 \log ^2(4)+18 e^x \left (1+\log ^2(4)\right )\right )-(-6+x)^2 x^2 \log \left (2 e^{-\frac {5}{(-6+x) x}}\right )\right )}{(6-x)^2 x^2} \, dx\\ &=2 \int \left (\frac {2 x^4 \left (x+\log ^2(4)\right )}{(-6+x)^2}+\frac {30 \log ^2(4) \left (x+\log ^2(4)\right )}{(-6+x)^2 x}-\frac {10 x \left (1-\frac {18 \log ^2(4)}{5}\right ) \left (x+\log ^2(4)\right )}{(-6+x)^2}+\frac {72 x^2 \left (1-\frac {\log ^2(4)}{6}\right ) \left (x+\log ^2(4)\right )}{(-6+x)^2}-\frac {24 x^3 \left (1-\frac {\log ^2(4)}{24}\right ) \left (x+\log ^2(4)\right )}{(-6+x)^2}-\frac {10 \left (-3+\log ^2(4)\right ) \left (x+\log ^2(4)\right )}{(-6+x)^2}+e^{2 x} \left (x^2+\log ^2(4) \left (1+\log ^2(4)\right )+x \left (1+2 \log ^2(4)\right )\right )-x \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(-6+x) x}}\right )-\frac {2 x^3 \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(-6+x) x}}\right )}{(-6+x)^2}-\frac {30 \log ^2(4) \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(-6+x) x}}\right )}{(-6+x)^2 x^2}+\frac {10 \left (1-\frac {18 \log ^2(4)}{5}\right ) \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(-6+x) x}}\right )}{(-6+x)^2}-\frac {72 x \left (1-\frac {\log ^2(4)}{6}\right ) \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(-6+x) x}}\right )}{(-6+x)^2}+\frac {24 x^2 \left (1-\frac {\log ^2(4)}{24}\right ) \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(-6+x) x}}\right )}{(-6+x)^2}+\frac {10 \left (-3+\log ^2(4)\right ) \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(-6+x) x}}\right )}{(-6+x)^2 x}+\left (x+\log ^2(4)\right ) \log ^2\left (2 e^{-\frac {5}{(-6+x) x}}\right )+\frac {e^x \left (x+\log ^2(4)\right ) \left (x^6+30 \log ^2(4)-11 x^4 \log ^2(4)-10 x^2 \left (1-\frac {18 \log ^2(4)}{5}\right )+30 x \left (1-\frac {\log ^2(4)}{3}\right )-9 x^5 \left (1-\frac {\log ^2(4)}{9}\right )+108 x^3 \left (1+\frac {2 \log ^2(4)}{9}\right )-x^5 \log \left (2 e^{-\frac {5}{(-6+x) x}}\right )-12 x^3 \left (1-\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(-6+x) x}}\right )+10 x^4 \left (1-\frac {\log ^2(4)}{10}\right ) \log \left (2 e^{-\frac {5}{(-6+x) x}}\right )-72 x^2 \left (1+\frac {\log ^2(4)}{2}\right ) \log \left (2 e^{-\frac {5}{(-6+x) x}}\right )\right )}{(6-x)^2 x^2}\right ) \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.67, size = 376, normalized size = 10.74 \begin {gather*} \frac {-300 x+x^8-25 \log ^4(4)+2 x^7 \left (-6+e^x+\log ^2(4)\right )+x^2 \left (-2110-720 \log ^2(4)+36 e^{2 x} \log ^4(4)\right )+x^6 \left (36+e^{2 x}-24 \log ^2(4)+\log ^4(4)+4 e^x \left (-6+\log ^2(4)\right )\right )-12 x^3 \left (-6 e^x \log ^4(4)+e^{2 x} \log ^2(4) \left (-6+\log ^2(4)\right )-20 \left (3+\log ^2(4)\right )\right )+2 x^5 \left (e^{2 x} \left (-6+\log ^2(4)\right )-6 \log ^2(4) \left (-6+\log ^2(4)\right )+e^x \left (36-24 \log ^2(4)+\log ^4(4)\right )\right )+x^4 \left (-24 e^x \log ^2(4) \left (-6+\log ^2(4)\right )+e^{2 x} \left (36-24 \log ^2(4)+\log ^4(4)\right )+4 \left (-15-5 \log ^2(4)+9 \log ^4(4)\right )\right )-2 (-6+x) x \left (x^5+5 \log ^4(4)+x^4 \left (-6+e^x+2 \log ^2(4)\right )-6 x \left (-5+e^x \log ^4(4)\right )+x^2 \left (-5-6 \log ^4(4)+e^x \log ^2(4) \left (-12+\log ^2(4)\right )\right )+x^3 \left (\log ^2(4) \left (-12+\log ^2(4)\right )+2 e^x \left (-3+\log ^2(4)\right )\right )\right ) \log \left (2 e^{-\frac {5}{(-6+x) x}}\right )+(-6+x)^2 x^3 \left (x+2 \log ^2(4)\right ) \log ^2\left (2 e^{-\frac {5}{(-6+x) x}}\right )}{(-6+x)^2 x^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(60*x^3 - 20*x^4 + 144*x^5 - 48*x^6 + 4*x^7 + (120*x^2 - 40*x^3 + 216*x^4 - 72*x^5 + 6*x^6)*Log[4]^2
+ (60*x - 20*x^2 + 72*x^3 - 24*x^4 + 2*x^5)*Log[4]^4 + E^(2*x)*(72*x^3 + 48*x^4 - 22*x^5 + 2*x^6 + (72*x^2 +
120*x^3 - 46*x^4 + 4*x^5)*Log[4]^2 + (72*x^2 - 24*x^3 + 2*x^4)*Log[4]^4) + E^x*(60*x^2 - 20*x^3 + 216*x^4 - 18
*x^6 + 2*x^7 + (120*x - 40*x^2 + 288*x^3 + 48*x^4 - 40*x^5 + 4*x^6)*Log[4]^2 + (60 - 20*x + 72*x^2 + 48*x^3 -
22*x^4 + 2*x^5)*Log[4]^4) + (-60*x^2 + 20*x^3 - 216*x^4 + 72*x^5 - 6*x^6 + (-120*x + 40*x^2 - 288*x^3 + 96*x^4
- 8*x^5)*Log[4]^2 + (-60 + 20*x - 72*x^2 + 24*x^3 - 2*x^4)*Log[4]^4 + E^x*(-144*x^3 - 24*x^4 + 20*x^5 - 2*x^6
+ (-144*x^2 - 96*x^3 + 44*x^4 - 4*x^5)*Log[4]^2 + (-72*x^2 + 24*x^3 - 2*x^4)*Log[4]^4))*Log[2/E^(5/(-6*x + x^
2))] + (72*x^3 - 24*x^4 + 2*x^5 + (72*x^2 - 24*x^3 + 2*x^4)*Log[4]^2)*Log[2/E^(5/(-6*x + x^2))]^2)/(36*x^2 - 1
2*x^3 + x^4),x]

