3.60.35 \(\int \frac {-19073486328125+6866455078125 x^2-1098632812500 x^4+102539062500 x^6-6152343750 x^8+246093750 x^{10}-6562500 x^{12}+112500 x^{14}-1125 x^{16}+5 x^{18}+e^{\frac {3}{610351562500-195312500000 x^2+27343750000 x^4-2187500000 x^6+109375000 x^8-3500000 x^{10}+70000 x^{12}-800 x^{14}+4 x^{16}}} (30517578125000-10986328125000 x^2+1757812500000 x^4-164062500000 x^6+9843750000 x^8-393750000 x^{10}[phone] x^{12}-180000 x^{14}+1800 x^{16}-8 x^{18})+e^{\frac {6}{610351562500-195312500000 x^2+27343750000 x^4-2187500000 x^6+109375000 x^8-3500000 x^{10}+70000 x^{12}-800 x^{14}+4 x^{16}}} (-15258789062500+5493164062404 x^2-878906250000 x^4+82031250000 x^6-4921875000 x^8+196875000 x^{10}-5250000 x^{12}+90000 x^{14}-900 x^{16}+4 x^{18})+(-30517578125000+10986328125000 x^2-1757812500000 x^4+164062500000 x^6-9843750000 x^8+393750000 x^{10}-10500000 x^{12}+180000 x^{14}-1800 x^{16}+8 x^{18}+e^{\frac {3}{610351562500-195312500000 x^2+27343750000 x^4-2187500000 x^6+109375000 x^8-3500000 x^{10}+70000 x^{12}-800 x^{14}+4 x^{16}}} (30517578125000-10986328124904 x^2+1757812500000 x^4-164062500000 x^6+9843750000 x^8-393750000 x^{10}[phone] x^{12}-180000 x^{14}+1800 x^{16}-8 x^{18})) \log (x)+(-15258789062500+5493164062500 x^2-878906250000 x^4+82031250000 x^6-4921875000 x^8+196875000 x^{10}-5250000 x^{12}+90000 x^{14}-900 x^{16}+4 x^{18}) \log ^2(x)}{-3814697265625+1373291015625 x^2-219726562500 x^4+20507812500 x^6-1230468750 x^8+49218750 x^{10}-1312500 x^{12}+22500 x^{14}-225 x^{16}+x^{18}} \, dx\)

Optimal. Leaf size=28 \[ x \left (5+4 \left (e^{\frac {3}{4 \left (25-x^2\right )^8}}-\log (x)\right )^2\right ) \]

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Rubi [F]  time = 180.00, 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*} \text {\$Aborted} \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-19073486328125 + 6866455078125*x^2 - 1098632812500*x^4 + 102539062500*x^6 - 6152343750*x^8 + 246093750*x
^10 - 6562500*x^12 + 112500*x^14 - 1125*x^16 + 5*x^18 + E^(3/(610351562500 - 195312500000*x^2 + 27343750000*x^
4 - 2187500000*x^6 + 109375000*x^8 - 3500000*x^10 + 70000*x^12 - 800*x^14 + 4*x^16))*(30517578125000 - 1098632
8125000*x^2 + 1757812500000*x^4 - 164062500000*x^6 + 9843750000*x^8 - 393750000*x^10 + 10500000*x^12 - 180000*
x^14 + 1800*x^16 - 8*x^18) + E^(6/(610351562500 - 195312500000*x^2 + 27343750000*x^4 - 2187500000*x^6 + 109375
000*x^8 - 3500000*x^10 + 70000*x^12 - 800*x^14 + 4*x^16))*(-15258789062500 + 5493164062404*x^2 - 878906250000*
x^4 + 82031250000*x^6 - 4921875000*x^8 + 196875000*x^10 - 5250000*x^12 + 90000*x^14 - 900*x^16 + 4*x^18) + (-3
0517578125000 + 10986328125000*x^2 - 1757812500000*x^4 + 164062500000*x^6 - 9843750000*x^8 + 393750000*x^10 -
10500000*x^12 + 180000*x^14 - 1800*x^16 + 8*x^18 + E^(3/(610351562500 - 195312500000*x^2 + 27343750000*x^4 - 2
187500000*x^6 + 109375000*x^8 - 3500000*x^10 + 70000*x^12 - 800*x^14 + 4*x^16))*(30517578125000 - 109863281249
04*x^2 + 1757812500000*x^4 - 164062500000*x^6 + 9843750000*x^8 - 393750000*x^10 + 10500000*x^12 - 180000*x^14
+ 1800*x^16 - 8*x^18))*Log[x] + (-15258789062500 + 5493164062500*x^2 - 878906250000*x^4 + 82031250000*x^6 - 49
21875000*x^8 + 196875000*x^10 - 5250000*x^12 + 90000*x^14 - 900*x^16 + 4*x^18)*Log[x]^2)/(-3814697265625 + 137
3291015625*x^2 - 219726562500*x^4 + 20507812500*x^6 - 1230468750*x^8 + 49218750*x^10 - 1312500*x^12 + 22500*x^
14 - 225*x^16 + x^18),x]

