3.10.71 \(\int \frac {48 x^2-28 x^3+4 x^4+(96 x^2+104 x^3-40 x^4) \log (x)+e^{2 e^{x/2}} (63700992-249495552 x+452984832 x^2-505331712 x^3+386967552 x^4-215183872 x^5+89609472 x^6-28389312 x^7+6876012 x^8-1267047 x^9+174861 x^{10}-17526 x^{11}+1206 x^{12}-51 x^{13}+x^{14}+e^{x/2} (63700992 x-249495552 x^2+452984832 x^3-505331712 x^4+386967552 x^5-215183872 x^6+89609472 x^7-28389312 x^8+6876012 x^9-1267047 x^{10}+174861 x^{11}-17526 x^{12}+1206 x^{13}-51 x^{14}+x^{15}) \log (x))+e^{e^{x/2}} (110592 x-248832 x^2+244224 x^3-136576 x^4+47600 x^5-10588 x^6+1468 x^7-116 x^8+4 x^9+(110592 x-64512 x^2-118272 x^3+168064 x^4-94224 x^5+28916 x^6-5116 x^7+492 x^8-20 x^9+e^{x/2} (55296 x^2-124416 x^3+122112 x^4-68288 x^5+23800 x^6-5294 x^7+734 x^8-58 x^9+2 x^{10})) \log (x))}{63700992 x-249495552 x^2+452984832 x^3-505331712 x^4+386967552 x^5-215183872 x^6+89609472 x^7-28389312 x^8+6876012 x^9-1267047 x^{10}+174861 x^{11}-17526 x^{12}+1206 x^{13}-51 x^{14}+x^{15}} \, dx\)

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

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Rubi [F]  time = 50.53, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {48 x^2-28 x^3+4 x^4+\left (96 x^2+104 x^3-40 x^4\right ) \log (x)+e^{2 e^{x/2}} \left (63700992-249495552 x+452984832 x^2-505331712 x^3+386967552 x^4-215183872 x^5+89609472 x^6-28389312 x^7+6876012 x^8-1267047 x^9+174861 x^{10}-17526 x^{11}+1206 x^{12}-51 x^{13}+x^{14}+e^{x/2} \left (63700992 x-249495552 x^2+452984832 x^3-505331712 x^4+386967552 x^5-215183872 x^6+89609472 x^7-28389312 x^8+6876012 x^9-1267047 x^{10}+174861 x^{11}-17526 x^{12}+1206 x^{13}-51 x^{14}+x^{15}\right ) \log (x)\right )+e^{e^{x/2}} \left (110592 x-248832 x^2+244224 x^3-136576 x^4+47600 x^5-10588 x^6+1468 x^7-116 x^8+4 x^9+\left (110592 x-64512 x^2-118272 x^3+168064 x^4-94224 x^5+28916 x^6-5116 x^7+492 x^8-20 x^9+e^{x/2} \left (55296 x^2-124416 x^3+122112 x^4-68288 x^5+23800 x^6-5294 x^7+734 x^8-58 x^9+2 x^{10}\right )\right ) \log (x)\right )}{63700992 x-249495552 x^2+452984832 x^3-505331712 x^4+386967552 x^5-215183872 x^6+89609472 x^7-28389312 x^8+6876012 x^9-1267047 x^{10}+174861 x^{11}-17526 x^{12}+1206 x^{13}-51 x^{14}+x^{15}} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(48*x^2 - 28*x^3 + 4*x^4 + (96*x^2 + 104*x^3 - 40*x^4)*Log[x] + E^(2*E^(x/2))*(63700992 - 249495552*x + 45
2984832*x^2 - 505331712*x^3 + 386967552*x^4 - 215183872*x^5 + 89609472*x^6 - 28389312*x^7 + 6876012*x^8 - 1267
047*x^9 + 174861*x^10 - 17526*x^11 + 1206*x^12 - 51*x^13 + x^14 + E^(x/2)*(63700992*x - 249495552*x^2 + 452984
832*x^3 - 505331712*x^4 + 386967552*x^5 - 215183872*x^6 + 89609472*x^7 - 28389312*x^8 + 6876012*x^9 - 1267047*
x^10 + 174861*x^11 - 17526*x^12 + 1206*x^13 - 51*x^14 + x^15)*Log[x]) + E^E^(x/2)*(110592*x - 248832*x^2 + 244
224*x^3 - 136576*x^4 + 47600*x^5 - 10588*x^6 + 1468*x^7 - 116*x^8 + 4*x^9 + (110592*x - 64512*x^2 - 118272*x^3
+ 168064*x^4 - 94224*x^5 + 28916*x^6 - 5116*x^7 + 492*x^8 - 20*x^9 + E^(x/2)*(55296*x^2 - 124416*x^3 + 122112
*x^4 - 68288*x^5 + 23800*x^6 - 5294*x^7 + 734*x^8 - 58*x^9 + 2*x^10))*Log[x]))/(63700992*x - 249495552*x^2 + 4
52984832*x^3 - 505331712*x^4 + 386967552*x^5 - 215183872*x^6 + 89609472*x^7 - 28389312*x^8 + 6876012*x^9 - 126
7047*x^10 + 174861*x^11 - 17526*x^12 + 1206*x^13 - 51*x^14 + x^15),x]

[Out]