[Out]

(-300*x + x^8 - 25*Log[4]^4 + 2*x^7*(-6 + E^x + Log[4]^2) + x^2*(-2110 - 720*Log[4]^2 + 36*E^(2*x)*Log[4]^4) +
x^6*(36 + E^(2*x) - 24*Log[4]^2 + Log[4]^4 + 4*E^x*(-6 + Log[4]^2)) - 12*x^3*(-6*E^x*Log[4]^4 + E^(2*x)*Log[4
]^2*(-6 + Log[4]^2) - 20*(3 + Log[4]^2)) + 2*x^5*(E^(2*x)*(-6 + Log[4]^2) - 6*Log[4]^2*(-6 + Log[4]^2) + E^x*(
36 - 24*Log[4]^2 + Log[4]^4)) + x^4*(-24*E^x*Log[4]^2*(-6 + Log[4]^2) + E^(2*x)*(36 - 24*Log[4]^2 + Log[4]^4)
+ 4*(-15 - 5*Log[4]^2 + 9*Log[4]^4)) - 2*(-6 + x)*x*(x^5 + 5*Log[4]^4 + x^4*(-6 + E^x + 2*Log[4]^2) - 6*x*(-5
+ E^x*Log[4]^4) + x^2*(-5 - 6*Log[4]^4 + E^x*Log[4]^2*(-12 + Log[4]^2)) + x^3*(Log[4]^2*(-12 + Log[4]^2) + 2*E
^x*(-3 + Log[4]^2)))*Log[2/E^(5/((-6 + x)*x))] + (-6 + x)^2*x^3*(x + 2*Log[4]^2)*Log[2/E^(5/((-6 + x)*x))]^2)/
((-6 + x)^2*x^2)

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fricas [B]  time = 1.07, size = 412, normalized size = 11.77 \begin {gather*} \frac {x^{8} - 12 \, x^{7} + 36 \, x^{6} - 32 \, {\left (x^{5} - 12 \, x^{4} + 36 \, x^{3} + 5 \, x^{2} - 30 \, x\right )} \log \relax (2)^{5} + 10 \, x^{5} + 8 \, {\left (2 \, x^{6} - 23 \, x^{5} + 60 \, x^{4} + 56 \, x^{3} - 120 \, x^{2} + 50\right )} \log \relax (2)^{4} - 120 \, x^{4} - 16 \, {\left (x^{6} - 12 \, x^{5} + 36 \, x^{4} + 5 \, x^{3} - 30 \, x^{2}\right )} \log \relax (2)^{3} + 720 \, x^{3} + {\left (8 \, x^{7} - 95 \, x^{6} + 276 \, x^{5} + 36 \, x^{4} + 480 \, x^{3} - 2880 \, x^{2} + 200 \, x\right )} \log \relax (2)^{2} - 2135 \, x^{2} + {\left (x^{6} - 12 \, x^{5} + 16 \, {\left (x^{4} - 12 \, x^{3} + 36 \, x^{2}\right )} \log \relax (2)^{4} + 36 \, x^{4} + 8 \, {\left (x^{5} - 12 \, x^{4} + 36 \, x^{3}\right )} \log \relax (2)^{2}\right )} e^{\left (2 \, x\right )} + 2 \, {\left (x^{7} - 12 \, x^{6} - 16 \, {\left (x^{4} - 12 \, x^{3} + 36 \, x^{2}\right )} \log \relax (2)^{5} + 36 \, x^{5} + 16 \, {\left (x^{5} - 12 \, x^{4} + 36 \, x^{3} + 5 \, x^{2} - 30 \, x\right )} \log \relax (2)^{4} + 5 \, x^{4} - 8 \, {\left (x^{5} - 12 \, x^{4} + 36 \, x^{3}\right )} \log \relax (2)^{3} - 30 \, x^{3} + 8 \, {\left (x^{6} - 12 \, x^{5} + 36 \, x^{4} + 5 \, x^{3} - 30 \, x^{2}\right )} \log \relax (2)^{2} - {\left (x^{6} - 12 \, x^{5} + 36 \, x^{4}\right )} \log \relax (2)\right )} e^{x} - 2 \, {\left (x^{7} - 12 \, x^{6} + 36 \, x^{5} + 30 \, x^{3} - 180 \, x^{2}\right )} \log \relax (2)}{x^{4} - 12 \, x^{3} + 36 \, x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*(2*x^4-24*x^3+72*x^2)*log(2)^2+2*x^5-24*x^4+72*x^3)*log(2/exp(5/(x^2-6*x)))^2+((16*(-2*x^4+24*x^
3-72*x^2)*log(2)^4+4*(-4*x^5+44*x^4-96*x^3-144*x^2)*log(2)^2-2*x^6+20*x^5-24*x^4-144*x^3)*exp(x)+16*(-2*x^4+24
*x^3-72*x^2+20*x-60)*log(2)^4+4*(-8*x^5+96*x^4-288*x^3+40*x^2-120*x)*log(2)^2-6*x^6+72*x^5-216*x^4+20*x^3-60*x
^2)*log(2/exp(5/(x^2-6*x)))+(16*(2*x^4-24*x^3+72*x^2)*log(2)^4+4*(4*x^5-46*x^4+120*x^3+72*x^2)*log(2)^2+2*x^6-
22*x^5+48*x^4+72*x^3)*exp(x)^2+(16*(2*x^5-22*x^4+48*x^3+72*x^2-20*x+60)*log(2)^4+4*(4*x^6-40*x^5+48*x^4+288*x^
3-40*x^2+120*x)*log(2)^2+2*x^7-18*x^6+216*x^4-20*x^3+60*x^2)*exp(x)+16*(2*x^5-24*x^4+72*x^3-20*x^2+60*x)*log(2
)^4+4*(6*x^6-72*x^5+216*x^4-40*x^3+120*x^2)*log(2)^2+4*x^7-48*x^6+144*x^5-20*x^4+60*x^3)/(x^4-12*x^3+36*x^2),x
, algorithm="fricas")