[Out]

$Aborted

Rubi steps

Aborted

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Mathematica [A]  time = 0.34, size = 42, normalized size = 1.50 \begin {gather*} x \left (5+4 e^{\frac {3}{2 \left (-25+x^2\right )^8}}-8 e^{\frac {3}{4 \left (-25+x^2\right )^8}} \log (x)+4 \log ^2(x)\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-19073486328125 + 6866455078125*x^2 - 1098632812500*x^4 + 102539062500*x^6 - 6152343750*x^8 + 24609
3750*x^10 - 6562500*x^12 + 112500*x^14 - 1125*x^16 + 5*x^18 + E^(3/(610351562500 - 195312500000*x^2 + 27343750
000*x^4 - 2187500000*x^6 + 109375000*x^8 - 3500000*x^10 + 70000*x^12 - 800*x^14 + 4*x^16))*(30517578125000 - 1
0986328125000*x^2 + 1757812500000*x^4 - 164062500000*x^6 + 9843750000*x^8 - 393750000*x^10 + 10500000*x^12 - 1
80000*x^14 + 1800*x^16 - 8*x^18) + E^(6/(610351562500 - 195312500000*x^2 + 27343750000*x^4 - 2187500000*x^6 +
109375000*x^8 - 3500000*x^10 + 70000*x^12 - 800*x^14 + 4*x^16))*(-15258789062500 + 5493164062404*x^2 - 8789062
50000*x^4 + 82031250000*x^6 - 4921875000*x^8 + 196875000*x^10 - 5250000*x^12 + 90000*x^14 - 900*x^16 + 4*x^18)
+ (-30517578125000 + 10986328125000*x^2 - 1757812500000*x^4 + 164062500000*x^6 - 9843750000*x^8 + 393750000*x
^10 - 10500000*x^12 + 180000*x^14 - 1800*x^16 + 8*x^18 + E^(3/(610351562500 - 195312500000*x^2 + 27343750000*x
^4 - 2187500000*x^6 + 109375000*x^8 - 3500000*x^10 + 70000*x^12 - 800*x^14 + 4*x^16))*(30517578125000 - 109863
28124904*x^2 + 1757812500000*x^4 - 164062500000*x^6 + 9843750000*x^8 - 393750000*x^10 + 10500000*x^12 - 180000
*x^14 + 1800*x^16 - 8*x^18))*Log[x] + (-15258789062500 + 5493164062500*x^2 - 878906250000*x^4 + 82031250000*x^
6 - 4921875000*x^8 + 196875000*x^10 - 5250000*x^12 + 90000*x^14 - 900*x^16 + 4*x^18)*Log[x]^2)/(-3814697265625
+ 1373291015625*x^2 - 219726562500*x^4 + 20507812500*x^6 - 1230468750*x^8 + 49218750*x^10 - 1312500*x^12 + 22
500*x^14 - 225*x^16 + x^18),x]

[Out]

x*(5 + 4*E^(3/(2*(-25 + x^2)^8)) - 8*E^(3/(4*(-25 + x^2)^8))*Log[x] + 4*Log[x]^2)

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fricas [B]  time = 0.75, size = 109, normalized size = 3.89 \begin {gather*} -8 \, x e^{\left (\frac {3}{4 \, {\left (x^{16} - 200 \, x^{14} + 17500 \, x^{12} - 875000 \, x^{10} + 27343750 \, x^{8} - 546875000 \, x^{6} + 6835937500 \, x^{4} - 48828125000 \, x^{2} + 152587890625\right )}}\right )} \log \relax (x) + 4 \, x \log \relax (x)^{2} + 4 \, x e^{\left (\frac {3}{2 \, {\left (x^{16} - 200 \, x^{14} + 17500 \, x^{12} - 875000 \, x^{10} + 27343750 \, x^{8} - 546875000 \, x^{6} + 6835937500 \, x^{4} - 48828125000 \, x^{2} + 152587890625\right )}}\right )} + 5 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x^18-900*x^16+90000*x^14-5250000*x^12+196875000*x^10-4921875000*x^8+82031250000*x^6-878906250000
*x^4+5493164062500*x^2-15258789062500)*log(x)^2+((-8*x^18+1800*x^16-180000*x^14+10500000*x^12-393750000*x^10+9
843750000*x^8-164062500000*x^6+1757812500000*x^4-10986328124904*x^2+30517578125000)*exp(3/(4*x^16-800*x^14+700
00*x^12-3500000*x^10+109375000*x^8-2187500000*x^6+27343750000*x^4-195312500000*x^2+610351562500))+8*x^18-1800*
x^16+180000*x^14-10500000*x^12+393750000*x^10-9843750000*x^8+164062500000*x^6-1757812500000*x^4+10986328125000
*x^2-30517578125000)*log(x)+(4*x^18-900*x^16+90000*x^14-5250000*x^12+196875000*x^10-4921875000*x^8+82031250000
*x^6-878906250000*x^4+5493164062404*x^2-15258789062500)*exp(3/(4*x^16-800*x^14+70000*x^12-3500000*x^10+1093750
00*x^8-2187500000*x^6+27343750000*x^4-195312500000*x^2+610351562500))^2+(-8*x^18+1800*x^16-180000*x^14+1050000
0*x^12-393750000*x^10+9843750000*x^8-164062500000*x^6+1757812500000*x^4-10986328125000*x^2+30517578125000)*exp
(3/(4*x^16-800*x^14+70000*x^12-3500000*x^10+109375000*x^8-2187500000*x^6+27343750000*x^4-195312500000*x^2+6103
51562500))+5*x^18-1125*x^16+112500*x^14-6562500*x^12+246093750*x^10-6152343750*x^8+102539062500*x^6-1098632812
500*x^4+6866455078125*x^2-19073486328125)/(x^18-225*x^16+22500*x^14-1312500*x^12+49218750*x^10-1230468750*x^8+
20507812500*x^6-219726562500*x^4+1373291015625*x^2-3814697265625),x, algorithm="fricas")