(-1304*Log[x])/3 + E^(2*E^(x/2))*Log[x] + (36*Log[x])/(3 - x)^4 - (312*Log[x])/(3 - x)^3 + (1492*Log[x])/(3 -
x)^2 + (64*Log[x])/(4 - x)^8 + (224*Log[x])/(4 - x)^7 + (516*Log[x])/(4 - x)^6 + (976*Log[x])/(4 - x)^5 + (164
0*Log[x])/(4 - x)^4 + (2544*Log[x])/(4 - x)^3 + (3724*Log[x])/(4 - x)^2 - (5216*x*Log[x])/(3*(3 - x)) + (1304*
x*Log[x])/(4 - x) - 64*Log[x]*Defer[Int][E^E^(x/2)/(-4 + x)^5, x] + 4*Defer[Int][E^E^(x/2)/(-4 + x)^4, x] + 84
*Log[x]*Defer[Int][E^E^(x/2)/(-4 + x)^4, x] + 8*Log[x]*Defer[Int][E^((2*E^(x/2) + x)/2)/(-4 + x)^4, x] - 8*Def
er[Int][E^E^(x/2)/(-4 + x)^3, x] - 80*Log[x]*Defer[Int][E^E^(x/2)/(-4 + x)^3, x] - 14*Log[x]*Defer[Int][E^((2*
E^(x/2) + x)/2)/(-4 + x)^3, x] + 12*Defer[Int][E^E^(x/2)/(-4 + x)^2, x] + 52*Log[x]*Defer[Int][E^E^(x/2)/(-4 +
x)^2, x] + 20*Log[x]*Defer[Int][E^((2*E^(x/2) + x)/2)/(-4 + x)^2, x] - 16*Defer[Int][E^E^(x/2)/(-4 + x), x] -
26*Log[x]*Defer[Int][E^((2*E^(x/2) + x)/2)/(-4 + x), x] - 24*Log[x]*Defer[Int][E^E^(x/2)/(-3 + x)^3, x] + 4*D
efer[Int][E^E^(x/2)/(-3 + x)^2, x] - 52*Log[x]*Defer[Int][E^E^(x/2)/(-3 + x)^2, x] + 6*Log[x]*Defer[Int][E^((2
*E^(x/2) + x)/2)/(-3 + x)^2, x] + 16*Defer[Int][E^E^(x/2)/(-3 + x), x] + 26*Log[x]*Defer[Int][E^((2*E^(x/2) +
x)/2)/(-3 + x), x] + 64*Defer[Int][Defer[Int][E^E^(x/2)/(-4 + x)^5, x]/x, x] - 84*Defer[Int][Defer[Int][E^E^(x
/2)/(-4 + x)^4, x]/x, x] - 8*Defer[Int][Defer[Int][E^((2*E^(x/2) + x)/2)/(-4 + x)^4, x]/x, x] + 80*Defer[Int][
Defer[Int][E^E^(x/2)/(-4 + x)^3, x]/x, x] + 14*Defer[Int][Defer[Int][E^((2*E^(x/2) + x)/2)/(-4 + x)^3, x]/x, x
] - 52*Defer[Int][Defer[Int][E^E^(x/2)/(-4 + x)^2, x]/x, x] - 20*Defer[Int][Defer[Int][E^((2*E^(x/2) + x)/2)/(
-4 + x)^2, x]/x, x] + 26*Defer[Int][Defer[Int][E^((2*E^(x/2) + x)/2)/(-4 + x), x]/x, x] + 24*Defer[Int][Defer[
Int][E^E^(x/2)/(-3 + x)^3, x]/x, x] + 52*Defer[Int][Defer[Int][E^E^(x/2)/(-3 + x)^2, x]/x, x] - 6*Defer[Int][D
efer[Int][E^((2*E^(x/2) + x)/2)/(-3 + x)^2, x]/x, x] - 26*Defer[Int][Defer[Int][E^((2*E^(x/2) + x)/2)/(-3 + x)
, x]/x, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {\left (e^{e^{x/2}} (-4+x)^4 (-3+x)^2+2 x\right ) \left (\left (e^{e^{x/2}} (-4+x)^4 (-3+x)^2+2 x\right ) \left (12-7 x+x^2\right )+x \left (48+e^{e^{x/2}+\frac {x}{2}} (-4+x)^5 (-3+x)^3+52 x-20 x^2\right ) \log (x)\right )}{(3-x)^5 (4-x)^9 x} \, dx\\ &=\int \left (\frac {\left (2304 e^{e^{x/2}}+2 x-3840 e^{e^{x/2}} x+2656 e^{e^{x/2}} x^2-976 e^{e^{x/2}} x^3+201 e^{e^{x/2}} x^4-22 e^{e^{x/2}} x^5+e^{e^{x/2}} x^6\right )^2}{(-4+x)^8 (-3+x)^4 x}+\frac {e^{\frac {1}{2} \left (2 e^{x/2}+x\right )} \left (2304 e^{e^{x/2}}+2 x-3840 e^{e^{x/2}} x+2656 e^{e^{x/2}} x^2-976 e^{e^{x/2}} x^3+201 e^{e^{x/2}} x^4-22 e^{e^{x/2}} x^5+e^{e^{x/2}} x^6\right ) \log (x)}{(3-x)^2 (4-x)^4}+\frac {48 \left (2304 e^{e^{x/2}}+2 x-3840 e^{e^{x/2}} x+2656 e^{e^{x/2}} x^2-976 e^{e^{x/2}} x^3+201 e^{e^{x/2}} x^4-22 e^{e^{x/2}} x^5+e^{e^{x/2}} x^6\right ) \log (x)}{(-4+x)^9 (-3+x)^5}+\frac {52 x \left (2304 e^{e^{x/2}}+2 x-3840 e^{e^{x/2}} x+2656 e^{e^{x/2}} x^2-976 e^{e^{x/2}} x^3+201 e^{e^{x/2}} x^4-22 e^{e^{x/2}} x^5+e^{e^{x/2}} x^6\right ) \log (x)}{(-4+x)^9 (-3+x)^5}-\frac {20 x^2 \left (2304 e^{e^{x/2}}+2 x-3840 e^{e^{x/2}} x+2656 e^{e^{x/2}} x^2-976 e^{e^{x/2}} x^3+201 e^{e^{x/2}} x^4-22 e^{e^{x/2}} x^5+e^{e^{x/2}} x^6\right ) \log (x)}{(-4+x)^9 (-3+x)^5}\right ) \, dx\\ &=-\left (20 \int \frac {x^2 \left (2304 e^{e^{x/2}}+2 x-3840 e^{e^{x/2}} x+2656 e^{e^{x/2}} x^2-976 e^{e^{x/2}} x^3+201 e^{e^{x/2}} x^4-22 e^{e^{x/2}} x^5+e^{e^{x/2}} x^6\right ) \log (x)}{(-4+x)^9 (-3+x)^5} \, dx\right )+48 \int \frac {\left (2304 e^{e^{x/2}}+2 x-3840 e^{e^{x/2}} x+2656 e^{e^{x/2}} x^2-976 e^{e^{x/2}} x^3+201 e^{e^{x/2}} x^4-22 e^{e^{x/2}} x^5+e^{e^{x/2}} x^6\right ) \log (x)}{(-4+x)^9 (-3+x)^5} \, dx+52 \int \frac {x \left (2304 e^{e^{x/2}}+2 x-3840 e^{e^{x/2}} x+2656 e^{e^{x/2}} x^2-976 e^{e^{x/2}} x^3+201 e^{e^{x/2}} x^4-22 e^{e^{x/2}} x^5+e^{e^{x/2}} x^6\right ) \log (x)}{(-4+x)^9 (-3+x)^5} \, dx+\int \frac {\left (2304 e^{e^{x/2}}+2 x-3840 e^{e^{x/2}} x+2656 e^{e^{x/2}} x^2-976 e^{e^{x/2}} x^3+201 e^{e^{x/2}} x^4-22 e^{e^{x/2}} x^5+e^{e^{x/2}} x^6\right )^2}{(-4+x)^8 (-3+x)^4 x} \, dx+\int \frac {e^{\frac {1}{2} \left (2 e^{x/2}+x\right )} \left (2304 e^{e^{x/2}}+2 x-3840 e^{e^{x/2}} x+2656 e^{e^{x/2}} x^2-976 e^{e^{x/2}} x^3+201 e^{e^{x/2}} x^4-22 e^{e^{x/2}} x^5+e^{e^{x/2}} x^6\right ) \log (x)}{(3-x)^2 (4-x)^4} \, dx\\ &=e^{2 e^{x/2}} \log (x)-20 \int \frac {x^2 \left (e^{e^{x/2}} (-4+x)^4 (-3+x)^2+2 x\right ) \log (x)}{(3-x)^5 (4-x)^9} \, dx+48 \int \frac {\left (e^{e^{x/2}} (-4+x)^4 (-3+x)^2+2 x\right ) \log (x)}{(3-x)^5 (4-x)^9} \, dx+52 \int \frac {x \left (e^{e^{x/2}} (-4+x)^4 (-3+x)^2+2 x\right ) \log (x)}{(3-x)^5 (4-x)^9} \, dx+(6 \log (x)) \int \frac {e^{\frac {1}{2} \left (2 e^{x/2}+x\right )}}{(-3+x)^2} \, dx+(8 \log (x)) \int \frac {e^{\frac {1}{2} \left (2 e^{x/2}+x\right )}}{(-4+x)^4} \, dx-(14 \log (x)) \int \frac {e^{\frac {1}{2} \left (2 