3.18.31 \(\int \frac {e^{\frac {5 (12+3 x)}{3+x}} (90 x+60 x^2+10 x^3)+e^{\frac {4 (12+3 x)}{3+x}} (-108 x^3-186 x^4-84 x^5-10 x^6)+e^{\frac {4 (12+3 x)}{3+x}} (-144 x^2-168 x^3-64 x^4-8 x^5) \log (x)+e^{\frac {4 (12+3 x)}{3+x}} (-36 x^2-102 x^3-52 x^4-6 x^5) \log ^2(x)}{288 x^{10}+912 x^{11}+1232 x^{12}+920 x^{13}+410 x^{14}+109 x^{15}+16 x^{16}+x^{17}+e^{\frac {5 (12+3 x)}{3+x}} (28125+18750 x+3125 x^2)+e^{\frac {4 (12+3 x)}{3+x}} (56250 x^2+65625 x^3+25000 x^4+3125 x^5)+e^{\frac {3 (12+3 x)}{3+x}} (45000 x^4+75000 x^5+46250 x^6+12500 x^7+1250 x^8)+e^{\frac {2 (12+3 x)}{3+x}} (18000 x^6+39000 x^7+33500 x^8+14250 x^9+3000 x^{10}+250 x^{11})+e^{\frac {12+3 x}{3+x}} (3600 x^8+9600 x^9+10600 x^{10}+6200 x^{11}+2025 x^{12}+350 x^{13}+25 x^{14})+(1440 x^9+4560 x^{10}+6160 x^{11}+4600 x^{12}+2050 x^{13}+545 x^{14}+80 x^{15}+5 x^{16}+e^{\frac {4 (12+3 x)}{3+x}} (56250 x+65625 x^2+25000 x^3+3125 x^4)+e^{\frac {3 (12+3 x)}{3+x}} (90000 x^3+150000 x^4+92500 x^5+25000 x^6+2500 x^7)+e^{\frac {2 (12+3 x)}{3+x}} (54000 x^5+117000 x^6+100500 x^7+42750 x^8+9000 x^9+750 x^{10})+e^{\frac {12+3 x}{3+x}} (14400 x^7+38400 x^8+42400 x^9+24800 x^{10}+8100 x^{11}+1400 x^{12}+100 x^{13})) \log ^2(x)+(2880 x^8+9120 x^9+12320 x^{10}+9200 x^{11}+4100 x^{12}+1090 x^{13}+160 x^{14}+10 x^{15}+e^{\frac {3 (12+3 x)}{3+x}} (45000 x^2+75000 x^3+46250 x^4+12500 x^5+1250 x^6)+e^{\frac {2 (12+3 x)}{3+x}} (54000 x^4+117000 x^5+100500 x^6+42750 x^7+9000 x^8+750 x^9)+e^{\frac {12+3 x}{3+x}} (21600 x^6+57600 x^7+63600 x^8+37200 x^9+12150 x^{10}+2100 x^{11}+150 x^{12})) \log ^4(x)+(2880 x^7+9120 x^8+12320 x^9+9200 x^{10}+4100 x^{11}+1090 x^{12}+160 x^{13}+10 x^{14}+e^{\frac {2 (12+3 x)}{3+x}} (18000 x^3+39000 x^4+33500 x^5+14250 x^6+3000 x^7+250 x^8)+e^{\frac {12+3 x}{3+x}} (14400 x^5+38400 x^6+42400 x^7+24800 x^8+8100 x^9+1400 x^{10}+100 x^{11})) \log ^6(x)+(1440 x^6+4560 x^7+6160 x^8+4600 x^9+2050 x^{10}+545 x^{11}+80 x^{12}+5 x^{13}+e^{\frac {12+3 x}{3+x}} (3600 x^4+9600 x^5+10600 x^6+6200 x^7+2025 x^8+350 x^9+25 x^{10})) \log ^8(x)+(288 x^5+912 x^6+1232 x^7+920 x^8+410 x^9+109 x^{10}+16 x^{11}+x^{12}) \log ^{10}(x)} \, dx\)

Optimal. Leaf size=30 \[ \frac {x^2}{\left (5+e^{-3-\frac {3}{3+x}} x (2+x) \left (x+\log ^2(x)\right )\right )^4} \]