[Out]

-8*x*e^(3/4/(x^16 - 200*x^14 + 17500*x^12 - 875000*x^10 + 27343750*x^8 - 546875000*x^6 + 6835937500*x^4 - 4882
8125000*x^2 + 152587890625))*log(x) + 4*x*log(x)^2 + 4*x*e^(3/2/(x^16 - 200*x^14 + 17500*x^12 - 875000*x^10 +
27343750*x^8 - 546875000*x^6 + 6835937500*x^4 - 48828125000*x^2 + 152587890625)) + 5*x

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giac [B]  time = 2.09, size = 191, normalized size = 6.82 \begin {gather*} -8 \, x e^{\left (-\frac {3 \, {\left (x^{16} - 200 \, x^{14} + 17500 \, x^{12} - 875000 \, x^{10} + 27343750 \, x^{8} - 546875000 \, x^{6} + 6835937500 \, x^{4} - 48828125000 \, x^{2}\right )}}{610351562500 \, {\left (x^{16} - 200 \, x^{14} + 17500 \, x^{12} - 875000 \, x^{10} + 27343750 \, x^{8} - 546875000 \, x^{6} + 6835937500 \, x^{4} - 48828125000 \, x^{2} + 152587890625\right )}} + \frac {3}{610351562500}\right )} \log \relax (x) + 4 \, x \log \relax (x)^{2} + 4 \, x e^{\left (-\frac {3 \, {\left (x^{16} - 200 \, x^{14} + 17500 \, x^{12} - 875000 \, x^{10} + 27343750 \, x^{8} - 546875000 \, x^{6} + 6835937500 \, x^{4} - 48828125000 \, x^{2}\right )}}{305175781250 \, {\left (x^{16} - 200 \, x^{14} + 17500 \, x^{12} - 875000 \, x^{10} + 27343750 \, x^{8} - 546875000 \, x^{6} + 6835937500 \, x^{4} - 48828125000 \, x^{2} + 152587890625\right )}} + \frac {3}{305175781250}\right )} + 5 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x^18-900*x^16+90000*x^14-5250000*x^12+196875000*x^10-4921875000*x^8+82031250000*x^6-878906250000
*x^4+5493164062500*x^2-15258789062500)*log(x)^2+((-8*x^18+1800*x^16-180000*x^14+10500000*x^12-393750000*x^10+9
843750000*x^8-164062500000*x^6+1757812500000*x^4-10986328124904*x^2+30517578125000)*exp(3/(4*x^16-800*x^14+700
00*x^12-3500000*x^10+109375000*x^8-2187500000*x^6+27343750000*x^4-195312500000*x^2+610351562500))+8*x^18-1800*
x^16+180000*x^14-10500000*x^12+393750000*x^10-9843750000*x^8+164062500000*x^6-1757812500000*x^4+10986328125000
*x^2-30517578125000)*log(x)+(4*x^18-900*x^16+90000*x^14-5250000*x^12+196875000*x^10-4921875000*x^8+82031250000
*x^6-878906250000*x^4+5493164062404*x^2-15258789062500)*exp(3/(4*x^16-800*x^14+70000*x^12-3500000*x^10+1093750
00*x^8-2187500000*x^6+27343750000*x^4-195312500000*x^2+610351562500))^2+(-8*x^18+1800*x^16-180000*x^14+1050000
0*x^12-393750000*x^10+9843750000*x^8-164062500000*x^6+1757812500000*x^4-10986328125000*x^2+30517578125000)*exp
(3/(4*x^16-800*x^14+70000*x^12-3500000*x^10+109375000*x^8-2187500000*x^6+27343750000*x^4-195312500000*x^2+6103
51562500))+5*x^18-1125*x^16+112500*x^14-6562500*x^12+246093750*x^10-6152343750*x^8+102539062500*x^6-1098632812
500*x^4+6866455078125*x^2-19073486328125)/(x^18-225*x^16+22500*x^14-1312500*x^12+49218750*x^10-1230468750*x^8+
20507812500*x^6-219726562500*x^4+1373291015625*x^2-3814697265625),x, algorithm="giac")