[Out]

(x^8 - 12*x^7 + 36*x^6 - 32*(x^5 - 12*x^4 + 36*x^3 + 5*x^2 - 30*x)*log(2)^5 + 10*x^5 + 8*(2*x^6 - 23*x^5 + 60*
x^4 + 56*x^3 - 120*x^2 + 50)*log(2)^4 - 120*x^4 - 16*(x^6 - 12*x^5 + 36*x^4 + 5*x^3 - 30*x^2)*log(2)^3 + 720*x
^3 + (8*x^7 - 95*x^6 + 276*x^5 + 36*x^4 + 480*x^3 - 2880*x^2 + 200*x)*log(2)^2 - 2135*x^2 + (x^6 - 12*x^5 + 16
*(x^4 - 12*x^3 + 36*x^2)*log(2)^4 + 36*x^4 + 8*(x^5 - 12*x^4 + 36*x^3)*log(2)^2)*e^(2*x) + 2*(x^7 - 12*x^6 - 1
6*(x^4 - 12*x^3 + 36*x^2)*log(2)^5 + 36*x^5 + 16*(x^5 - 12*x^4 + 36*x^3 + 5*x^2 - 30*x)*log(2)^4 + 5*x^4 - 8*(
x^5 - 12*x^4 + 36*x^3)*log(2)^3 - 30*x^3 + 8*(x^6 - 12*x^5 + 36*x^4 + 5*x^3 - 30*x^2)*log(2)^2 - (x^6 - 12*x^5
+ 36*x^4)*log(2))*e^x - 2*(x^7 - 12*x^6 + 36*x^5 + 30*x^3 - 180*x^2)*log(2))/(x^4 - 12*x^3 + 36*x^2)

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giac [B]  time = 0.37, size = 626, normalized size = 17.89 \begin {gather*} \frac {16 \, x^{6} \log \relax (2)^{4} + 32 \, x^{5} e^{x} \log \relax (2)^{4} - 32 \, x^{5} \log \relax (2)^{5} - 32 \, x^{4} e^{x} \log \relax (2)^{5} + 8 \, x^{7} \log \relax (2)^{2} + 16 \, x^{6} e^{x} \log \relax (2)^{2} - 16 \, x^{6} \log \relax (2)^{3} - 16 \, x^{5} e^{x} \log \relax (2)^{3} - 184 \, x^{5} \log \relax (2)^{4} + 16 \, x^{4} e^{\left (2 \, x\right )} \log \relax (2)^{4} - 384 \, x^{4} e^{x} \log \relax (2)^{4} + 384 \, x^{4} \log \relax (2)^{5} + 384 \, x^{3} e^{x} \log \relax (2)^{5} + x^{8} + 2 \, x^{7} e^{x} - 2 \, x^{7} \log \relax (2) - 2 \, x^{6} e^{x} \log \relax (2) - 95 \, x^{6} \log \relax (2)^{2} + 8 \, x^{5} e^{\left (2 \, x\right )} \log \relax (2)^{2} - 192 \, x^{5} e^{x} \log \relax (2)^{2} + 192 \, x^{5} \log \relax (2)^{3} + 192 \, x^{4} e^{x} \log \relax (2)^{3} + 480 \, x^{4} \log \relax (2)^{4} - 192 \, x^{3} e^{\left (2 \, x\right )} \log \relax (2)^{4} + 1152 \, x^{3} e^{x} \log \relax (2)^{4} - 1152 \, x^{3} \log \relax (2)^{5} - 1152 \, x^{2} e^{x} \log \relax (2)^{5} - 12 \, x^{7} + x^{6} e^{\left (2 \, x\right )} - 24 \, x^{6} e^{x} + 24 \, x^{6} \log \relax (2) + 24 \, x^{5} e^{x} \log \relax (2) + 276 \, x^{5} \log \relax (2)^{2} - 96 \, x^{4} e^{\left (2 \, x\right )} \log \relax (2)^{2} + 576 \, x^{4} e^{x} \log \relax (2)^{2} - 576 \, x^{4} \log \relax (2)^{3} - 576 \, x^{3} e^{x} \log \relax (2)^{3} + 448 \, x^{3} \log \relax (2)^{4} + 576 \, x^{2} e^{\left (2 \, x\right )} \log \relax (2)^{4} + 160 \, x^{2} e^{x} \log \relax (2)^{4} - 160 \, x^{2} \log \relax (2)^{5} + 36 \, x^{6} - 12 \, x^{5} e^{\left (2 \, x\right )} + 72 \, x^{5} e^{x} - 72 \, x^{5} \log \relax (2) - 72 \, x^{4} e^{x} \log \relax (2) + 36 \, x^{4} \log \relax (2)^{2} + 288 \, x^{3} e^{\left (2 \, x\right )} \log \relax (2)^{2} + 80 \, x^{3} e^{x} \log \relax (2)^{2} - 80 \, x^{3} \log \relax (2)^{3} - 960 \, x^{2} \log \relax (2)^{4} - 960 \, x e^{x} \log \relax (2)^{4} + 960 \, x \log \relax (2)^{5} + 10 \, x^{5} + 36 \, x^{4} e^{\left (2 \, x\right )} + 10 \, x^{4} e^{x} + 480 \, x^{3} \log \relax (2)^{2} - 480 \, x^{2} e^{x} \log \relax (2)^{2} + 480 \, x^{2} \log \relax (2)^{3} - 120 \, x^{4} - 60 \, x^{3} e^{x} - 60 \, x^{3} \log \relax (2) - 2880 \, x^{2} \log \relax (2)^{2} + 400 \, \log \relax (2)^{4} + 720 \, x^{3} + 360 \, x^{2} \log \relax (2) + 200 \, x \log \relax (2)^{2} - 2135 \, x^{2}}{x^{4} - 12 \, x^{3} + 36 \, x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*(2*x^4-24*x^3+72*x^2)*log(2)^2+2*x^5-24*x^4+72*x^3)*log(2/exp(5/(x^2-6*x)))^2+((16*(-2*x^4+24*x^
3-72*x^2)*log(2)^4+4*(-4*x^5+44*x^4-96*x^3-144*x^2)*log(2)^2-2*x^6+20*x^5-24*x^4-144*x^3)*exp(x)+16*(-2*x^4+24
*x^3-72*x^2+20*x-60)*log(2)^4+4*(-8*x^5+96*x^4-288*x^3+40*x^2-120*x)*log(2)^2-6*x^6+72*x^5-216*x^4+20*x^3-60*x
^2)*log(2/exp(5/(x^2-6*x)))+(16*(2*x^4-24*x^3+72*x^2)*log(2)^4+4*(4*x^5-46*x^4+120*x^3+72*x^2)*log(2)^2+2*x^6-
22*x^5+48*x^4+72*x^3)*exp(x)^2+(16*(2*x^5-22*x^4+48*x^3+72*x^2-20*x+60)*log(2)^4+4*(4*x^6-40*x^5+48*x^4+288*x^
3-40*x^2+120*x)*log(2)^2+2*x^7-18*x^6+216*x^4-20*x^3+60*x^2)*exp(x)+16*(2*x^5-24*x^4+72*x^3-20*x^2+60*x)*log(2
)^4+4*(6*x^6-72*x^5+216*x^4-40*x^3+120*x^2)*log(2)^2+4*x^7-48*x^6+144*x^5-20*x^4+60*x^3)/(x^4-12*x^3+36*x^2),x
, algorithm="giac")