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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[(E^((5*(12 + 3*x))/(3 + x))*(90*x + 60*x^2 + 10*x^3) + E^((4*(12 + 3*x))/(3 + x))*(-108*x^3 - 186*x^4 - 84
*x^5 - 10*x^6) + E^((4*(12 + 3*x))/(3 + x))*(-144*x^2 - 168*x^3 - 64*x^4 - 8*x^5)*Log[x] + E^((4*(12 + 3*x))/(
3 + x))*(-36*x^2 - 102*x^3 - 52*x^4 - 6*x^5)*Log[x]^2)/(288*x^10 + 912*x^11 + 1232*x^12 + 920*x^13 + 410*x^14
+ 109*x^15 + 16*x^16 + x^17 + E^((5*(12 + 3*x))/(3 + x))*(28125 + 18750*x + 3125*x^2) + E^((4*(12 + 3*x))/(3 +
x))*(56250*x^2 + 65625*x^3 + 25000*x^4 + 3125*x^5) + E^((3*(12 + 3*x))/(3 + x))*(45000*x^4 + 75000*x^5 + 4625
0*x^6 + 12500*x^7 + 1250*x^8) + E^((2*(12 + 3*x))/(3 + x))*(18000*x^6 + 39000*x^7 + 33500*x^8 + 14250*x^9 + 30
00*x^10 + 250*x^11) + E^((12 + 3*x)/(3 + x))*(3600*x^8 + 9600*x^9 + 10600*x^10 + 6200*x^11 + 2025*x^12 + 350*x
^13 + 25*x^14) + (1440*x^9 + 4560*x^10 + 6160*x^11 + 4600*x^12 + 2050*x^13 + 545*x^14 + 80*x^15 + 5*x^16 + E^(
(4*(12 + 3*x))/(3 + x))*(56250*x + 65625*x^2 + 25000*x^3 + 3125*x^4) + E^((3*(12 + 3*x))/(3 + x))*(90000*x^3 +
150000*x^4 + 92500*x^5 + 25000*x^6 + 2500*x^7) + E^((2*(12 + 3*x))/(3 + x))*(54000*x^5 + 117000*x^6 + 100500*
x^7 + 42750*x^8 + 9000*x^9 + 750*x^10) + E^((12 + 3*x)/(3 + x))*(14400*x^7 + 38400*x^8 + 42400*x^9 + 24800*x^1
0 + 8100*x^11 + 1400*x^12 + 100*x^13))*Log[x]^2 + (2880*x^8 + 9120*x^9 + 12320*x^10 + 9200*x^11 + 4100*x^12 +
1090*x^13 + 160*x^14 + 10*x^15 + E^((3*(12 + 3*x))/(3 + x))*(45000*x^2 + 75000*x^3 + 46250*x^4 + 12500*x^5 + 1
250*x^6) + E^((2*(12 + 3*x))/(3 + x))*(54000*x^4 + 117000*x^5 + 100500*x^6 + 42750*x^7 + 9000*x^8 + 750*x^9) +
E^((12 + 3*x)/(3 + x))*(21600*x^6 + 57600*x^7 + 63600*x^8 + 37200*x^9 + 12150*x^10 + 2100*x^11 + 150*x^12))*L
og[x]^4 + (2880*x^7 + 9120*x^8 + 12320*x^9 + 9200*x^10 + 4100*x^11 + 1090*x^12 + 160*x^13 + 10*x^14 + E^((2*(1
2 + 3*x))/(3 + x))*(18000*x^3 + 39000*x^4 + 33500*x^5 + 14250*x^6 + 3000*x^7 + 250*x^8) + E^((12 + 3*x)/(3 + x
))*(14400*x^5 + 38400*x^6 + 42400*x^7 + 24800*x^8 + 8100*x^9 + 1400*x^10 + 100*x^11))*Log[x]^6 + (1440*x^6 + 4
560*x^7 + 6160*x^8 + 4600*x^9 + 2050*x^10 + 545*x^11 + 80*x^12 + 5*x^13 + E^((12 + 3*x)/(3 + x))*(3600*x^4 + 9
600*x^5 + 10600*x^6 + 6200*x^7 + 2025*x^8 + 350*x^9 + 25*x^10))*Log[x]^8 + (288*x^5 + 912*x^6 + 1232*x^7 + 920
*x^8 + 410*x^9 + 109*x^10 + 16*x^11 + x^12)*Log[x]^10),x]

[Out]

$Aborted

Rubi steps

Aborted

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Mathematica [A]  time = 0.35, size = 47, normalized size = 1.57 \begin {gather*} \frac {e^{12 \left (1+\frac {1}{3+x}\right )} x^2}{\left (5 e^{3+\frac {3}{3+x}}+x^2 (2+x)+x (2+x) \log ^2(x)\right )^4} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^((5*(12 + 3*x))/(3 + x))*(90*x + 60*x^2 + 10*x^3) + E^((4*(12 + 3*x))/(3 + x))*(-108*x^3 - 186*x^
4 - 84*x^5 - 10*x^6) + E^((4*(12 + 3*x))/(3 + x))*(-144*x^2 - 168*x^3 - 64*x^4 - 8*x^5)*Log[x] + E^((4*(12 + 3
*x))/(3 + x))*(-36*x^2 - 102*x^3 - 52*x^4 - 6*x^5)*Log[x]^2)/(288*x^10 + 912*x^11 + 1232*x^12 + 920*x^13 + 410
*x^14 + 109*x^15 + 16*x^16 + x^17 + E^((5*(12 + 3*x))/(3 + x))*(28125 + 18750*x + 3125*x^2) + E^((4*(12 + 3*x)
)/(3 + x))*(56250*x^2 + 65625*x^3 + 25000*x^4 + 3125*x^5) + E^((3*(12 + 3*x))/(3 + x))*(45000*x^4 + 75000*x^5
+ 46250*x^6 + 12500*x^7 + 1250*x^8) + E^((2*(12 + 3*x))/(3 + x))*(18000*x^6 + 39000*x^7 + 33500*x^8 + 14250*x^
9 + 3000*x^10 + 250*x^11) + E^((12 + 3*x)/(3 + x))*(3600*x^8 + 9600*x^9 + 10600*x^10 + 6200*x^11 + 2025*x^12 +
350*x^13 + 25*x^14) + (1440*x^9 + 4560*x^10 + 6160*x^11 + 4600*x^12 + 2050*x^13 + 545*x^14 + 80*x^15 + 5*x^16
+ E^((4*(12 + 3*x))/(3 + x))*(56250*x + 65625*x^2 + 25000*x^3 + 3125*x^4) + E^((3*(12 + 3*x))/(3 + x))*(90000
*x^3 + 150000*x^4 + 92500*x^5 + 25000*x^6 + 2500*x^7) + E^((2*(12 + 3*x))/(3 + x))*(54000*x^5 + 117000*x^6 + 1
00500*x^7 + 42750*x^8 + 9000*x^9 + 750*x^10) + E^((12 + 3*x)/(3 + x))*(14400*x^7 + 38400*x^8 + 42400*x^9 + 248
00*x^10 + 8100*x^11 + 1400*x^12 + 100*x^13))*Log[x]^2 + (2880*x^8 + 9120*x^9 + 12320*x^10 + 9200*x^11 + 4100*x
^12 + 1090*x^13 + 160*x^14 + 10*x^15 + E^((3*(12 + 3*x))/(3 + x))*(45000*x^2 + 75000*x^3 + 46250*x^4 + 12500*x
^5 + 1250*x^6) + E^((2*(12 + 3*x))/(3 + x))*(54000*x^4 + 117000*x^5 + 100500*x^6 + 42750*x^7 + 9000*x^8 + 750*
x^9) + E^((12 + 3*x)/(3 + x))*(21600*x^6 + 57600*x^7 + 63600*x^8 + 37200*x^9 + 12150*x^10 + 2100*x^11 + 150*x^
12))*Log[x]^4 + (2880*x^7 + 9120*x^8 + 12320*x^9 + 9200*x^10 + 4100*x^11 + 1090*x^12 + 160*x^13 + 10*x^14 + E^
((2*(12 + 3*x))/(3 + x))*(18000*x^3 + 39000*x^4 + 33500*x^5 + 14250*x^6 + 3000*x^7 + 250*x^8) + E^((12 + 3*x)/
(3 + x))*(14400*x^5 + 38400*x^6 + 42400*x^7 + 24800*x^8 + 8100*x^9 + 1400*x^10 + 100*x^11))*Log[x]^6 + (1440*x
^6 + 4560*x^7 + 6160*x^8 + 4600*x^9 + 2050*x^10 + 545*x^11 + 80*x^12 + 5*x^13 + E^((12 + 3*x)/(3 + x))*(3600*x
^4 + 9600*x^5 + 10600*x^6 + 6200*x^7 + 2025*x^8 + 350*x^9 + 25*x^10))*Log[x]^8 + (288*x^5 + 912*x^6 + 1232*x^7
+ 920*x^8 + 410*x^9 + 109*x^10 + 16*x^11 + x^12)*Log[x]^10),x]