[Out]

-8*x*e^(-3/610351562500*(x^16 - 200*x^14 + 17500*x^12 - 875000*x^10 + 27343750*x^8 - 546875000*x^6 + 683593750
0*x^4 - 48828125000*x^2)/(x^16 - 200*x^14 + 17500*x^12 - 875000*x^10 + 27343750*x^8 - 546875000*x^6 + 68359375
00*x^4 - 48828125000*x^2 + 152587890625) + 3/610351562500)*log(x) + 4*x*log(x)^2 + 4*x*e^(-3/305175781250*(x^1
6 - 200*x^14 + 17500*x^12 - 875000*x^10 + 27343750*x^8 - 546875000*x^6 + 6835937500*x^4 - 48828125000*x^2)/(x^
16 - 200*x^14 + 17500*x^12 - 875000*x^10 + 27343750*x^8 - 546875000*x^6 + 6835937500*x^4 - 48828125000*x^2 + 1
52587890625) + 3/305175781250) + 5*x

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maple [A]  time = 0.12, size = 46, normalized size = 1.64

method	result	size
risch	\(4 x \,{\mathrm e}^{\frac {3}{2 \left (x -5\right )^{8} \left (5+x \right )^{8}}}-8 x \,{\mathrm e}^{\frac {3}{4 \left (x -5\right )^{8} \left (5+x \right )^{8}}} \ln \relax (x )+4 x \ln \relax (x )^{2}+5 x\)	\(46\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((4*x^18-900*x^16+90000*x^14-5250000*x^12+196875000*x^10-4921875000*x^8+82031250000*x^6-878906250000*x^4+5
493164062500*x^2-15258789062500)*ln(x)^2+((-8*x^18+1800*x^16-180000*x^14+10500000*x^12-393750000*x^10+98437500
00*x^8-164062500000*x^6+1757812500000*x^4-10986328124904*x^2+30517578125000)*exp(3/(4*x^16-800*x^14+70000*x^12
-3500000*x^10+109375000*x^8-2187500000*x^6+27343750000*x^4-195312500000*x^2+610351562500))+8*x^18-1800*x^16+18
0000*x^14-10500000*x^12+393750000*x^10-9843750000*x^8+164062500000*x^6-1757812500000*x^4+10986328125000*x^2-30
517578125000)*ln(x)+(4*x^18-900*x^16+90000*x^14-5250000*x^12+196875000*x^10-4921875000*x^8+82031250000*x^6-878
906250000*x^4+5493164062404*x^2-15258789062500)*exp(3/(4*x^16-800*x^14+70000*x^12-3500000*x^10+109375000*x^8-2
187500000*x^6+27343750000*x^4-195312500000*x^2+610351562500))^2+(-8*x^18+1800*x^16-180000*x^14+10500000*x^12-3
93750000*x^10+9843750000*x^8-164062500000*x^6+1757812500000*x^4-10986328125000*x^2+30517578125000)*exp(3/(4*x^
16-800*x^14+70000*x^12-3500000*x^10+109375000*x^8-2187500000*x^6+27343750000*x^4-195312500000*x^2+610351562500
))+5*x^18-1125*x^16+112500*x^14-6562500*x^12+246093750*x^10-6152343750*x^8+102539062500*x^6-1098632812500*x^4+
6866455078125*x^2-19073486328125)/(x^18-225*x^16+22500*x^14-1312500*x^12+49218750*x^10-1230468750*x^8+20507812
500*x^6-219726562500*x^4+1373291015625*x^2-3814697265625),x,method=_RETURNVERBOSE)

[Out]