[Out]

(16*x^6*log(2)^4 + 32*x^5*e^x*log(2)^4 - 32*x^5*log(2)^5 - 32*x^4*e^x*log(2)^5 + 8*x^7*log(2)^2 + 16*x^6*e^x*l
og(2)^2 - 16*x^6*log(2)^3 - 16*x^5*e^x*log(2)^3 - 184*x^5*log(2)^4 + 16*x^4*e^(2*x)*log(2)^4 - 384*x^4*e^x*log
(2)^4 + 384*x^4*log(2)^5 + 384*x^3*e^x*log(2)^5 + x^8 + 2*x^7*e^x - 2*x^7*log(2) - 2*x^6*e^x*log(2) - 95*x^6*l
og(2)^2 + 8*x^5*e^(2*x)*log(2)^2 - 192*x^5*e^x*log(2)^2 + 192*x^5*log(2)^3 + 192*x^4*e^x*log(2)^3 + 480*x^4*lo
g(2)^4 - 192*x^3*e^(2*x)*log(2)^4 + 1152*x^3*e^x*log(2)^4 - 1152*x^3*log(2)^5 - 1152*x^2*e^x*log(2)^5 - 12*x^7
+ x^6*e^(2*x) - 24*x^6*e^x + 24*x^6*log(2) + 24*x^5*e^x*log(2) + 276*x^5*log(2)^2 - 96*x^4*e^(2*x)*log(2)^2 +
576*x^4*e^x*log(2)^2 - 576*x^4*log(2)^3 - 576*x^3*e^x*log(2)^3 + 448*x^3*log(2)^4 + 576*x^2*e^(2*x)*log(2)^4
+ 160*x^2*e^x*log(2)^4 - 160*x^2*log(2)^5 + 36*x^6 - 12*x^5*e^(2*x) + 72*x^5*e^x - 72*x^5*log(2) - 72*x^4*e^x*
log(2) + 36*x^4*log(2)^2 + 288*x^3*e^(2*x)*log(2)^2 + 80*x^3*e^x*log(2)^2 - 80*x^3*log(2)^3 - 960*x^2*log(2)^4
- 960*x*e^x*log(2)^4 + 960*x*log(2)^5 + 10*x^5 + 36*x^4*e^(2*x) + 10*x^4*e^x + 480*x^3*log(2)^2 - 480*x^2*e^x
*log(2)^2 + 480*x^2*log(2)^3 - 120*x^4 - 60*x^3*e^x - 60*x^3*log(2) - 2880*x^2*log(2)^2 + 400*log(2)^4 + 720*x
^3 + 360*x^2*log(2) + 200*x*log(2)^2 - 2135*x^2)/(x^4 - 12*x^3 + 36*x^2)