[Out]

(E^(12*(1 + (3 + x)^(-1)))*x^2)/(5*E^(3 + 3/(3 + x)) + x^2*(2 + x) + x*(2 + x)*Log[x]^2)^4

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fricas [B]  time = 0.81, size = 424, normalized size = 14.13 \begin {gather*} \frac {x^{2} e^{\left (\frac {12 \, {\left (x + 4\right )}}{x + 3}\right )}}{x^{12} + 8 \, x^{11} + 24 \, x^{10} + 32 \, x^{9} + {\left (x^{8} + 8 \, x^{7} + 24 \, x^{6} + 32 \, x^{5} + 16 \, x^{4}\right )} \log \relax (x)^{8} + 16 \, x^{8} + 4 \, {\left (x^{9} + 8 \, x^{8} + 24 \, x^{7} + 32 \, x^{6} + 16 \, x^{5} + 5 \, {\left (x^{6} + 6 \, x^{5} + 12 \, x^{4} + 8 \, x^{3}\right )} e^{\left (\frac {3 \, {\left (x + 4\right )}}{x + 3}\right )}\right )} \log \relax (x)^{6} + 6 \, {\left (x^{10} + 8 \, x^{9} + 24 \, x^{8} + 32 \, x^{7} + 16 \, x^{6} + 25 \, {\left (x^{4} + 4 \, x^{3} + 4 \, x^{2}\right )} e^{\left (\frac {6 \, {\left (x + 4\right )}}{x + 3}\right )} + 10 \, {\left (x^{7} + 6 \, x^{6} + 12 \, x^{5} + 8 \, x^{4}\right )} e^{\left (\frac {3 \, {\left (x + 4\right )}}{x + 3}\right )}\right )} \log \relax (x)^{4} + 4 \, {\left (x^{11} + 8 \, x^{10} + 24 \, x^{9} + 32 \, x^{8} + 16 \, x^{7} + 125 \, {\left (x^{2} + 2 \, x\right )} e^{\left (\frac {9 \, {\left (x + 4\right )}}{x + 3}\right )} + 75 \, {\left (x^{5} + 4 \, x^{4} + 4 \, x^{3}\right )} e^{\left (\frac {6 \, {\left (x + 4\right )}}{x + 3}\right )} + 15 \, {\left (x^{8} + 6 \, x^{7} + 12 \, x^{6} + 8 \, x^{5}\right )} e^{\left (\frac {3 \, {\left (x + 4\right )}}{x + 3}\right )}\right )} \log \relax (x)^{2} + 500 \, {\left (x^{3} + 2 \, x^{2}\right )} e^{\left (\frac {9 \, {\left (x + 4\right )}}{x + 3}\right )} + 150 \, {\left (x^{6} + 4 \, x^{5} + 4 \, x^{4}\right )} e^{\left (\frac {6 \, {\left (x + 4\right )}}{x + 3}\right )} + 20 \, {\left (x^{9} + 6 \, x^{8} + 12 \, x^{7} + 8 \, x^{6}\right )} e^{\left (\frac {3 \, {\left (x + 4\right )}}{x + 3}\right )} + 625 \, e^{\left (\frac {12 \, {\left (x + 4\right )}}{x + 3}\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-6*x^5-52*x^4-102*x^3-36*x^2)*exp((3*x+12)/(3+x))^4*log(x)^2+(-8*x^5-64*x^4-168*x^3-144*x^2)*exp((
3*x+12)/(3+x))^4*log(x)+(10*x^3+60*x^2+90*x)*exp((3*x+12)/(3+x))^5+(-10*x^6-84*x^5-186*x^4-108*x^3)*exp((3*x+1
2)/(3+x))^4)/((x^12+16*x^11+109*x^10+410*x^9+920*x^8+1232*x^7+912*x^6+288*x^5)*log(x)^10+((25*x^10+350*x^9+202
5*x^8+6200*x^7+10600*x^6+9600*x^5+3600*x^4)*exp((3*x+12)/(3+x))+5*x^13+80*x^12+545*x^11+2050*x^10+4600*x^9+616
0*x^8+4560*x^7+1440*x^6)*log(x)^8+((250*x^8+3000*x^7+14250*x^6+33500*x^5+39000*x^4+18000*x^3)*exp((3*x+12)/(3+
x))^2+(100*x^11+1400*x^10+8100*x^9+24800*x^8+42400*x^7+38400*x^6+14400*x^5)*exp((3*x+12)/(3+x))+10*x^14+160*x^
13+1090*x^12+4100*x^11+9200*x^10+12320*x^9+9120*x^8+2880*x^7)*log(x)^6+((1250*x^6+12500*x^5+46250*x^4+75000*x^
3+45000*x^2)*exp((3*x+12)/(3+x))^3+(750*x^9+9000*x^8+42750*x^7+100500*x^6+117000*x^5+54000*x^4)*exp((3*x+12)/(
3+x))^2+(150*x^12+2100*x^11+12150*x^10+37200*x^9+63600*x^8+57600*x^7+21600*x^6)*exp((3*x+12)/(3+x))+10*x^15+16
0*x^14+1090*x^13+4100*x^12+9200*x^11+12320*x^10+9120*x^9+2880*x^8)*log(x)^4+((3125*x^4+25000*x^3+65625*x^2+562
50*x)*exp((3*x+12)/(3+x))^4+(2500*x^7+25000*x^6+92500*x^5+150000*x^4+90000*x^3)*exp((3*x+12)/(3+x))^3+(750*x^1
0+9000*x^9+42750*x^8+100500*x^7+117000*x^6+54000*x^5)*exp((3*x+12)/(3+x))^2+(100*x^13+1400*x^12+8100*x^11+2480
0*x^10+42400*x^9+38400*x^8+14400*x^7)*exp((3*x+12)/(3+x))+5*x^16+80*x^15+545*x^14+2050*x^13+4600*x^12+6160*x^1
1+4560*x^10+1440*x^9)*log(x)^2+(3125*x^2+18750*x+28125)*exp((3*x+12)/(3+x))^5+(3125*x^5+25000*x^4+65625*x^3+56
250*x^2)*exp((3*x+12)/(3+x))^4+(1250*x^8+12500*x^7+46250*x^6+75000*x^5+45000*x^4)*exp((3*x+12)/(3+x))^3+(250*x
^11+3000*x^10+14250*x^9+33500*x^8+39000*x^7+18000*x^6)*exp((3*x+12)/(3+x))^2+(25*x^14+350*x^13+2025*x^12+6200*
x^11+10600*x^10+9600*x^9+3600*x^8)*exp((3*x+12)/(3+x))+x^17+16*x^16+109*x^15+410*x^14+920*x^13+1232*x^12+912*x
^11+288*x^10),x, algorithm="fricas")