4*x*exp(3/2/(x-5)^8/(5+x)^8)-8*x*exp(3/4/(x-5)^8/(5+x)^8)*ln(x)+4*x*ln(x)^2+5*x

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maxima [B]  time = 11.46, size = 1730, normalized size = 61.79 result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x^18-900*x^16+90000*x^14-5250000*x^12+196875000*x^10-4921875000*x^8+82031250000*x^6-878906250000
*x^4+5493164062500*x^2-15258789062500)*log(x)^2+((-8*x^18+1800*x^16-180000*x^14+10500000*x^12-393750000*x^10+9
843750000*x^8-164062500000*x^6+1757812500000*x^4-10986328124904*x^2+30517578125000)*exp(3/(4*x^16-800*x^14+700
00*x^12-3500000*x^10+109375000*x^8-2187500000*x^6+27343750000*x^4-195312500000*x^2+610351562500))+8*x^18-1800*
x^16+180000*x^14-10500000*x^12+393750000*x^10-9843750000*x^8+164062500000*x^6-1757812500000*x^4+10986328125000
*x^2-30517578125000)*log(x)+(4*x^18-900*x^16+90000*x^14-5250000*x^12+196875000*x^10-4921875000*x^8+82031250000
*x^6-878906250000*x^4+5493164062404*x^2-15258789062500)*exp(3/(4*x^16-800*x^14+70000*x^12-3500000*x^10+1093750
00*x^8-2187500000*x^6+27343750000*x^4-195312500000*x^2+610351562500))^2+(-8*x^18+1800*x^16-180000*x^14+1050000
0*x^12-393750000*x^10+9843750000*x^8-164062500000*x^6+1757812500000*x^4-10986328125000*x^2+30517578125000)*exp
(3/(4*x^16-800*x^14+70000*x^12-3500000*x^10+109375000*x^8-2187500000*x^6+27343750000*x^4-195312500000*x^2+6103
51562500))+5*x^18-1125*x^16+112500*x^14-6562500*x^12+246093750*x^10-6152343750*x^8+102539062500*x^6-1098632812
500*x^4+6866455078125*x^2-19073486328125)/(x^18-225*x^16+22500*x^14-1312500*x^12+49218750*x^10-1230468750*x^8+
20507812500*x^6-219726562500*x^4+1373291015625*x^2-3814697265625),x, algorithm="maxima")

[Out]