e^{x/2}+x\right )}}{(-4+x)^3} \, dx+(20 \log (x)) \int \frac {e^{\frac {1}{2} \left (2 e^{x/2}+x\right )}}{(-4+x)^2} \, dx-(26 \log (x)) \int \frac {e^{\frac {1}{2} \left (2 e^{x/2}+x\right )}}{-4+x} \, dx+(26 \log (x)) \int \frac {e^{\frac {1}{2} \left (2 e^{x/2}+x\right )}}{-3+x} \, dx+\int \frac {\left (e^{e^{x/2}} (-4+x)^4 (-3+x)^2+2 x\right )^2}{(3-x)^4 (4-x)^8 x} \, dx-\int \frac {e^{2 e^{x/2}}+8 \int \frac {e^{e^{x/2}+\frac {x}{2}}}{(-4+x)^4} \, dx-14 \int \frac {e^{e^{x/2}+\frac {x}{2}}}{(-4+x)^3} \, dx+20 \int \frac {e^{e^{x/2}+\frac {x}{2}}}{(-4+x)^2} \, dx-26 \int \frac {e^{e^{x/2}+\frac {x}{2}}}{-4+x} \, dx+6 \int \frac {e^{e^{x/2}+\frac {x}{2}}}{(-3+x)^2} \, dx+26 \int \frac {e^{e^{x/2}+\frac {x}{2}}}{-3+x} \, dx}{x} \, dx\\ &=e^{2 e^{x/2}} \log (x)-20 \int \left (\frac {e^{e^{x/2}} x^2 \log (x)}{(-4+x)^5 (-3+x)^3}+\frac {2 x^3 \log (x)}{(-4+x)^9 (-3+x)^5}\right ) \, dx+48 \int \left (\frac {e^{e^{x/2}} \log (x)}{(-4+x)^5 (-3+x)^3}+\frac {2 x \log (x)}{(-4+x)^9 (-3+x)^5}\right ) \, dx+52 \int \left (\frac {e^{e^{x/2}} x \log (x)}{(-4+x)^5 (-3+x)^3}+\frac {2 x^2 \log (x)}{(-4+x)^9 (-3+x)^5}\right ) \, dx+(6 \log (x)) \int \frac {e^{\frac {1}{2} \left (2 e^{x/2}+x\right )}}{(-3+x)^2} \, dx+(8 \log (x)) \int \frac {e^{\frac {1}{2} \left (2 e^{x/2}+x\right )}}{(-4+x)^4} \, dx-(14 \log (x)) \int \frac {e^{\frac {1}{2} \left (2 e^{x/2}+x\right )}}{(-4+x)^3} \, dx+(20 \log (x)) \int \frac {e^{\frac {1}{2} \left (2 e^{x/2}+x\right )}}{(-4+x)^2} \, dx-(26 \log (x)) \int \frac {e^{\frac {1}{2} \left (2 e^{x/2}+x\right )}}{-4+x} \, dx+(26 \log (x)) \int \frac {e^{\frac {1}{2} \left (2 e^{x/2}+x\right )}}{-3+x} \, dx+\int \left (\frac {4 e^{e^{x/2}}}{(-4+x)^4 (-3+x)^2}+\frac {e^{2 e^{x/2}}}{x}+\frac {4 x}{(-4+x)^8 (-3+x)^4}\right ) \, dx-\int \left (\frac {e^{2 e^{x/2}}}{x}+\frac {2 \left (4 \int \frac {e^{e^{x/2}+\frac {x}{2}}}{(-4+x)^4} \, dx-7 \int \frac {e^{e^{x/2}+\frac {x}{2}}}{(-4+x)^3} \, dx+10 \int \frac {e^{e^{x/2}+\frac {x}{2}}}{(-4+x)^2} \, dx-13 \int \frac {e^{e^{x/2}+\frac {x}{2}}}{-4+x} \, dx+3 \int \frac {e^{e^{x/2}+\frac {x}{2}}}{(-3+x)^2} \, dx+13 \int \frac {e^{e^{x/2}+\frac {x}{2}}}{-3+x} \, dx\right )}{x}\right ) \, dx\\ &=e^{2 e^{x/2}} \log (x)-2 \int \frac {3 \int \frac {e^{\frac {1}{2} \left (2 e^{x/2}+x\right )}}{(3-x)^2} \, dx+4 \int \frac {e^{\frac {1}{2} \left (2 e^{x/2}+x\right )}}{(4-x)^4} \, dx+10 \int \frac {e^{\frac {1}{2} \left (2 e^{x/2}+x\right )}}{(4-x)^2} \, dx-7 \int \frac {e^{\frac {1}{2} \left (2 e^{x/2}+x\right )}}{(-4+x)^3} \, dx-13 \int \frac {e^{\frac {1}{2} \left (2 e^{x/2}+x\right )}}{-4+x} \, dx+13 \int \frac {e^{\frac {1}{2} \left (2 e^{x/2}+x\right )}}{-3+x} \, dx}{x} \, dx+4 \int \frac {e^{e^{x/2}}}{(-4+x)^4 (-3+x)^2} \, dx+4 \int \frac {x}{(-4+x)^8 (-3+x)^4} \, dx-20 \int \frac {e^{e^{x/2}} x^2 \log (x)}{(-4+x)^5 (-3+x)^3} \, dx-40 \int \frac {x^3 \log (x)}{(-4+x)^9 (-3+x)^5} \, dx+48 \int \frac {e^{e^{x/2}} \log (x)}{(-4+x)^5 (-3+x)^3} \, dx+52 \int \frac {e^{e^{x/2}} x \log (x)}{(-4+x)^5 (-3+x)^3} \, dx+96 \int \frac {x \log (x)}{(-4+x)^9 (-3+x)^5} \, dx+104 \int \frac {x^2 \log (x)}{(-4+x)^9 (-3+x)^5} \, dx+(6 \log (x)) \int \frac {e^{\frac {1}{2} \left (2 e^{x/2}+x\right )}}{(-3+x)^2} \, dx+(8 \log (x)) \int \frac {e^{\frac {1}{2} \left (2 e^{x/2}+x\right )}}{(-4+x)^4} \, dx-(14 \log (x)) \int \frac {e^{\frac {1}{2} \left (2 e^{x/2}+x\right )}}{(-4+x)^3} \, dx+(20 \log (x)) \int \frac {e^{\frac {1}{2} \left (2 e^{x/2}+x\right )}}{(-4+x)^2} \, dx-(26 \log (x)) \int \frac {e^{\frac {1}{2} \left (2 e^{x/2}+x\right )}}{-4+x} \, dx+(26 \log (x)) \int \frac {e^{\frac {1}{2} \left (2 e^{x/2}+x\right )}}{-3+x} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.27, size = 39, normalized size = 1.22 \begin {gather*} \frac {\left (e^{e^{x/2}} (-4+x)^4 (-3+x)^2+2 x\right )^2 \log (x)}{(-4+x)^8 (-3+x)^4} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(48*x^2 - 28*x^3 + 4*x^4 + (96*x^2 + 104*x^3 - 40*x^4)*Log[x] + E^(2*E^(x/2))*(63700992 - 249495552*
x + 452984832*x^2 - 505331712*x^3 + 386967552*x^4 - 215183872*x^5 + 89609472*x^6 - 28389312*x^7 + 6876012*x^8
- 1267047*x^9 + 174861*x^10 - 17526*x^11 + 1206*x^12 - 51*x^13 + x^14 + E^(x/2)*(63700992*x - 249495552*x^2 +
452984832*x^3 - 505331712*x^4 + 386967552*x^5 - 215183872*x^6 + 89609472*x^7 - 28389312*x^8 + 6876012*x^9 - 12
67047*x^10 + 174861*x^11 - 17526*x^12 + 1206*x^13 - 51*x^14 + x^15)*Log[x]) + E^E^(x/2)*(110592*x - 248832*x^2
+ 244224*x^3 - 136576*x^4 + 47600*x^5 - 10588*x^6 + 1468*x^7 - 116*x^8 + 4*x^9 + (110592*x - 64512*x^2 - 1182
72*x^3 + 168064*x^4 - 94224*x^5 + 28916*x^6 - 5116*x^7 + 492*x^8 - 20*x^9 + E^(x/2)*(55296*x^2 - 124416*x^3 +
122112*x^4 - 68288*x^5 + 23800*x^6 - 5294*x^7 + 734*x^8 - 58*x^9 + 2*x^10))*Log[x]))/(63700992*x - 249495552*x
^2 + 452984832*x^3 - 505331712*x^4 + 386967552*x^5 - 215183872*x^6 + 89609472*x^7 - 28389312*x^8 + 6876012*x^9
- 1267047*x^10 + 174861*x^11 - 17526*x^12 + 1206*x^13 - 51*x^14 + x^15),x]