[Out]

x^2*e^(12*(x + 4)/(x + 3))/(x^12 + 8*x^11 + 24*x^10 + 32*x^9 + (x^8 + 8*x^7 + 24*x^6 + 32*x^5 + 16*x^4)*log(x)
^8 + 16*x^8 + 4*(x^9 + 8*x^8 + 24*x^7 + 32*x^6 + 16*x^5 + 5*(x^6 + 6*x^5 + 12*x^4 + 8*x^3)*e^(3*(x + 4)/(x + 3
)))*log(x)^6 + 6*(x^10 + 8*x^9 + 24*x^8 + 32*x^7 + 16*x^6 + 25*(x^4 + 4*x^3 + 4*x^2)*e^(6*(x + 4)/(x + 3)) + 1
0*(x^7 + 6*x^6 + 12*x^5 + 8*x^4)*e^(3*(x + 4)/(x + 3)))*log(x)^4 + 4*(x^11 + 8*x^10 + 24*x^9 + 32*x^8 + 16*x^7
+ 125*(x^2 + 2*x)*e^(9*(x + 4)/(x + 3)) + 75*(x^5 + 4*x^4 + 4*x^3)*e^(6*(x + 4)/(x + 3)) + 15*(x^8 + 6*x^7 +
12*x^6 + 8*x^5)*e^(3*(x + 4)/(x + 3)))*log(x)^2 + 500*(x^3 + 2*x^2)*e^(9*(x + 4)/(x + 3)) + 150*(x^6 + 4*x^5 +
4*x^4)*e^(6*(x + 4)/(x + 3)) + 20*(x^9 + 6*x^8 + 12*x^7 + 8*x^6)*e^(3*(x + 4)/(x + 3)) + 625*e^(12*(x + 4)/(x
+ 3)))