4*(x*e^(3/250000000/(x^7 - 35*x^6 + 525*x^5 - 4375*x^4 + 21875*x^3 - 65625*x^2 + 109375*x - 78125) + 9/5000000
000/(x^5 - 25*x^4 + 250*x^3 - 1250*x^2 + 3125*x - 3125) + 297/2500000000000/(x^3 - 15*x^2 + 75*x - 125) + 1287
/250000000000000/(x - 5))*log(x)^2 - 2*x*e^(3/400000000/(x^8 + 40*x^7 + 700*x^6 + 7000*x^5 + 43750*x^4 + 17500
0*x^3 + 437500*x^2 + 625000*x + 390625) + 3/400000000/(x^8 - 40*x^7 + 700*x^6 - 7000*x^5 + 43750*x^4 - 175000*
x^3 + 437500*x^2 - 625000*x + 390625) + 3/500000000/(x^7 + 35*x^6 + 525*x^5 + 4375*x^4 + 21875*x^3 + 65625*x^2
+ 109375*x + 78125) + 3/500000000/(x^7 - 35*x^6 + 525*x^5 - 4375*x^4 + 21875*x^3 - 65625*x^2 + 109375*x - 781
25) + 27/10000000000/(x^6 + 30*x^5 + 375*x^4 + 2500*x^3 + 9375*x^2 + 18750*x + 15625) + 27/10000000000/(x^6 -
30*x^5 + 375*x^4 - 2500*x^3 + 9375*x^2 - 18750*x + 15625) + 9/10000000000/(x^5 + 25*x^4 + 250*x^3 + 1250*x^2 +
3125*x + 3125) + 9/10000000000/(x^5 - 25*x^4 + 250*x^3 - 1250*x^2 + 3125*x - 3125) + 99/400000000000/(x^4 + 2
0*x^3 + 150*x^2 + 500*x + 625) + 99/400000000000/(x^4 - 20*x^3 + 150*x^2 - 500*x + 625) + 297/5000000000000/(x
^3 + 15*x^2 + 75*x + 125) + 297/5000000000000/(x^3 - 15*x^2 + 75*x - 125) + 1287/100000000000000/(x^2 + 10*x +
25) + 1287/100000000000000/(x^2 - 10*x + 25) + 1287/500000000000000/(x + 5) + 1287/500000000000000/(x - 5))*l
og(x) + x*e^(3/200000000/(x^8 + 40*x^7 + 700*x^6 + 7000*x^5 + 43750*x^4 + 175000*x^3 + 437500*x^2 + 625000*x +
390625) + 3/200000000/(x^8 - 40*x^7 + 700*x^6 - 7000*x^5 + 43750*x^4 - 175000*x^3 + 437500*x^2 - 625000*x + 3
90625) + 3/250000000/(x^7 + 35*x^6 + 525*x^5 + 4375*x^4 + 21875*x^3 + 65625*x^2 + 109375*x + 78125) + 27/50000
00000/(x^6 + 30*x^5 + 375*x^4 + 2500*x^3 + 9375*x^2 + 18750*x + 15625) + 27/5000000000/(x^6 - 30*x^5 + 375*x^4
- 2500*x^3 + 9375*x^2 - 18750*x + 15625) + 9/5000000000/(x^5 + 25*x^4 + 250*x^3 + 1250*x^2 + 3125*x + 3125) +
99/200000000000/(x^4 + 20*x^3 + 150*x^2 + 500*x + 625) + 99/200000000000/(x^4 - 20*x^3 + 150*x^2 - 500*x + 62
5) + 297/2500000000000/(x^3 + 15*x^2 + 75*x + 125) + 1287/50000000000000/(x^2 + 10*x + 25) + 1287/500000000000
00/(x^2 - 10*x + 25) + 1287/250000000000000/(x + 5)))*e^(-3/250000000/(x^7 - 35*x^6 + 525*x^5 - 4375*x^4 + 218
75*x^3 - 65625*x^2 + 109375*x - 78125) - 9/5000000000/(x^5 - 25*x^4 + 250*x^3 - 1250*x^2 + 3125*x - 3125) - 29
7/2500000000000/(x^3 - 15*x^2 + 75*x - 125) - 1287/250000000000000/(x - 5)) + 5*x - 125/229376*(1298619*x^15 -
180089175*x^13 + 11434066875*x^11 - 417986859375*x^9 + 9377528515625*x^7 - 128222705078125*x^5 + 985316650390
625*x^3 - 3273858642578125*x)/(x^16 - 200*x^14 + 17500*x^12 - 875000*x^10 + 27343750*x^8 - 546875000*x^6 + 683
5937500*x^4 - 48828125000*x^2 + 152587890625) + 1125/229376*(184331*x^15 - 20038375*x^13 + 1144836875*x^11 - 3
9345109375*x^9 + 846772265625*x^7 - 11231923828125*x^5 + 84312744140625*x^3 - 274932861328125*x)/(x^16 - 200*x
^14 + 17500*x^12 - 875000*x^10 + 27343750*x^8 - 546875000*x^6 + 6835937500*x^4 - 48828125000*x^2 + 15258789062
5) - 375/57344*(9009*x^15 + 4007675*x^13 - 228967375*x^11 + 7869021875*x^9 - 169354453125*x^7 + 2246384765625*
x^5 - 16862548828125*x^3 + 54986572265625*x)/(x^16 - 200*x^14 + 17500*x^12 - 875000*x^10 + 27343750*x^8 - 5468
75000*x^6 + 6835937500*x^4 - 48828125000*x^2 + 152587890625) - 375/229376*(9009*x^15 - 1726725*x^13 + 14376862
5*x^11 - 6774178125*x^9 + 196725546875*x^7 - 3577615234375*x^5 + 39137451171875*x^3 + 54986572265625*x)/(x^16
- 200*x^14 + 17500*x^12 - 875000*x^10 + 27343750*x^8 - 546875000*x^6 + 6835937500*x^4 - 48828125000*x^2 + 1525
87890625) - 625/229376*(9009*x^15 - 1726725*x^13 + 143768625*x^11 - 6774178125*x^9 + 196725546875*x^7 - 357761
5234375*x^5 + 39137451171875*x^3 - 225013427734375*x)/(x^16 - 200*x^14 + 17500*x^12 - 875000*x^10 + 27343750*x
^8 - 546875000*x^6 + 6835937500*x^4 - 48828125000*x^2 + 152587890625) - 1125/57344*(693*x^15 - 132825*x^13 + 1
1059125*x^11 - 521090625*x^9 + 15132734375*x^7 - 275201171875*x^5 - 1297119140625*x^3 + 4229736328125*x)/(x^16
- 200*x^14 + 17500*x^12 - 875000*x^10 + 27343750*x^8 - 546875000*x^6 + 6835937500*x^4 - 48828125000*x^2 + 152
587890625) - 375/8192*(693*x^15 - 132825*x^13 - 17612875*x^11 + 605309375*x^9 - 13027265625*x^7 + 172798828125
*x^5 - 1297119140625*x^3 + 4229736328125*x)/(x^16 - 200*x^14 + 17500*x^12 - 875000*x^10 + 27343750*x^8 - 54687
5000*x^6 + 6835937500*x^4 - 48828125000*x^2 + 152587890625) - 5625/16384*(63*x^15 - 12075*x^13 + 1005375*x^11
+ 55028125*x^9 - 1184296875*x^7 + 15708984375*x^5 - 117919921875*x^3 + 384521484375*x)/(x^16 - 200*x^14 + 1750
0*x^12 - 875000*x^10 + 27343750*x^8 - 546875000*x^6 + 6835937500*x^4 - 48828125000*x^2 + 152587890625) - 1875/
8192*(63*x^15 - 12075*x^13 + 1005375*x^11 - 47371875*x^9 + 1375703125*x^7 + 15708984375*x^5 - 117919921875*x^3
+ 384521484375*x)/(x^16 - 200*x^14 + 17500*x^12 - 875000*x^10 + 27343750*x^8 - 546875000*x^6 + 6835937500*x^4
- 48828125000*x^2 + 152587890625) - 13125/16384*(21*x^15 - 4025*x^13 + 335125*x^11 - 15790625*x^9 - 394765625
*x^7 + 5236328125*x^5 - 39306640625*x^3 + 128173828125*x)/(x^16 - 200*x^14 + 17500*x^12 - 875000*x^10 + 273437
50*x^8 - 546875000*x^6 + 6835937500*x^4 - 48828125000*x^2 + 152587890625)