[Out]

((E^E^(x/2)*(-4 + x)^4*(-3 + x)^2 + 2*x)^2*Log[x])/((-4 + x)^8*(-3 + x)^4)

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fricas [B]  time = 0.66, size = 178, normalized size = 5.56 \begin {gather*} \frac {4 \, x^{2} \log \relax (x) + {\left (x^{12} - 44 \, x^{11} + 886 \, x^{10} - 10796 \, x^{9} + 88657 \, x^{8} - 516896 \, x^{7} + 2193856 \, x^{6} - 6829568 \, x^{5} + 15476224 \, x^{4} - 24895488 \, x^{3} + 26984448 \, x^{2} - 17694720 \, x + 5308416\right )} e^{\left (2 \, e^{\left (\frac {1}{2} \, x\right )}\right )} \log \relax (x) + 4 \, {\left (x^{7} - 22 \, x^{6} + 201 \, x^{5} - 976 \, x^{4} + 2656 \, x^{3} - 3840 \, x^{2} + 2304 \, x\right )} e^{\left (e^{\left (\frac {1}{2} \, x\right )}\right )} \log \relax (x)}{x^{12} - 44 \, x^{11} + 886 \, x^{10} - 10796 \, x^{9} + 88657 \, x^{8} - 516896 \, x^{7} + 2193856 \, x^{6} - 6829568 \, x^{5} + 15476224 \, x^{4} - 24895488 \, x^{3} + 26984448 \, x^{2} - 17694720 \, x + 5308416} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((x^15-51*x^14+1206*x^13-17526*x^12+174861*x^11-1267047*x^10+6876012*x^9-28389312*x^8+89609472*x^7-
215183872*x^6+386967552*x^5-505331712*x^4+452984832*x^3-249495552*x^2+63700992*x)*exp(1/2*x)*log(x)+x^14-51*x^
13+1206*x^12-17526*x^11+174861*x^10-1267047*x^9+6876012*x^8-28389312*x^7+89609472*x^6-215183872*x^5+386967552*
x^4-505331712*x^3+452984832*x^2-249495552*x+63700992)*exp(exp(1/2*x))^2+(((2*x^10-58*x^9+734*x^8-5294*x^7+2380
0*x^6-68288*x^5+122112*x^4-124416*x^3+55296*x^2)*exp(1/2*x)-20*x^9+492*x^8-5116*x^7+28916*x^6-94224*x^5+168064
*x^4-118272*x^3-64512*x^2+110592*x)*log(x)+4*x^9-116*x^8+1468*x^7-10588*x^6+47600*x^5-136576*x^4+244224*x^3-24
8832*x^2+110592*x)*exp(exp(1/2*x))+(-40*x^4+104*x^3+96*x^2)*log(x)+4*x^4-28*x^3+48*x^2)/(x^15-51*x^14+1206*x^1
3-17526*x^12+174861*x^11-1267047*x^10+6876012*x^9-28389312*x^8+89609472*x^7-215183872*x^6+386967552*x^5-505331
712*x^4+452984832*x^3-249495552*x^2+63700992*x),x, algorithm="fricas")