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giac [B]  time = 8.38, size = 775, normalized size = 25.83 \begin {gather*} \frac {x^{2} e^{\left (-\frac {4 \, x}{x + 3} + 16\right )}}{x^{8} \log \relax (x)^{8} + 4 \, x^{9} \log \relax (x)^{6} + 8 \, x^{7} \log \relax (x)^{8} + 6 \, x^{10} \log \relax (x)^{4} + 32 \, x^{8} \log \relax (x)^{6} + 24 \, x^{6} \log \relax (x)^{8} + 4 \, x^{11} \log \relax (x)^{2} + 48 \, x^{9} \log \relax (x)^{4} + 96 \, x^{7} \log \relax (x)^{6} + 20 \, x^{6} e^{\left (-\frac {x}{x + 3} + 4\right )} \log \relax (x)^{6} + 32 \, x^{5} \log \relax (x)^{8} + x^{12} + 32 \, x^{10} \log \relax (x)^{2} + 144 \, x^{8} \log \relax (x)^{4} + 60 \, x^{7} e^{\left (-\frac {x}{x + 3} + 4\right )} \log \relax (x)^{4} + 128 \, x^{6} \log \relax (x)^{6} + 120 \, x^{5} e^{\left (-\frac {x}{x + 3} + 4\right )} \log \relax (x)^{6} + 16 \, x^{4} \log \relax (x)^{8} + 8 \, x^{11} + 96 \, x^{9} \log \relax (x)^{2} + 60 \, x^{8} e^{\left (-\frac {x}{x + 3} + 4\right )} \log \relax (x)^{2} + 192 \, x^{7} \log \relax (x)^{4} + 360 \, x^{6} e^{\left (-\frac {x}{x + 3} + 4\right )} \log \relax (x)^{4} + 64 \, x^{5} \log \relax (x)^{6} + 240 \, x^{4} e^{\left (-\frac {x}{x + 3} + 4\right )} \log \relax (x)^{6} + 24 \, x^{10} + 20 \, x^{9} e^{\left (-\frac {x}{x + 3} + 4\right )} + 128 \, x^{8} \log \relax (x)^{2} + 360 \, x^{7} e^{\left (-\frac {x}{x + 3} + 4\right )} \log \relax (x)^{2} + 96 \, x^{6} \log \relax (x)^{4} + 720 \, x^{5} e^{\left (-\frac {x}{x + 3} + 4\right )} \log \relax (x)^{4} + 160 \, x^{3} e^{\left (-\frac {x}{x + 3} + 4\right )} \log \relax (x)^{6} + 32 \, x^{9} + 120 \, x^{8} e^{\left (-\frac {x}{x + 3} + 4\right )} + 64 \, x^{7} \log \relax (x)^{2} + 720 \, x^{6} e^{\left (-\frac {x}{x + 3} + 4\right )} \log \relax (x)^{2} + 480 \, x^{4} e^{\left (-\frac {x}{x + 3} + 4\right )} \log \relax (x)^{4} + 150 \, x^{4} e^{\left (-\frac {2 \, x}{x + 3} + 8\right )} \log \relax (x)^{4} + 16 \, x^{8} + 240 \, x^{7} e^{\left (-\frac {x}{x + 3} + 4\right )} + 480 \, x^{5} e^{\left (-\frac {x}{x + 3} + 4\right )} \log \relax (x)^{2} + 300 \, x^{5} e^{\left (-\frac {2 \, x}{x + 3} + 8\right )} \log \relax (x)^{2} + 600 \, x^{3} e^{\left (-\frac {2 \, x}{x + 3} + 8\right )} \log \relax (x)^{4} + 160 \, x^{6} e^{\left (-\frac {x}{x + 3} + 4\right )} + 150 \, x^{6} e^{\left (-\frac {2 \, x}{x + 3} + 8\right )} + 1200 \, x^{4} e^{\left (-\frac {2 \, x}{x + 3} + 8\right )} \log \relax (x)^{2} + 600 \, x^{2} e^{\left (-\frac {2 \, x}{x + 3} + 8\right )} \log \relax (x)^{4} + 600 \, x^{5} e^{\left (-\frac {2 \, x}{x + 3} + 8\right )} + 1200 \, x^{3} e^{\left (-\frac {2 \, x}{x + 3} + 8\right )} \log \relax (x)^{2} + 600 \, x^{4} e^{\left (-\frac {2 \, x}{x + 3} + 8\right )} + 500 \, x^{2} e^{\left (-\frac {3 \, x}{x + 3} + 12\right )} \log \relax (x)^{2} + 500 \, x^{3} e^{\left (-\frac {3 \, x}{x + 3} + 12\right )} + 1000 \, x e^{\left (-\frac {3 \, x}{x + 3} + 12\right )} \log \relax (x)^{2} + 1000 \, x^{2} e^{\left (-\frac {3 \, x}{x + 3} + 12\right )} + 625 \, e^{\left (-\frac {4 \, x}{x + 3} + 16\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-6*x^5-52*x^4-102*x^3-36*x^2)*exp((3*x+12)/(3+x))^4*log(x)^2+(-8*x^5-64*x^4-168*x^3-144*x^2)*exp((
3*x+12)/(3+x))^4*log(x)+(10*x^3+60*x^2+90*x)*exp((3*x+12)/(3+x))^5+(-10*x^6-84*x^5-186*x^4-108*x^3)*exp((3*x+1
2)/(3+x))^4)/((x^12+16*x^11+109*x^10+410*x^9+920*x^8+1232*x^7+912*x^6+288*x^5)*log(x)^10+((25*x^10+350*x^9+202
5*x^8+6200*x^7+10600*x^6+9600*x^5+3600*x^4)*exp((3*x+12)/(3+x))+5*x^13+80*x^12+545*x^11+2050*x^10+4600*x^9+616
0*x^8+4560*x^7+1440*x^6)*log(x)^8+((250*x^8+3000*x^7+14250*x^6+33500*x^5+39000*x^4+18000*x^3)*exp((3*x+12)/(3+
x))^2+(100*x^11+1400*x^10+8100*x^9+24800*x^8+42400*x^7+38400*x^6+14400*x^5)*exp((3*x+12)/(3+x))+10*x^14+160*x^
13+1090*x^12+4100*x^11+9200*x^10+12320*x^9+9120*x^8+2880*x^7)*log(x)^6+((1250*x^6+12500*x^5+46250*x^4+75000*x^
3+45000*x^2)*exp((3*x+12)/(3+x))^3+(750*x^9+9000*x^8+42750*x^7+100500*x^6+117000*x^5+54000*x^4)*exp((3*x+12)/(
3+x))^2+(150*x^12+2100*x^11+12150*x^10+37200*x^9+63600*x^8+57600*x^7+21600*x^6)*exp((3*x+12)/(3+x))+10*x^15+16
0*x^14+1090*x^13+4100*x^12+9200*x^11+12320*x^10+9120*x^9+2880*x^8)*log(x)^4+((3125*x^4+25000*x^3+65625*x^2+562
50*x)*exp((3*x+12)/(3+x))^4+(2500*x^7+25000*x^6+92500*x^5+150000*x^4+90000*x^3)*exp((3*x+12)/(3+x))^3+(750*x^1
0+9000*x^9+42750*x^8+100500*x^7+117000*x^6+54000*x^5)*exp((3*x+12)/(3+x))^2+(100*x^13+1400*x^12+8100*x^11+2480
0*x^10+42400*x^9+38400*x^8+14400*x^7)*exp((3*x+12)/(3+x))+5*x^16+80*x^15+545*x^14+2050*x^13+4600*x^12+6160*x^1
1+4560*x^10+1440*x^9)*log(x)^2+(3125*x^2+18750*x+28125)*exp((3*x+12)/(3+x))^5+(3125*x^5+25000*x^4+65625*x^3+56
250*x^2)*exp((3*x+12)/(3+x))^4+(1250*x^8+12500*x^7+46250*x^6+75000*x^5+45000*x^4)*exp((3*x+12)/(3+x))^3+(250*x
^11+3000*x^10+14250*x^9+33500*x^8+39000*x^7+18000*x^6)*exp((3*x+12)/(3+x))^2+(25*x^14+350*x^13+2025*x^12+6200*
x^11+10600*x^10+9600*x^9+3600*x^8)*exp((3*x+12)/(3+x))+x^17+16*x^16+109*x^15+410*x^14+920*x^13+1232*x^12+912*x
^11+288*x^10),x, algorithm="giac")