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mupad [F]  time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int \frac {{\mathrm {e}}^{\frac {6}{4\,x^{16}-800\,x^{14}+70000\,x^{12}-3500000\,x^{10}[phone]\,x^8-2187500000\,x^6+27343750000\,x^4-195312500000\,x^2+610351562500}}\,\left (4\,x^{18}-900\,x^{16}+90000\,x^{14}-5250000\,x^{12}[phone]\,x^{10}-4921875000\,x^8+82031250000\,x^6-878906250000\,x^4+5493164062404\,x^2-15258789062500\right )-\ln \relax (x)\,\left ({\mathrm {e}}^{\frac {3}{4\,x^{16}-800\,x^{14}+70000\,x^{12}-3500000\,x^{10}[phone]\,x^8-2187500000\,x^6+27343750000\,x^4-195312500000\,x^2+610351562500}}\,\left (8\,x^{18}-1800\,x^{16}+180000\,x^{14}-10500000\,x^{12}[phone]\,x^{10}-9843750000\,x^8+164062500000\,x^6-1757812500000\,x^4+10986328124904\,x^2-30517578125000\right )-10986328125000\,x^2+1757812500000\,x^4-164062500000\,x^6+9843750000\,x^8-393750000\,x^{10}[phone]\,x^{12}-180000\,x^{14}+1800\,x^{16}-8\,x^{18}[phone]\right )+{\ln \relax (x)}^2\,\left (4\,x^{18}-900\,x^{16}+90000\,x^{14}-5250000\,x^{12}[phone]\,x^{10}-4921875000\,x^8+82031250000\,x^6-878906250000\,x^4+5493164062500\,x^2-15258789062500\right )-{\mathrm {e}}^{\frac {3}{4\,x^{16}-800\,x^{14}+70000\,x^{12}-3500000\,x^{10}[phone]\,x^8-2187500000\,x^6+27343750000\,x^4-195312500000\,x^2+610351562500}}\,\left (8\,x^{18}-1800\,x^{16}+180000\,x^{14}-10500000\,x^{12}[phone]\,x^{10}-9843750000\,x^8+164062500000\,x^6-1757812500000\,x^4+10986328125000\,x^2-30517578125000\right )[phone]\,x^2-1098632812500\,x^4+102539062500\,x^6-6152343750\,x^8+246093750\,x^{10}-6562500\,x^{12}+112500\,x^{14}-1125\,x^{16}+5\,x^{18}-19073486328125}{x^{18}-225\,x^{16}+22500\,x^{14}-1312500\,x^{12}[phone]\,x^{10}-1230468750\,x^8+20507812500\,x^6-219726562500\,x^4+1373291015625\,x^2-3814697265625} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(6/(27343750000*x^4 - 195312500000*x^2 - 2187500000*x^6 + 109375000*x^8 - 3500000*x^10 + 70000*x^12 -
800*x^14 + 4*x^16 + 610351562500))*(5493164062404*x^2 - 878906250000*x^4 + 82031250000*x^6 - 4921875000*x^8 +
196875000*x^10 - 5250000*x^12 + 90000*x^14 - 900*x^16 + 4*x^18 - 15258789062500) - log(x)*(exp(3/(27343750000*
x^4 - 195312500000*x^2 - 2187500000*x^6 + 109375000*x^8 - 3500000*x^10 + 70000*x^12 - 800*x^14 + 4*x^16 + 6103
51562500))*(10986328124904*x^2 - 1757812500000*x^4 + 164062500000*x^6 - 9843750000*x^8 + 393750000*x^10 - 1050
0000*x^12 + 180000*x^14 - 1800*x^16 + 8*x^18 - 30517578125000) - 10986328125000*x^2 + 1757812500000*x^4 - 1640
62500000*x^6 + 9843750000*x^8 - 393750000*x^10 + 10500000*x^12 - 180000*x^14 + 1800*x^16 - 8*x^18 + 3051757812
5000) + log(x)^2*(5493164062500*x^2 - 878906250000*x^4 + 82031250000*x^6 - 4921875000*x^8 + 196875000*x^10 - 5
250000*x^12 + 90000*x^14 - 900*x^16 + 4*x^18 - 15258789062500) - exp(3/(27343750000*x^4 - 195312500000*x^2 - 2
187500000*x^6 + 109375000*x^8 - 3500000*x^10 + 70000*x^12 - 800*x^14 + 4*x^16 + 610351562500))*(10986328125000
*x^2 - 1757812500000*x^4 + 164062500000*x^6 - 9843750000*x^8 + 393750000*x^10 - 10500000*x^12 + 180000*x^14 -
1800*x^16 + 8*x^18 - 30517578125000) + 6866455078125*x^2 - 1098632812500*x^4 + 102539062500*x^6 - 6152343750*x
^8 + 246093750*x^10 - 6562500*x^12 + 112500*x^14 - 1125*x^16 + 5*x^18 - 19073486328125)/(1373291015625*x^2 - 2
19726562500*x^4 + 20507812500*x^6 - 1230468750*x^8 + 49218750*x^10 - 1312500*x^12 + 22500*x^14 - 225*x^16 + x^
18 - 3814697265625),x)