[Out]

(4*x^2*log(x) + (x^12 - 44*x^11 + 886*x^10 - 10796*x^9 + 88657*x^8 - 516896*x^7 + 2193856*x^6 - 6829568*x^5 +
15476224*x^4 - 24895488*x^3 + 26984448*x^2 - 17694720*x + 5308416)*e^(2*e^(1/2*x))*log(x) + 4*(x^7 - 22*x^6 +
201*x^5 - 976*x^4 + 2656*x^3 - 3840*x^2 + 2304*x)*e^(e^(1/2*x))*log(x))/(x^12 - 44*x^11 + 886*x^10 - 10796*x^9
+ 88657*x^8 - 516896*x^7 + 2193856*x^6 - 6829568*x^5 + 15476224*x^4 - 24895488*x^3 + 26984448*x^2 - 17694720*
x + 5308416)

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {4 \, x^{4} - 28 \, x^{3} + 48 \, x^{2} + {\left (x^{14} - 51 \, x^{13} + 1206 \, x^{12} - 17526 \, x^{11} + 174861 \, x^{10} - 1267047 \, x^{9} + 6876012 \, x^{8} - 28389312 \, x^{7} + 89609472 \, x^{6} - 215183872 \, x^{5} + 386967552 \, x^{4} - 505331712 \, x^{3} + {\left (x^{15} - 51 \, x^{14} + 1206 \, x^{13} - 17526 \, x^{12} + 174861 \, x^{11} - 1267047 \, x^{10} + 6876012 \, x^{9} - 28389312 \, x^{8} + 89609472 \, x^{7} - 215183872 \, x^{6} + 386967552 \, x^{5} - 505331712 \, x^{4} + 452984832 \, x^{3} - 249495552 \, x^{2} + 63700992 \, x\right )} e^{\left (\frac {1}{2} \, x\right )} \log \relax (x) + 452984832 \, x^{2} - 249495552 \, x + 63700992\right )} e^{\left (2 \, e^{\left (\frac {1}{2} \, x\right )}\right )} + 2 \, {\left (2 \, x^{9} - 58 \, x^{8} + 734 \, x^{7} - 5294 \, x^{6} + 23800 \, x^{5} - 68288 \, x^{4} + 122112 \, x^{3} - 124416 \, x^{2} - {\left (10 \, x^{9} - 246 \, x^{8} + 2558 \, x^{7} - 14458 \, x^{6} + 47112 \, x^{5} - 84032 \, x^{4} + 59136 \, x^{3} + 32256 \, x^{2} - {\left (x^{10} - 29 \, x^{9} + 367 \, x^{8} - 2647 \, x^{7} + 11900 \, x^{6} - 34144 \, x^{5} + 61056 \, x^{4} - 62208 \, x^{3} + 27648 \, x^{2}\right )} e^{\left (\frac {1}{2} \, x\right )} - 55296 \, x\right )} \log \relax (x) + 55296 \, x\right )} e^{\left (e^{\left (\frac {1}{2} \, x\right )}\right )} - 8 \, {\left (5 \, x^{4} - 13 \, x^{3} - 12 \, x^{2}\right )} \log \relax (x)}{x^{15} - 51 \, x^{14} + 1206 \, x^{13} - 17526 \, x^{12} + 174861 \, x^{11} - 1267047 \, x^{10} + 6876012 \, x^{9} - 28389312 \, x^{8} + 89609472 \, x^{7} - 215183872 \, x^{6} + 386967552 \, x^{5} - 505331712 \, x^{4} + 452984832 \, x^{3} - 249495552 \, x^{2} + 63700992 \, x}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((x^15-51*x^14+1206*x^13-17526*x^12+174861*x^11-1267047*x^10+6876012*x^9-28389312*x^8+89609472*x^7-
215183872*x^6+386967552*x^5-505331712*x^4+452984832*x^3-249495552*x^2+63700992*x)*exp(1/2*x)*log(x)+x^14-51*x^
13+1206*x^12-17526*x^11+174861*x^10-1267047*x^9+6876012*x^8-28389312*x^7+89609472*x^6-215183872*x^5+386967552*
x^4-505331712*x^3+452984832*x^2-249495552*x+63700992)*exp(exp(1/2*x))^2+(((2*x^10-58*x^9+734*x^8-5294*x^7+2380
0*x^6-68288*x^5+122112*x^4-124416*x^3+55296*x^2)*exp(1/2*x)-20*x^9+492*x^8-5116*x^7+28916*x^6-94224*x^5+168064
*x^4-118272*x^3-64512*x^2+110592*x)*log(x)+4*x^9-116*x^8+1468*x^7-10588*x^6+47600*x^5-136576*x^4+244224*x^3-24
8832*x^2+110592*x)*exp(exp(1/2*x))+(-40*x^4+104*x^3+96*x^2)*log(x)+4*x^4-28*x^3+48*x^2)/(x^15-51*x^14+1206*x^1
3-17526*x^12+174861*x^11-1267047*x^10+6876012*x^9-28389312*x^8+89609472*x^7-215183872*x^6+386967552*x^5-505331
712*x^4+452984832*x^3-249495552*x^2+63700992*x),x, algorithm="giac")