[Out]

x^2*e^(-4*x/(x + 3) + 16)/(x^8*log(x)^8 + 4*x^9*log(x)^6 + 8*x^7*log(x)^8 + 6*x^10*log(x)^4 + 32*x^8*log(x)^6
+ 24*x^6*log(x)^8 + 4*x^11*log(x)^2 + 48*x^9*log(x)^4 + 96*x^7*log(x)^6 + 20*x^6*e^(-x/(x + 3) + 4)*log(x)^6 +
32*x^5*log(x)^8 + x^12 + 32*x^10*log(x)^2 + 144*x^8*log(x)^4 + 60*x^7*e^(-x/(x + 3) + 4)*log(x)^4 + 128*x^6*l
og(x)^6 + 120*x^5*e^(-x/(x + 3) + 4)*log(x)^6 + 16*x^4*log(x)^8 + 8*x^11 + 96*x^9*log(x)^2 + 60*x^8*e^(-x/(x +
3) + 4)*log(x)^2 + 192*x^7*log(x)^4 + 360*x^6*e^(-x/(x + 3) + 4)*log(x)^4 + 64*x^5*log(x)^6 + 240*x^4*e^(-x/(
x + 3) + 4)*log(x)^6 + 24*x^10 + 20*x^9*e^(-x/(x + 3) + 4) + 128*x^8*log(x)^2 + 360*x^7*e^(-x/(x + 3) + 4)*log
(x)^2 + 96*x^6*log(x)^4 + 720*x^5*e^(-x/(x + 3) + 4)*log(x)^4 + 160*x^3*e^(-x/(x + 3) + 4)*log(x)^6 + 32*x^9 +
120*x^8*e^(-x/(x + 3) + 4) + 64*x^7*log(x)^2 + 720*x^6*e^(-x/(x + 3) + 4)*log(x)^2 + 480*x^4*e^(-x/(x + 3) +
4)*log(x)^4 + 150*x^4*e^(-2*x/(x + 3) + 8)*log(x)^4 + 16*x^8 + 240*x^7*e^(-x/(x + 3) + 4) + 480*x^5*e^(-x/(x +
3) + 4)*log(x)^2 + 300*x^5*e^(-2*x/(x + 3) + 8)*log(x)^2 + 600*x^3*e^(-2*x/(x + 3) + 8)*log(x)^4 + 160*x^6*e^
(-x/(x + 3) + 4) + 150*x^6*e^(-2*x/(x + 3) + 8) + 1200*x^4*e^(-2*x/(x + 3) + 8)*log(x)^2 + 600*x^2*e^(-2*x/(x
+ 3) + 8)*log(x)^4 + 600*x^5*e^(-2*x/(x + 3) + 8) + 1200*x^3*e^(-2*x/(x + 3) + 8)*log(x)^2 + 600*x^4*e^(-2*x/(
x + 3) + 8) + 500*x^2*e^(-3*x/(x + 3) + 12)*log(x)^2 + 500*x^3*e^(-3*x/(x + 3) + 12) + 1000*x*e^(-3*x/(x + 3)
+ 12)*log(x)^2 + 1000*x^2*e^(-3*x/(x + 3) + 12) + 625*e^(-4*x/(x + 3) + 16))