________________________________________________________________________________________

maple [B]  time = 0.52, size = 560, normalized size = 16.00

method	result	size
default	\(8 x \ln \relax (2)^{2} {\mathrm e}^{2 x}+16 x^{2} \ln \relax (2)^{4}+x^{4}+10 \,{\mathrm e}^{x}+8 x^{3} \ln \relax (2)^{2}+{\mathrm e}^{2 x} x^{2}+2 \,{\mathrm e}^{x} x^{3}-16 \,{\mathrm e}^{x} \ln \relax (2)^{2} x \left (\ln \left (2 \,{\mathrm e}^{-\frac {5}{x^{2}-6 x}}\right )+\ln \left ({\mathrm e}^{\frac {5}{x^{2}-6 x}}\right )\right )+16 \,{\mathrm e}^{x} \ln \relax (2)^{2} x \left (\ln \left ({\mathrm e}^{\frac {5}{x^{2}-6 x}}\right )-\frac {5}{x^{2}-6 x}\right )-\frac {100 \ln \relax (2)^{4}}{27 x}+\frac {100 \ln \relax (2)^{4}}{27 \left (x -6\right )}+\frac {60 \,{\mathrm e}^{x}}{x -6}-\frac {100 \ln \relax (2)^{4}}{9 x^{2}}-\frac {100 \ln \relax (2)^{4}}{9 \left (x -6\right )^{2}}+32 \,{\mathrm e}^{x} \ln \relax (2)^{4} x +16 \,{\mathrm e}^{x} \ln \relax (2)^{2} x^{2}-2 \,{\mathrm e}^{x} \left (\ln \left (2 \,{\mathrm e}^{-\frac {5}{x^{2}-6 x}}\right )+\ln \left ({\mathrm e}^{\frac {5}{x^{2}-6 x}}\right )\right ) x^{2}+2 \,{\mathrm e}^{x} \left (\ln \left ({\mathrm e}^{\frac {5}{x^{2}-6 x}}\right )-\frac {5}{x^{2}-6 x}\right ) x^{2}+\frac {80 \ln \relax (2)^{2} {\mathrm e}^{x}}{x -6}+\frac {80 \ln \relax (2)^{4} {\mathrm e}^{x}}{3 \left (x -6\right )}+32 \,{\mathrm e}^{x} \ln \relax (2)^{4} \left (\ln \left ({\mathrm e}^{\frac {5}{x^{2}-6 x}}\right )-\frac {5}{x^{2}-6 x}\right )-\frac {80 \ln \relax (2)^{4} {\mathrm e}^{x}}{3 x}-32 \,{\mathrm e}^{x} \ln \relax (2)^{4} \left (\ln \left (2 \,{\mathrm e}^{-\frac {5}{x^{2}-6 x}}\right )+\ln \left ({\mathrm e}^{\frac {5}{x^{2}-6 x}}\right )\right )+8 \ln \left (2 \,{\mathrm e}^{-\frac {5}{x^{2}-6 x}}\right )^{2} \ln \relax (2)^{2} x -16 \ln \left (2 \,{\mathrm e}^{-\frac {5}{x^{2}-6 x}}\right ) \ln \relax (2)^{2} x^{2}-32 \ln \left (2 \,{\mathrm e}^{-\frac {5}{x^{2}-6 x}}\right ) x \ln \relax (2)^{4}-\frac {80 \ln \left (2 \,{\mathrm e}^{-\frac {5}{x^{2}-6 x}}\right ) \ln \relax (2)^{4}}{3 \left (x -6\right )}+\frac {80 \ln \left (2 \,{\mathrm e}^{-\frac {5}{x^{2}-6 x}}\right ) \ln \relax (2)^{4}}{3 x}+16 \,{\mathrm e}^{2 x} \ln \relax (2)^{4}-2 \ln \left (2 \,{\mathrm e}^{-\frac {5}{x^{2}-6 x}}\right ) x^{3}+\ln \left (2 \,{\mathrm e}^{-\frac {5}{x^{2}-6 x}}\right )^{2} x^{2}\)	\(560\)
risch	\(\left (8 x \ln \relax (2)^{2}+x^{2}\right ) \ln \left ({\mathrm e}^{\frac {5}{x \left (x -6\right )}}\right )^{2}+\frac {\left (-192 x^{2} \ln \relax (2)^{4}+32 x^{3} \ln \relax (2)^{4}-16 x^{3} \ln \relax (2)^{3}+160 \ln \relax (2)^{4}+2 x^{5}-12 x^{4}+96 x^{2} \ln \relax (2)^{3}+16 x^{4} \ln \relax (2)^{2}-96 x^{3} \ln \relax (2)^{2}-2 x^{4} \ln \relax (2)+2 \,{\mathrm e}^{x} x^{4}+12 x^{3} \ln \relax (2)-12 \,{\mathrm e}^{x} x^{3}+32 \,{\mathrm e}^{x} \ln \relax (2)^{4} x^{2}-192 \,{\mathrm e}^{x} \ln \relax (2)^{4} x +16 \,{\mathrm e}^{x} \ln \relax (2)^{2} x^{3}-96 \,{\mathrm e}^{x} \ln \relax (2)^{2} x^{2}\right ) \ln \left ({\mathrm e}^{\frac {5}{x \left (x -6\right )}}\right )}{x \left (x -6\right )}+\frac {1152 x^{3} \ln \relax (2)^{4}+64 x^{6} \ln \relax (2)^{4}-736 x^{5} \ln \relax (2)^{4}+768 x^{5} \ln \relax (2)^{3}-64 x^{6} \ln \relax (2)^{3}-380 x^{6} \ln \relax (2)^{2}+8 x^{7} {\mathrm e}^{x}+288 x^{5} {\mathrm e}^{x}-1600 \ln \relax (2)^{4}-48 x^{7}+4 x^{8}+144 x^{6}-2304 x^{4} \ln \relax (2)^{3}-4608 x^{3} \ln \relax (2)^{5}+1104 x^{5} \ln \relax (2)^{2}+32 x^{7} \ln \relax (2)^{2}-8 x^{7} \ln \relax (2)+144 x^{4} \ln \relax (2)^{2}-48 x^{5} {\mathrm e}^{2 x}-96 x^{6} {\mathrm e}^{x}-288 x^{5} \ln \relax (2)+96 x^{6} \ln \relax (2)+3840 x \ln \relax (2)^{5}+1920 \ln \relax (2)^{4} x^{4}+128 \,{\mathrm e}^{x} \ln \relax (2)^{4} x^{5}-1536 \,{\mathrm e}^{x} \ln \relax (2)^{4} x^{4}+64 \,{\mathrm e}^{x} \ln \relax (2)^{2} x^{6}+4608 \,{\mathrm e}^{x} \ln \relax (2)^{4} x^{3}-768 \,{\mathrm e}^{x} \ln \relax (2)^{2} x^{5}+2304 \,{\mathrm e}^{x} \ln \relax (2)^{2} x^{4}+64 \,{\mathrm e}^{2 x} \ln \relax (2)^{4} x^{4}+32 \,{\mathrm e}^{2 x} \ln \relax (2)^{2} x^{5}-384 \,{\mathrm e}^{2 x} \ln \relax (2)^{2} x^{4}-768 \,{\mathrm e}^{2 x} \ln \relax (2)^{4} x^{3}+2304 \,{\mathrm e}^{2 x} \ln \relax (2)^{4} x^{2}+1152 \,{\mathrm e}^{2 x} \ln \relax (2)^{2} x^{3}+1536 \ln \relax (2)^{5} x^{4}-640 \ln \relax (2)^{5} x^{2}-128 \ln \relax (2)^{5} x^{5}-128 \ln \relax (2)^{5} x^{4} {\mathrm e}^{x}+1536 \ln \relax (2)^{5} x^{3} {\mathrm e}^{x}-64 \ln \relax (2)^{3} x^{5} {\mathrm e}^{x}-4608 \ln \relax (2)^{5} x^{2} {\mathrm e}^{x}+768 \ln \relax (2)^{3} x^{4} {\mathrm e}^{x}-8 \ln \relax (2) x^{6} {\mathrm e}^{x}-2304 \ln \relax (2)^{3} x^{3} {\mathrm e}^{x}+96 \ln \relax (2) x^{5} {\mathrm e}^{x}-288 \ln \relax (2) x^{4} {\mathrm e}^{x}+4 x^{6} {\mathrm e}^{2 x}+144 \,{\mathrm e}^{2 x} x^{4}}{4 x^{2} \left (x^{2}-12 x +36\right )}\)	\(675\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((4*(2*x^4-24*x^3+72*x^2)*ln(2)^2+2*x^5-24*x^4+72*x^3)*ln(2/exp(5/(x^2-6*x)))^2+((16*(-2*x^4+24*x^3-72*x^2
)*ln(2)^4+4*(-4*x^5+44*x^4-96*x^3-144*x^2)*ln(2)^2-2*x^6+20*x^5-24*x^4-144*x^3)*exp(x)+16*(-2*x^4+24*x^3-72*x^
2+20*x-60)*ln(2)^4+4*(-8*x^5+96*x^4-288*x^3+40*x^2-120*x)*ln(2)^2-6*x^6+72*x^5-216*x^4+20*x^3-60*x^2)*ln(2/exp
(5/(x^2-6*x)))+(16*(2*x^4-24*x^3+72*x^2)*ln(2)^4+4*(4*x^5-46*x^4+120*x^3+72*x^2)*ln(2)^2+2*x^6-22*x^5+48*x^4+7
2*x^3)*exp(x)^2+(16*(2*x^5-22*x^4+48*x^3+72*x^2-20*x+60)*ln(2)^4+4*(4*x^6-40*x^5+48*x^4+288*x^3-40*x^2+120*x)*
ln(2)^2+2*x^7-18*x^6+216*x^4-20*x^3+60*x^2)*exp(x)+16*(2*x^5-24*x^4+72*x^3-20*x^2+60*x)*ln(2)^4+4*(6*x^6-72*x^
5+216*x^4-40*x^3+120*x^2)*ln(2)^2+4*x^7-48*x^6+144*x^5-20*x^4+60*x^3)/(x^4-12*x^3+36*x^2),x,method=_RETURNVERB
OSE)