[Out]

integrate((4*x^4 - 28*x^3 + 48*x^2 + (x^14 - 51*x^13 + 1206*x^12 - 17526*x^11 + 174861*x^10 - 1267047*x^9 + 68
76012*x^8 - 28389312*x^7 + 89609472*x^6 - 215183872*x^5 + 386967552*x^4 - 505331712*x^3 + (x^15 - 51*x^14 + 12
06*x^13 - 17526*x^12 + 174861*x^11 - 1267047*x^10 + 6876012*x^9 - 28389312*x^8 + 89609472*x^7 - 215183872*x^6
+ 386967552*x^5 - 505331712*x^4 + 452984832*x^3 - 249495552*x^2 + 63700992*x)*e^(1/2*x)*log(x) + 452984832*x^2
- 249495552*x + 63700992)*e^(2*e^(1/2*x)) + 2*(2*x^9 - 58*x^8 + 734*x^7 - 5294*x^6 + 23800*x^5 - 68288*x^4 +
122112*x^3 - 124416*x^2 - (10*x^9 - 246*x^8 + 2558*x^7 - 14458*x^6 + 47112*x^5 - 84032*x^4 + 59136*x^3 + 32256
*x^2 - (x^10 - 29*x^9 + 367*x^8 - 2647*x^7 + 11900*x^6 - 34144*x^5 + 61056*x^4 - 62208*x^3 + 27648*x^2)*e^(1/2
*x) - 55296*x)*log(x) + 55296*x)*e^(e^(1/2*x)) - 8*(5*x^4 - 13*x^3 - 12*x^2)*log(x))/(x^15 - 51*x^14 + 1206*x^
13 - 17526*x^12 + 174861*x^11 - 1267047*x^10 + 6876012*x^9 - 28389312*x^8 + 89609472*x^7 - 215183872*x^6 + 386
967552*x^5 - 505331712*x^4 + 452984832*x^3 - 249495552*x^2 + 63700992*x), x)

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maple [B]  time = 0.07, size = 119, normalized size = 3.72

method	result	size
risch	\(\frac {4 x^{2} \ln \relax (x )}{x^{12}-44 x^{11}+886 x^{10}-10796 x^{9}+88657 x^{8}-516896 x^{7}+2193856 x^{6}-6829568 x^{5}[phone] x^{4}-24895488 x^{3}[phone] x^{2}-17694720 x +5308416}+\ln \relax (x ) {\mathrm e}^{2 \,{\mathrm e}^{\frac {x}{2}}}+\frac {4 x \ln \relax (x ) {\mathrm e}^{{\mathrm e}^{\frac {x}{2}}}}{x^{6}-22 x^{5}+201 x^{4}-976 x^{3}+2656 x^{2}-3840 x +2304}\)	\(119\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((x^15-51*x^14+1206*x^13-17526*x^12+174861*x^11-1267047*x^10+6876012*x^9-28389312*x^8+89609472*x^7-215183
872*x^6+386967552*x^5-505331712*x^4+452984832*x^3-249495552*x^2+63700992*x)*exp(1/2*x)*ln(x)+x^14-51*x^13+1206
*x^12-17526*x^11+174861*x^10-1267047*x^9+6876012*x^8-28389312*x^7+89609472*x^6-215183872*x^5+386967552*x^4-505
331712*x^3+452984832*x^2-249495552*x+63700992)*exp(exp(1/2*x))^2+(((2*x^10-58*x^9+734*x^8-5294*x^7+23800*x^6-6
8288*x^5+122112*x^4-124416*x^3+55296*x^2)*exp(1/2*x)-20*x^9+492*x^8-5116*x^7+28916*x^6-94224*x^5+168064*x^4-11
8272*x^3-64512*x^2+110592*x)*ln(x)+4*x^9-116*x^8+1468*x^7-10588*x^6+47600*x^5-136576*x^4+244224*x^3-248832*x^2
+110592*x)*exp(exp(1/2*x))+(-40*x^4+104*x^3+96*x^2)*ln(x)+4*x^4-28*x^3+48*x^2)/(x^15-51*x^14+1206*x^13-17526*x
^12+174861*x^11-1267047*x^10+6876012*x^9-28389312*x^8+89609472*x^7-215183872*x^6+386967552*x^5-505331712*x^4+4
52984832*x^3-249495552*x^2+63700992*x),x,method=_RETURNVERBOSE)

[Out]

4*x^2/(x^12-44*x^11+886*x^10-10796*x^9+88657*x^8-516896*x^7+2193856*x^6-6829568*x^5+15476224*x^4-24895488*x^3+
26984448*x^2-17694720*x+5308416)*ln(x)+ln(x)*exp(2*exp(1/2*x))+4*x/(x^6-22*x^5+201*x^4-976*x^3+2656*x^2-3840*x
+2304)*ln(x)*exp(exp(1/2*x))