________________________________________________________________________________________

maple [A]  time = 0.26, size = 55, normalized size = 1.83

method	result	size
risch	\(\frac {x^{2} {\mathrm e}^{\frac {12 x +48}{3+x}}}{\left (x^{2} \ln \relax (x )^{2}+x^{3}+2 x \ln \relax (x )^{2}+2 x^{2}+5 \,{\mathrm e}^{\frac {3 x +12}{3+x}}\right )^{4}}\)	\(55\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-6*x^5-52*x^4-102*x^3-36*x^2)*exp((3*x+12)/(3+x))^4*ln(x)^2+(-8*x^5-64*x^4-168*x^3-144*x^2)*exp((3*x+12)
/(3+x))^4*ln(x)+(10*x^3+60*x^2+90*x)*exp((3*x+12)/(3+x))^5+(-10*x^6-84*x^5-186*x^4-108*x^3)*exp((3*x+12)/(3+x)
)^4)/((x^12+16*x^11+109*x^10+410*x^9+920*x^8+1232*x^7+912*x^6+288*x^5)*ln(x)^10+((25*x^10+350*x^9+2025*x^8+620
0*x^7+10600*x^6+9600*x^5+3600*x^4)*exp((3*x+12)/(3+x))+5*x^13+80*x^12+545*x^11+2050*x^10+4600*x^9+6160*x^8+456
0*x^7+1440*x^6)*ln(x)^8+((250*x^8+3000*x^7+14250*x^6+33500*x^5+39000*x^4+18000*x^3)*exp((3*x+12)/(3+x))^2+(100
*x^11+1400*x^10+8100*x^9+24800*x^8+42400*x^7+38400*x^6+14400*x^5)*exp((3*x+12)/(3+x))+10*x^14+160*x^13+1090*x^
12+4100*x^11+9200*x^10+12320*x^9+9120*x^8+2880*x^7)*ln(x)^6+((1250*x^6+12500*x^5+46250*x^4+75000*x^3+45000*x^2
)*exp((3*x+12)/(3+x))^3+(750*x^9+9000*x^8+42750*x^7+100500*x^6+117000*x^5+54000*x^4)*exp((3*x+12)/(3+x))^2+(15
0*x^12+2100*x^11+12150*x^10+37200*x^9+63600*x^8+57600*x^7+21600*x^6)*exp((3*x+12)/(3+x))+10*x^15+160*x^14+1090
*x^13+4100*x^12+9200*x^11+12320*x^10+9120*x^9+2880*x^8)*ln(x)^4+((3125*x^4+25000*x^3+65625*x^2+56250*x)*exp((3
*x+12)/(3+x))^4+(2500*x^7+25000*x^6+92500*x^5+150000*x^4+90000*x^3)*exp((3*x+12)/(3+x))^3+(750*x^10+9000*x^9+4
2750*x^8+100500*x^7+117000*x^6+54000*x^5)*exp((3*x+12)/(3+x))^2+(100*x^13+1400*x^12+8100*x^11+24800*x^10+42400
*x^9+38400*x^8+14400*x^7)*exp((3*x+12)/(3+x))+5*x^16+80*x^15+545*x^14+2050*x^13+4600*x^12+6160*x^11+4560*x^10+
1440*x^9)*ln(x)^2+(3125*x^2+18750*x+28125)*exp((3*x+12)/(3+x))^5+(3125*x^5+25000*x^4+65625*x^3+56250*x^2)*exp(
(3*x+12)/(3+x))^4+(1250*x^8+12500*x^7+46250*x^6+75000*x^5+45000*x^4)*exp((3*x+12)/(3+x))^3+(250*x^11+3000*x^10
+14250*x^9+33500*x^8+39000*x^7+18000*x^6)*exp((3*x+12)/(3+x))^2+(25*x^14+350*x^13+2025*x^12+6200*x^11+10600*x^
10+9600*x^9+3600*x^8)*exp((3*x+12)/(3+x))+x^17+16*x^16+109*x^15+410*x^14+920*x^13+1232*x^12+912*x^11+288*x^10)
,x,method=_RETURNVERBOSE)

[Out]

x^2*exp(12*(4+x)/(3+x))/(x^2*ln(x)^2+2*x*ln(x)^2+x^3+2*x^2+5*exp(3*(4+x)/(3+x)))^4