[Out]

8*x*ln(2)^2*exp(x)^2+16*x^2*ln(2)^4+x^4+10*exp(x)+8*x^3*ln(2)^2+exp(x)^2*x^2+2*exp(x)*x^3-16*exp(x)*ln(2)^2*x*
(ln(2/exp(5/(x^2-6*x)))+ln(exp(5/(x^2-6*x))))+16*exp(x)*ln(2)^2*x*(ln(exp(5/(x^2-6*x)))-5/(x^2-6*x))-100/27*ln
(2)^4/x+100/27/(x-6)*ln(2)^4+16*exp(x)^2*ln(2)^4+60*exp(x)/(x-6)-100/9*ln(2)^4/x^2-2*ln(2/exp(5/(x^2-6*x)))*x^
3-100/9*ln(2)^4/(x-6)^2+32*exp(x)*ln(2)^4*x+16*exp(x)*ln(2)^2*x^2+ln(2/exp(5/(x^2-6*x)))^2*x^2-2*exp(x)*(ln(2/
exp(5/(x^2-6*x)))+ln(exp(5/(x^2-6*x))))*x^2+2*exp(x)*(ln(exp(5/(x^2-6*x)))-5/(x^2-6*x))*x^2+80*ln(2)^2*exp(x)/
(x-6)+80/3*ln(2)^4*exp(x)/(x-6)-32*exp(x)*ln(2)^4*(ln(2/exp(5/(x^2-6*x)))+ln(exp(5/(x^2-6*x))))+32*exp(x)*ln(2
)^4*(ln(exp(5/(x^2-6*x)))-5/(x^2-6*x))-80/3*ln(2)^4/x*exp(x)+8*ln(2/exp(5/(x^2-6*x)))^2*ln(2)^2*x-16*ln(2/exp(
5/(x^2-6*x)))*ln(2)^2*x^2-32*ln(2/exp(5/(x^2-6*x)))*x*ln(2)^4-80/3*ln(2/exp(5/(x^2-6*x)))/(x-6)*ln(2)^4+80/3*l
n(2/exp(5/(x^2-6*x)))*ln(2)^4/x

________________________________________________________________________________________

maxima [B]  time = 0.54, size = 663, normalized size = 18.94 result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*(2*x^4-24*x^3+72*x^2)*log(2)^2+2*x^5-24*x^4+72*x^3)*log(2/exp(5/(x^2-6*x)))^2+((16*(-2*x^4+24*x^
3-72*x^2)*log(2)^4+4*(-4*x^5+44*x^4-96*x^3-144*x^2)*log(2)^2-2*x^6+20*x^5-24*x^4-144*x^3)*exp(x)+16*(-2*x^4+24
*x^3-72*x^2+20*x-60)*log(2)^4+4*(-8*x^5+96*x^4-288*x^3+40*x^2-120*x)*log(2)^2-6*x^6+72*x^5-216*x^4+20*x^3-60*x
^2)*log(2/exp(5/(x^2-6*x)))+(16*(2*x^4-24*x^3+72*x^2)*log(2)^4+4*(4*x^5-46*x^4+120*x^3+72*x^2)*log(2)^2+2*x^6-
22*x^5+48*x^4+72*x^3)*exp(x)^2+(16*(2*x^5-22*x^4+48*x^3+72*x^2-20*x+60)*log(2)^4+4*(4*x^6-40*x^5+48*x^4+288*x^
3-40*x^2+120*x)*log(2)^2+2*x^7-18*x^6+216*x^4-20*x^3+60*x^2)*exp(x)+16*(2*x^5-24*x^4+72*x^3-20*x^2+60*x)*log(2
)^4+4*(6*x^6-72*x^5+216*x^4-40*x^3+120*x^2)*log(2)^2+4*x^7-48*x^6+144*x^5-20*x^4+60*x^3)/(x^4-12*x^3+36*x^2),x
, algorithm="maxima")

[Out]