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maxima [B]  time = 0.92, size = 586, normalized size = 18.31 \begin {gather*} \frac {2552760 \, x^{11} - 103386780 \, x^{10} + 1900104360 \, x^{9} - 20917102710 \, x^{8} + 153240991512 \, x^{7} - 784453702788 \, x^{6} + 2863076933592 \, x^{5} - 7449941242557 \, x^{4} + 13543600742564 \, x^{3} - 16382097148104 \, x^{2} + 11865447305280 \, x - 3898411992288}{35 \, {\left (x^{12} - 44 \, x^{11} + 886 \, x^{10} - 10796 \, x^{9} + 88657 \, x^{8} - 516896 \, x^{7} + 2193856 \, x^{6} - 6829568 \, x^{5} + 15476224 \, x^{4} - 24895488 \, x^{3} + 26984448 \, x^{2} - 17694720 \, x + 5308416\right )}} - \frac {153720 \, x^{11} - 6225660 \, x^{10} + 114418920 \, x^{9} - 1259568870 \, x^{8} + 9227739864 \, x^{7} - 47237587236 \, x^{6} + 172406409624 \, x^{5} - 448614428229 \, x^{4} + 815557399108 \, x^{3} - 986483638730 \, x^{2} + 714503737040 \, x - 234751363800}{x^{12} - 44 \, x^{11} + 886 \, x^{10} - 10796 \, x^{9} + 88657 \, x^{8} - 516896 \, x^{7} + 2193856 \, x^{6} - 6829568 \, x^{5} + 15476224 \, x^{4} - 24895488 \, x^{3} + 26984448 \, x^{2} - 17694720 \, x + 5308416} + \frac {4 \, {\left (138600 \, x^{11} - 5613300 \, x^{10} + 103164600 \, x^{9} - 1135676850 \, x^{8} + 8320093320 \, x^{7} - 42591267180 \, x^{6} + 155448402120 \, x^{5} - 404488418895 \, x^{4} + 735338638540 \, x^{3} - 889452461150 \, x^{2} + 644224680940 \, x - 211661065722\right )}}{7 \, {\left (x^{12} - 44 \, x^{11} + 886 \, x^{10} - 10796 \, x^{9} + 88657 \, x^{8} - 516896 \, x^{7} + 2193856 \, x^{6} - 6829568 \, x^{5} + 15476224 \, x^{4} - 24895488 \, x^{3} + 26984448 \, x^{2} - 17694720 \, x + 5308416\right )}} + \frac {55440 \, x^{11} - 2245320 \, x^{10} + 41265840 \, x^{9} - 454270740 \, x^{8} + 3328037328 \, x^{7} - 17036506872 \, x^{6} + 62179360848 \, x^{5} - 161795367558 \, x^{4} + 294135455416 \, x^{3} + 140 \, x^{2} \log \relax (x) + 35 \, {\left (x^{12} - 44 \, x^{11} + 886 \, x^{10} - 10796 \, x^{9} + 88657 \, x^{8} - 516896 \, x^{7} + 2193856 \, x^{6} - 6829568 \, x^{5} + 15476224 \, x^{4} - 24895488 \, x^{3} + 26984448 \, x^{2} - 17694720 \, x + 5308416\right )} e^{\left (2 \, e^{\left (\frac {1}{2} \, x\right )}\right )} \log \relax (x) + 140 \, {\left (x^{7} - 22 \, x^{6} + 201 \, x^{5} - 976 \, x^{4} + 2656 \, x^{3} - 3840 \, x^{2} + 2304 \, x\right )} e^{\left (e^{\left (\frac {1}{2} \, x\right )}\right )} \log \relax (x) - 355780984446 \, x^{2} + 257689872320 \, x - 84664426272}{35 \, {\left (x^{12} - 44 \, x^{11} + 886 \, x^{10} - 10796 \, x^{9} + 88657 \, x^{8} - 516896 \, x^{7} + 2193856 \, x^{6} - 6829568 \, x^{5} + 15476224 \, x^{4} - 24895488 \, x^{3} + 26984448 \, x^{2} - 17694720 \, x + 5308416\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((x^15-51*x^14+1206*x^13-17526*x^12+174861*x^11-1267047*x^10+6876012*x^9-28389312*x^8+89609472*x^7-
215183872*x^6+386967552*x^5-505331712*x^4+452984832*x^3-249495552*x^2+63700992*x)*exp(1/2*x)*log(x)+x^14-51*x^
13+1206*x^12-17526*x^11+174861*x^10-1267047*x^9+6876012*x^8-28389312*x^7+89609472*x^6-215183872*x^5+386967552*
x^4-505331712*x^3+452984832*x^2-249495552*x+63700992)*exp(exp(1/2*x))^2+(((2*x^10-58*x^9+734*x^8-5294*x^7+2380
0*x^6-68288*x^5+122112*x^4-124416*x^3+55296*x^2)*exp(1/2*x)-20*x^9+492*x^8-5116*x^7+28916*x^6-94224*x^5+168064
*x^4-118272*x^3-64512*x^2+110592*x)*log(x)+4*x^9-116*x^8+1468*x^7-10588*x^6+47600*x^5-136576*x^4+244224*x^3-24
8832*x^2+110592*x)*exp(exp(1/2*x))+(-40*x^4+104*x^3+96*x^2)*log(x)+4*x^4-28*x^3+48*x^2)/(x^15-51*x^14+1206*x^1
3-17526*x^12+174861*x^11-1267047*x^10+6876012*x^9-28389312*x^8+89609472*x^7-215183872*x^6+386967552*x^5-505331
712*x^4+452984832*x^3-249495552*x^2+63700992*x),x, algorithm="maxima")

[Out]

1/35*(2552760*x^11 - 103386780*x^10 + 1900104360*x^9 - 20917102710*x^8 + 153240991512*x^7 - 784453702788*x^6 +
2863076933592*x^5 - 7449941242557*x^4 + 13543600742564*x^3 - 16382097148104*x^2 + 11865447305280*x - 38984119
92288)/(x^12 - 44*x^11 + 886*x^10 - 10796*x^9 + 88657*x^8 - 516896*x^7 + 2193856*x^6 - 6829568*x^5 + 15476224*
x^4 - 24895488*x^3 + 26984448*x^2 - 17694720*x + 5308416) - (153720*x^11 - 6225660*x^10 + 114418920*x^9 - 1259
568870*x^8 + 9227739864*x^7 - 47237587236*x^6 + 172406409624*x^5 - 448614428229*x^4 + 815557399108*x^3 - 98648
3638730*x^2 + 714503737040*x - 234751363800)/(x^12 - 44*x^11 + 886*x^10 - 10796*x^9 + 88657*x^8 - 516896*x^7 +
2193856*x^6 - 6829568*x^5 + 15476224*x^4 - 24895488*x^3 + 26984448*x^2 - 17694720*x + 5308416) + 4/7*(138600*
x^11 - 5613300*x^10 + 103164600*x^9 - 1135676850*x^8 + 8320093320*x^7 - 42591267180*x^6 + 155448402120*x^5 - 4
04488418895*x^4 + 735338638540*x^3 - 889452461150*x^2 + 644224680940*x - 211661065722)/(x^12 - 44*x^11 + 886*x
^10 - 10796*x^9 + 88657*x^8 - 516896*x^7 + 2193856*x^6 - 6829568*x^5 + 15476224*x^4 - 24895488*x^3 + 26984448*
x^2 - 17694720*x + 5308416) + 1/35*(55440*x^11 - 2245320*x^10 + 41265840*x^9 - 454270740*x^8 + 3328037328*x^7
- 17036506872*x^6 + 62179360848*x^5 - 161795367558*x^4 + 294135455416*x^3 + 140*x^2*log(x) + 35*(x^12 - 44*x^1
1 + 886*x^10 - 10796*x^9 + 88657*x^8 - 516896*x^7 + 2193856*x^6 - 6829568*x^5 + 15476224*x^4 - 24895488*x^3 +
26984448*x^2 - 17694720*x + 5308416)*e^(2*e^(1/2*x))*log(x) + 140*(x^7 - 22*x^6 + 201*x^5 - 976*x^4 + 2656*x^3
- 3840*x^2 + 2304*x)*e^(e^(1/2*x))*log(x) - 355780984446*x^2 + 257689872320*x - 84664426272)/(x^12 - 44*x^11
+ 886*x^10 - 10796*x^9 + 88657*x^8 - 516896*x^7 + 2193856*x^6 - 6829568*x^5 + 15476224*x^4 - 24895488*x^3 + 26
984448*x^2 - 17694720*x + 5308416)