[Out]

int((exp(6/(27343750000*x^4 - 195312500000*x^2 - 2187500000*x^6 + 109375000*x^8 - 3500000*x^10 + 70000*x^12 -
800*x^14 + 4*x^16 + 610351562500))*(5493164062404*x^2 - 878906250000*x^4 + 82031250000*x^6 - 4921875000*x^8 +
196875000*x^10 - 5250000*x^12 + 90000*x^14 - 900*x^16 + 4*x^18 - 15258789062500) - log(x)*(exp(3/(27343750000*
x^4 - 195312500000*x^2 - 2187500000*x^6 + 109375000*x^8 - 3500000*x^10 + 70000*x^12 - 800*x^14 + 4*x^16 + 6103
51562500))*(10986328124904*x^2 - 1757812500000*x^4 + 164062500000*x^6 - 9843750000*x^8 + 393750000*x^10 - 1050
0000*x^12 + 180000*x^14 - 1800*x^16 + 8*x^18 - 30517578125000) - 10986328125000*x^2 + 1757812500000*x^4 - 1640
62500000*x^6 + 9843750000*x^8 - 393750000*x^10 + 10500000*x^12 - 180000*x^14 + 1800*x^16 - 8*x^18 + 3051757812
5000) + log(x)^2*(5493164062500*x^2 - 878906250000*x^4 + 82031250000*x^6 - 4921875000*x^8 + 196875000*x^10 - 5
250000*x^12 + 90000*x^14 - 900*x^16 + 4*x^18 - 15258789062500) - exp(3/(27343750000*x^4 - 195312500000*x^2 - 2
187500000*x^6 + 109375000*x^8 - 3500000*x^10 + 70000*x^12 - 800*x^14 + 4*x^16 + 610351562500))*(10986328125000
*x^2 - 1757812500000*x^4 + 164062500000*x^6 - 9843750000*x^8 + 393750000*x^10 - 10500000*x^12 + 180000*x^14 -
1800*x^16 + 8*x^18 - 30517578125000) + 6866455078125*x^2 - 1098632812500*x^4 + 102539062500*x^6 - 6152343750*x
^8 + 246093750*x^10 - 6562500*x^12 + 112500*x^14 - 1125*x^16 + 5*x^18 - 19073486328125)/(1373291015625*x^2 - 2
19726562500*x^4 + 20507812500*x^6 - 1230468750*x^8 + 49218750*x^10 - 1312500*x^12 + 22500*x^14 - 225*x^16 + x^
18 - 3814697265625), 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(((4*x**18-900*x**16+90000*x**14-5250000*x**12+196875000*x**10-4921875000*x**8+82031250000*x**6-87890
6250000*x**4+5493164062500*x**2-15258789062500)*ln(x)**2+((-8*x**18+1800*x**16-180000*x**14+10500000*x**12-393
750000*x**10+9843750000*x**8-164062500000*x**6+1757812500000*x**4-10986328124904*x**2+30517578125000)*exp(3/(4
*x**16-800*x**14+70000*x**12-3500000*x**10+109375000*x**8-2187500000*x**6+27343750000*x**4-195312500000*x**2+6
10351562500))+8*x**18-1800*x**16+180000*x**14-10500000*x**12+393750000*x**10-9843750000*x**8+164062500000*x**6
-1757812500000*x**4+10986328125000*x**2-30517578125000)*ln(x)+(4*x**18-900*x**16+90000*x**14-5250000*x**12+196
875000*x**10-4921875000*x**8+82031250000*x**6-878906250000*x**4+5493164062404*x**2-15258789062500)*exp(3/(4*x*
*16-800*x**14+70000*x**12-3500000*x**10+109375000*x**8-2187500000*x**6+27343750000*x**4-195312500000*x**2+6103
51562500))**2+(-8*x**18+1800*x**16-180000*x**14+10500000*x**12-393750000*x**10+9843750000*x**8-164062500000*x*
*6+1757812500000*x**4-10986328125000*x**2+30517578125000)*exp(3/(4*x**16-800*x**14+70000*x**12-3500000*x**10+1
09375000*x**8-2187500000*x**6+27343750000*x**4-195312500000*x**2+610351562500))+5*x**18-1125*x**16+112500*x**1
4-6562500*x**12+246093750*x**10-6152343750*x**8+102539062500*x**6-1098632812500*x**4+6866455078125*x**2-190734
86328125)/(x**18-225*x**16+22500*x**14-1312500*x**12+49218750*x**10-1230468750*x**8+20507812500*x**6-219726562
500*x**4+1373291015625*x**2-3814697265625),x)

[Out]

Timed out

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