16*(x^2 + 24*x - 432/(x - 6) + 216*log(x - 6))*log(2)^4 - 384*(x - 36/(x - 6) + 12*log(x - 6))*log(2)^4 - 80/3
*(6/(x - 6) + log(x - 6) - log(x))*log(2)^4 - 1152*(6/(x - 6) - log(x - 6))*log(2)^4 - 80/3*log(2)^4*log(x) +
x^4 + 8*(x^3 + 18*x^2 + 324*x - 3888/(x - 6) + 2592*log(x - 6))*log(2)^2 - 144*(x^2 + 24*x - 432/(x - 6) + 216
*log(x - 6))*log(2)^2 + 864*(x - 36/(x - 6) + 12*log(x - 6))*log(2)^2 + 160*(6/(x - 6) - log(x - 6))*log(2)^2
+ 320*log(2)^4/(x - 6) + 20/3*(4*log(2)^4 + 24*log(2)^2 + 27)*log(x - 6) - 20*x - 480*log(2)^2/(x - 6) - (2*x^
7*log(2) + (16*log(2)^3 - log(2)^2 - 24*log(2))*x^6 + 2*(16*log(2)^5 - 4*log(2)^4 - 96*log(2)^3 + 6*log(2)^2 +
36*log(2) - 15)*x^5 - 12*(32*log(2)^5 - 8*log(2)^4 - 48*log(2)^3 + 3*log(2)^2 - 30)*x^4 + 4*(288*log(2)^5 - 7
2*log(2)^4 + 20*log(2)^3 + 15*log(2) - 270)*x^3 - 400*log(2)^4 + 5*(32*log(2)^5 - 96*log(2)^3 - 72*log(2) - 5)
*x^2 - 40*(24*log(2)^5 + 5*log(2)^2)*x - (4*(2*log(2)^2 - 3)*x^5 + x^6 + 576*x^2*log(2)^4 + 4*(4*log(2)^4 - 24
*log(2)^2 + 9)*x^4 - 96*(2*log(2)^4 - 3*log(2)^2)*x^3)*e^(2*x) - 2*((8*log(2)^2 - log(2) - 12)*x^6 + x^7 + 4*(
4*log(2)^4 - 2*log(2)^3 - 24*log(2)^2 + 3*log(2) + 9)*x^5 - (16*log(2)^5 + 192*log(2)^4 - 96*log(2)^3 - 288*lo
g(2)^2 + 36*log(2) - 5)*x^4 - 480*x*log(2)^4 + 2*(96*log(2)^5 + 288*log(2)^4 - 144*log(2)^3 + 20*log(2)^2 - 15
)*x^3 - 16*(36*log(2)^5 - 5*log(2)^4 + 15*log(2)^2)*x^2)*e^x)/(x^4 - 12*x^3 + 36*x^2) + 360/(x - 6) - 180*log(
x - 6)

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mupad [B]  time = 4.17, size = 291, normalized size = 8.31 \begin {gather*} \frac {\left (480\,{\ln \relax (2)}^2-60\,\ln \relax (2)-80\,{\ln \relax (2)}^3+160\,{\ln \relax (2)}^4+360\right )\,x^3+\left (360\,\ln \relax (2)-2880\,{\ln \relax (2)}^2+480\,{\ln \relax (2)}^3-960\,{\ln \relax (2)}^4-160\,{\ln \relax (2)}^5-2135\right )\,x^2+\left (200\,{\ln \relax (2)}^2+960\,{\ln \relax (2)}^5\right )\,x+400\,{\ln \relax (2)}^4}{x^4-12\,x^3+36\,x^2}-x^3\,\left (2\,\ln \relax (2)-8\,{\ln \relax (2)}^2\right )+x\,\left (8\,{\ln \relax (2)}^4-32\,{\ln \relax (2)}^5+10\right )+{\mathrm {e}}^{2\,x}\,\left (x^2+8\,{\ln \relax (2)}^2\,x+16\,{\ln \relax (2)}^4\right )+x^2\,\left ({\ln \relax (2)}^2-16\,{\ln \relax (2)}^3+16\,{\ln \relax (2)}^4\right )+x^4-\frac {{\mathrm {e}}^x\,\left (2\,x^5+\left (16\,{\ln \relax (2)}^2-2\,\ln \relax (2)-12\right )\,x^4+\left (12\,\ln \relax (2)-96\,{\ln \relax (2)}^2-16\,{\ln \relax (2)}^3+32\,{\ln \relax (2)}^4\right )\,x^3+\left (96\,{\ln \relax (2)}^3-192\,{\ln \relax (2)}^4-32\,{\ln \relax (2)}^5+10\right )\,x^2+\left (80\,{\ln \relax (2)}^2+192\,{\ln \relax (2)}^5\right )\,x+160\,{\ln \relax (2)}^4\right )}{6\,x-x^2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((16*log(2)^4*(60*x - 20*x^2 + 72*x^3 - 24*x^4 + 2*x^5) + log(2*exp(5/(6*x - x^2)))^2*(4*log(2)^2*(72*x^2 -
24*x^3 + 2*x^4) + 72*x^3 - 24*x^4 + 2*x^5) + exp(x)*(16*log(2)^4*(72*x^2 - 20*x + 48*x^3 - 22*x^4 + 2*x^5 + 6
0) + 4*log(2)^2*(120*x - 40*x^2 + 288*x^3 + 48*x^4 - 40*x^5 + 4*x^6) + 60*x^2 - 20*x^3 + 216*x^4 - 18*x^6 + 2*
x^7) + exp(2*x)*(16*log(2)^4*(72*x^2 - 24*x^3 + 2*x^4) + 4*log(2)^2*(72*x^2 + 120*x^3 - 46*x^4 + 4*x^5) + 72*x
^3 + 48*x^4 - 22*x^5 + 2*x^6) - log(2*exp(5/(6*x - x^2)))*(16*log(2)^4*(72*x^2 - 20*x - 24*x^3 + 2*x^4 + 60) +
exp(x)*(16*log(2)^4*(72*x^2 - 24*x^3 + 2*x^4) + 4*log(2)^2*(144*x^2 + 96*x^3 - 44*x^4 + 4*x^5) + 144*x^3 + 24
*x^4 - 20*x^5 + 2*x^6) + 4*log(2)^2*(120*x - 40*x^2 + 288*x^3 - 96*x^4 + 8*x^5) + 60*x^2 - 20*x^3 + 216*x^4 -
72*x^5 + 6*x^6) + 4*log(2)^2*(120*x^2 - 40*x^3 + 216*x^4 - 72*x^5 + 6*x^6) + 60*x^3 - 20*x^4 + 144*x^5 - 48*x^
6 + 4*x^7)/(36*x^2 - 12*x^3 + x^4),x)

[Out]