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mupad [B]  time = 1.33, size = 83, normalized size = 2.59 \begin {gather*} \frac {\ln \relax (x)\,{\left (2\,x+2304\,{\mathrm {e}}^{\sqrt {{\mathrm {e}}^x}}-3840\,x\,{\mathrm {e}}^{\sqrt {{\mathrm {e}}^x}}+2656\,x^2\,{\mathrm {e}}^{\sqrt {{\mathrm {e}}^x}}-976\,x^3\,{\mathrm {e}}^{\sqrt {{\mathrm {e}}^x}}+201\,x^4\,{\mathrm {e}}^{\sqrt {{\mathrm {e}}^x}}-22\,x^5\,{\mathrm {e}}^{\sqrt {{\mathrm {e}}^x}}+x^6\,{\mathrm {e}}^{\sqrt {{\mathrm {e}}^x}}\right )}^2}{{\left (x-3\right )}^4\,{\left (x-4\right )}^8} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(exp(x/2))*(110592*x + log(x)*(110592*x - 64512*x^2 - 118272*x^3 + 168064*x^4 - 94224*x^5 + 28916*x^6
- 5116*x^7 + 492*x^8 - 20*x^9 + exp(x/2)*(55296*x^2 - 124416*x^3 + 122112*x^4 - 68288*x^5 + 23800*x^6 - 5294*x
^7 + 734*x^8 - 58*x^9 + 2*x^10)) - 248832*x^2 + 244224*x^3 - 136576*x^4 + 47600*x^5 - 10588*x^6 + 1468*x^7 - 1
16*x^8 + 4*x^9) + log(x)*(96*x^2 + 104*x^3 - 40*x^4) + exp(2*exp(x/2))*(452984832*x^2 - 249495552*x - 50533171
2*x^3 + 386967552*x^4 - 215183872*x^5 + 89609472*x^6 - 28389312*x^7 + 6876012*x^8 - 1267047*x^9 + 174861*x^10
- 17526*x^11 + 1206*x^12 - 51*x^13 + x^14 + exp(x/2)*log(x)*(63700992*x - 249495552*x^2 + 452984832*x^3 - 5053
31712*x^4 + 386967552*x^5 - 215183872*x^6 + 89609472*x^7 - 28389312*x^8 + 6876012*x^9 - 1267047*x^10 + 174861*
x^11 - 17526*x^12 + 1206*x^13 - 51*x^14 + x^15) + 63700992) + 48*x^2 - 28*x^3 + 4*x^4)/(63700992*x - 249495552
*x^2 + 452984832*x^3 - 505331712*x^4 + 386967552*x^5 - 215183872*x^6 + 89609472*x^7 - 28389312*x^8 + 6876012*x
^9 - 1267047*x^10 + 174861*x^11 - 17526*x^12 + 1206*x^13 - 51*x^14 + x^15),x)

[Out]

(log(x)*(2*x + 2304*exp(exp(x)^(1/2)) - 3840*x*exp(exp(x)^(1/2)) + 2656*x^2*exp(exp(x)^(1/2)) - 976*x^3*exp(ex
p(x)^(1/2)) + 201*x^4*exp(exp(x)^(1/2)) - 22*x^5*exp(exp(x)^(1/2)) + x^6*exp(exp(x)^(1/2)))^2)/((x - 3)^4*(x -
4)^8)

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sympy [B]  time = 1.03, size = 170, normalized size = 5.31 \begin {gather*} \frac {4 x^{2} \log {\relax (x )}}{x^{12} - 44 x^{11} + 886 x^{10} - 10796 x^{9} + 88657 x^{8} - 516896 x^{7} + 2193856 x^{6} - 6829568 x^{5} + 15476224 x^{4} - 24895488 x^{3} + 26984448 x^{2} - 17694720 x + 5308416} + \frac {4 x e^{e^{\frac {x}{2}}} \log {\relax (x )} + \left (x^{6} \log {\relax (x )} - 22 x^{5} \log {\relax (x )} + 201 x^{4} \log {\relax (x )} - 976 x^{3} \log {\relax (x )} + 2656 x^{2} \log {\relax (x )} - 3840 x \log {\relax (x )} + 2304 \log {\relax (x )}\right ) e^{2 e^{\frac {x}{2}}}}{x^{6} - 22 x^{5} + 201 x^{4} - 976 x^{3} + 2656 x^{2} - 3840 x + 2304} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((x**15-51*x**14+1206*x**13-17526*x**12+174861*x**11-1267047*x**10+6876012*x**9-28389312*x**8+89609
472*x**7-215183872*x**6+386967552*x**5-505331712*x**4+452984832*x**3-249495552*x**2+63700992*x)*exp(1/2*x)*ln(
x)+x**14-51*x**13+1206*x**12-17526*x**11+174861*x**10-1267047*x**9+6876012*x**8-28389312*x**7+89609472*x**6-21
5183872*x**5+386967552*x**4-505331712*x**3+452984832*x**2-249495552*x+63700992)*exp(exp(1/2*x))**2+(((2*x**10-
58*x**9+734*x**8-5294*x**7+23800*x**6-68288*x**5+122112*x**4-124416*x**3+55296*x**2)*exp(1/2*x)-20*x**9+492*x*
*8-5116*x**7+28916*x**6-94224*x**5+168064*x**4-118272*x**3-64512*x**2+110592*x)*ln(x)+4*x**9-116*x**8+1468*x**
7-10588*x**6+47600*x**5-136576*x**4+244224*x**3-248832*x**2+110592*x)*exp(exp(1/2*x))+(-40*x**4+104*x**3+96*x*
*2)*ln(x)+4*x**4-28*x**3+48*x**2)/(x**15-51*x**14+1206*x**13-17526*x**12+174861*x**11-1267047*x**10+6876012*x*
*9-28389312*x**8+89609472*x**7-215183872*x**6+386967552*x**5-505331712*x**4+452984832*x**3-249495552*x**2+6370
0992*x),x)

[Out]

4*x**2*log(x)/(x**12 - 44*x**11 + 886*x**10 - 10796*x**9 + 88657*x**8 - 516896*x**7 + 2193856*x**6 - 6829568*x
**5 + 15476224*x**4 - 24895488*x**3 + 26984448*x**2 - 17694720*x + 5308416) + (4*x*exp(exp(x/2))*log(x) + (x**
6*log(x) - 22*x**5*log(x) + 201*x**4*log(x) - 976*x**3*log(x) + 2656*x**2*log(x) - 3840*x*log(x) + 2304*log(x)
)*exp(2*exp(x/2)))/(x**6 - 22*x**5 + 201*x**4 - 976*x**3 + 2656*x**2 - 3840*x + 2304)

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