(x*(200*log(2)^2 + 960*log(2)^5) - x^2*(2880*log(2)^2 - 360*log(2) - 480*log(2)^3 + 960*log(2)^4 + 160*log(2)^
5 + 2135) + 400*log(2)^4 + x^3*(480*log(2)^2 - 60*log(2) - 80*log(2)^3 + 160*log(2)^4 + 360))/(36*x^2 - 12*x^3
+ x^4) - x^3*(2*log(2) - 8*log(2)^2) + x*(8*log(2)^4 - 32*log(2)^5 + 10) + exp(2*x)*(8*x*log(2)^2 + 16*log(2)
^4 + x^2) + x^2*(log(2)^2 - 16*log(2)^3 + 16*log(2)^4) + x^4 - (exp(x)*(x^2*(96*log(2)^3 - 192*log(2)^4 - 32*l
og(2)^5 + 10) - x^4*(2*log(2) - 16*log(2)^2 + 12) + x*(80*log(2)^2 + 192*log(2)^5) + 160*log(2)^4 + 2*x^5 + x^
3*(12*log(2) - 96*log(2)^2 - 16*log(2)^3 + 32*log(2)^4)))/(6*x - x^2)

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sympy [B]  time = 6.35, size = 350, normalized size = 10.00 \begin {gather*} x^{4} + x^{3} \left (- 2 \log {\relax (2 )} + 8 \log {\relax (2 )}^{2}\right ) + x^{2} \left (- 16 \log {\relax (2 )}^{3} + \log {\relax (2 )}^{2} + 16 \log {\relax (2 )}^{4}\right ) + x \left (- 32 \log {\relax (2 )}^{5} + 8 \log {\relax (2 )}^{4} + 10\right ) + \frac {x^{3} \left (- 60 \log {\relax (2 )} - 80 \log {\relax (2 )}^{3} + 160 \log {\relax (2 )}^{4} + 480 \log {\relax (2 )}^{2} + 360\right ) + x^{2} \left (-2135 - 2880 \log {\relax (2 )}^{2} - 960 \log {\relax (2 )}^{4} - 160 \log {\relax (2 )}^{5} + 480 \log {\relax (2 )}^{3} + 360 \log {\relax (2 )}\right ) + x \left (200 \log {\relax (2 )}^{2} + 960 \log {\relax (2 )}^{5}\right ) + 400 \log {\relax (2 )}^{4}}{x^{4} - 12 x^{3} + 36 x^{2}} + \frac {\left (x^{4} - 6 x^{3} + 8 x^{3} \log {\relax (2 )}^{2} - 48 x^{2} \log {\relax (2 )}^{2} + 16 x^{2} \log {\relax (2 )}^{4} - 96 x \log {\relax (2 )}^{4}\right ) e^{2 x} + \left (2 x^{5} - 12 x^{4} - 2 x^{4} \log {\relax (2 )} + 16 x^{4} \log {\relax (2 )}^{2} - 96 x^{3} \log {\relax (2 )}^{2} - 16 x^{3} \log {\relax (2 )}^{3} + 32 x^{3} \log {\relax (2 )}^{4} + 12 x^{3} \log {\relax (2 )} - 192 x^{2} \log {\relax (2 )}^{4} - 32 x^{2} \log {\relax (2 )}^{5} + 10 x^{2} + 96 x^{2} \log {\relax (2 )}^{3} + 192 x \log {\relax (2 )}^{5} + 80 x \log {\relax (2 )}^{2} + 160 \log {\relax (2 )}^{4}\right ) e^{x}}{x^{2} - 6 x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*(2*x**4-24*x**3+72*x**2)*ln(2)**2+2*x**5-24*x**4+72*x**3)*ln(2/exp(5/(x**2-6*x)))**2+((16*(-2*x*
*4+24*x**3-72*x**2)*ln(2)**4+4*(-4*x**5+44*x**4-96*x**3-144*x**2)*ln(2)**2-2*x**6+20*x**5-24*x**4-144*x**3)*ex
p(x)+16*(-2*x**4+24*x**3-72*x**2+20*x-60)*ln(2)**4+4*(-8*x**5+96*x**4-288*x**3+40*x**2-120*x)*ln(2)**2-6*x**6+
72*x**5-216*x**4+20*x**3-60*x**2)*ln(2/exp(5/(x**2-6*x)))+(16*(2*x**4-24*x**3+72*x**2)*ln(2)**4+4*(4*x**5-46*x
**4+120*x**3+72*x**2)*ln(2)**2+2*x**6-22*x**5+48*x**4+72*x**3)*exp(x)**2+(16*(2*x**5-22*x**4+48*x**3+72*x**2-2
0*x+60)*ln(2)**4+4*(4*x**6-40*x**5+48*x**4+288*x**3-40*x**2+120*x)*ln(2)**2+2*x**7-18*x**6+216*x**4-20*x**3+60
*x**2)*exp(x)+16*(2*x**5-24*x**4+72*x**3-20*x**2+60*x)*ln(2)**4+4*(6*x**6-72*x**5+216*x**4-40*x**3+120*x**2)*l
n(2)**2+4*x**7-48*x**6+144*x**5-20*x**4+60*x**3)/(x**4-12*x**3+36*x**2),x)

[Out]

x**4 + x**3*(-2*log(2) + 8*log(2)**2) + x**2*(-16*log(2)**3 + log(2)**2 + 16*log(2)**4) + x*(-32*log(2)**5 + 8
*log(2)**4 + 10) + (x**3*(-60*log(2) - 80*log(2)**3 + 160*log(2)**4 + 480*log(2)**2 + 360) + x**2*(-2135 - 288
0*log(2)**2 - 960*log(2)**4 - 160*log(2)**5 + 480*log(2)**3 + 360*log(2)) + x*(200*log(2)**2 + 960*log(2)**5)
+ 400*log(2)**4)/(x**4 - 12*x**3 + 36*x**2) + ((x**4 - 6*x**3 + 8*x**3*log(2)**2 - 48*x**2*log(2)**2 + 16*x**2
*log(2)**4 - 96*x*log(2)**4)*exp(2*x) + (2*x**5 - 12*x**4 - 2*x**4*log(2) + 16*x**4*log(2)**2 - 96*x**3*log(2)
**2 - 16*x**3*log(2)**3 + 32*x**3*log(2)**4 + 12*x**3*log(2) - 192*x**2*log(2)**4 - 32*x**2*log(2)**5 + 10*x**
2 + 96*x**2*log(2)**3 + 192*x*log(2)**5 + 80*x*log(2)**2 + 160*log(2)**4)*exp(x))/(x**2 - 6*x)

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