________________________________________________________________________________________

maxima [B]  time = 5.53, size = 435, normalized size = 14.50 \begin {gather*} \frac {x^{2} e^{\left (\frac {12}{x + 3} + 12\right )}}{x^{12} + 8 \, x^{11} + 24 \, x^{10} + 32 \, x^{9} + {\left (x^{8} + 8 \, x^{7} + 24 \, x^{6} + 32 \, x^{5} + 16 \, x^{4}\right )} \log \relax (x)^{8} + 16 \, x^{8} + 4 \, {\left (x^{9} + 8 \, x^{8} + 24 \, x^{7} + 32 \, x^{6} + 16 \, x^{5}\right )} \log \relax (x)^{6} + 6 \, {\left (x^{10} + 8 \, x^{9} + 24 \, x^{8} + 32 \, x^{7} + 16 \, x^{6}\right )} \log \relax (x)^{4} + 4 \, {\left (x^{11} + 8 \, x^{10} + 24 \, x^{9} + 32 \, x^{8} + 16 \, x^{7}\right )} \log \relax (x)^{2} + 500 \, {\left (x^{3} e^{9} + 2 \, x^{2} e^{9} + {\left (x^{2} e^{9} + 2 \, x e^{9}\right )} \log \relax (x)^{2}\right )} e^{\left (\frac {9}{x + 3}\right )} + 150 \, {\left (x^{6} e^{6} + 4 \, x^{5} e^{6} + 4 \, x^{4} e^{6} + {\left (x^{4} e^{6} + 4 \, x^{3} e^{6} + 4 \, x^{2} e^{6}\right )} \log \relax (x)^{4} + 2 \, {\left (x^{5} e^{6} + 4 \, x^{4} e^{6} + 4 \, x^{3} e^{6}\right )} \log \relax (x)^{2}\right )} e^{\left (\frac {6}{x + 3}\right )} + 20 \, {\left (x^{9} e^{3} + 6 \, x^{8} e^{3} + 12 \, x^{7} e^{3} + 8 \, x^{6} e^{3} + {\left (x^{6} e^{3} + 6 \, x^{5} e^{3} + 12 \, x^{4} e^{3} + 8 \, x^{3} e^{3}\right )} \log \relax (x)^{6} + 3 \, {\left (x^{7} e^{3} + 6 \, x^{6} e^{3} + 12 \, x^{5} e^{3} + 8 \, x^{4} e^{3}\right )} \log \relax (x)^{4} + 3 \, {\left (x^{8} e^{3} + 6 \, x^{7} e^{3} + 12 \, x^{6} e^{3} + 8 \, x^{5} e^{3}\right )} \log \relax (x)^{2}\right )} e^{\left (\frac {3}{x + 3}\right )} + 625 \, e^{\left (\frac {12}{x + 3} + 12\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-6*x^5-52*x^4-102*x^3-36*x^2)*exp((3*x+12)/(3+x))^4*log(x)^2+(-8*x^5-64*x^4-168*x^3-144*x^2)*exp((
3*x+12)/(3+x))^4*log(x)+(10*x^3+60*x^2+90*x)*exp((3*x+12)/(3+x))^5+(-10*x^6-84*x^5-186*x^4-108*x^3)*exp((3*x+1
2)/(3+x))^4)/((x^12+16*x^11+109*x^10+410*x^9+920*x^8+1232*x^7+912*x^6+288*x^5)*log(x)^10+((25*x^10+350*x^9+202
5*x^8+6200*x^7+10600*x^6+9600*x^5+3600*x^4)*exp((3*x+12)/(3+x))+5*x^13+80*x^12+545*x^11+2050*x^10+4600*x^9+616
0*x^8+4560*x^7+1440*x^6)*log(x)^8+((250*x^8+3000*x^7+14250*x^6+33500*x^5+39000*x^4+18000*x^3)*exp((3*x+12)/(3+
x))^2+(100*x^11+1400*x^10+8100*x^9+24800*x^8+42400*x^7+38400*x^6+14400*x^5)*exp((3*x+12)/(3+x))+10*x^14+160*x^
13+1090*x^12+4100*x^11+9200*x^10+12320*x^9+9120*x^8+2880*x^7)*log(x)^6+((1250*x^6+12500*x^5+46250*x^4+75000*x^
3+45000*x^2)*exp((3*x+12)/(3+x))^3+(750*x^9+9000*x^8+42750*x^7+100500*x^6+117000*x^5+54000*x^4)*exp((3*x+12)/(
3+x))^2+(150*x^12+2100*x^11+12150*x^10+37200*x^9+63600*x^8+57600*x^7+21600*x^6)*exp((3*x+12)/(3+x))+10*x^15+16
0*x^14+1090*x^13+4100*x^12+9200*x^11+12320*x^10+9120*x^9+2880*x^8)*log(x)^4+((3125*x^4+25000*x^3+65625*x^2+562
50*x)*exp((3*x+12)/(3+x))^4+(2500*x^7+25000*x^6+92500*x^5+150000*x^4+90000*x^3)*exp((3*x+12)/(3+x))^3+(750*x^1
0+9000*x^9+42750*x^8+100500*x^7+117000*x^6+54000*x^5)*exp((3*x+12)/(3+x))^2+(100*x^13+1400*x^12+8100*x^11+2480
0*x^10+42400*x^9+38400*x^8+14400*x^7)*exp((3*x+12)/(3+x))+5*x^16+80*x^15+545*x^14+2050*x^13+4600*x^12+6160*x^1
1+4560*x^10+1440*x^9)*log(x)^2+(3125*x^2+18750*x+28125)*exp((3*x+12)/(3+x))^5+(3125*x^5+25000*x^4+65625*x^3+56
250*x^2)*exp((3*x+12)/(3+x))^4+(1250*x^8+12500*x^7+46250*x^6+75000*x^5+45000*x^4)*exp((3*x+12)/(3+x))^3+(250*x
^11+3000*x^10+14250*x^9+33500*x^8+39000*x^7+18000*x^6)*exp((3*x+12)/(3+x))^2+(25*x^14+350*x^13+2025*x^12+6200*
x^11+10600*x^10+9600*x^9+3600*x^8)*exp((3*x+12)/(3+x))+x^17+16*x^16+109*x^15+410*x^14+920*x^13+1232*x^12+912*x
^11+288*x^10),x, algorithm="maxima")

[Out]

x^2*e^(12/(x + 3) + 12)/(x^12 + 8*x^11 + 24*x^10 + 32*x^9 + (x^8 + 8*x^7 + 24*x^6 + 32*x^5 + 16*x^4)*log(x)^8
+ 16*x^8 + 4*(x^9 + 8*x^8 + 24*x^7 + 32*x^6 + 16*x^5)*log(x)^6 + 6*(x^10 + 8*x^9 + 24*x^8 + 32*x^7 + 16*x^6)*l
og(x)^4 + 4*(x^11 + 8*x^10 + 24*x^9 + 32*x^8 + 16*x^7)*log(x)^2 + 500*(x^3*e^9 + 2*x^2*e^9 + (x^2*e^9 + 2*x*e^
9)*log(x)^2)*e^(9/(x + 3)) + 150*(x^6*e^6 + 4*x^5*e^6 + 4*x^4*e^6 + (x^4*e^6 + 4*x^3*e^6 + 4*x^2*e^6)*log(x)^4
+ 2*(x^5*e^6 + 4*x^4*e^6 + 4*x^3*e^6)*log(x)^2)*e^(6/(x + 3)) + 20*(x^9*e^3 + 6*x^8*e^3 + 12*x^7*e^3 + 8*x^6*
e^3 + (x^6*e^3 + 6*x^5*e^3 + 12*x^4*e^3 + 8*x^3*e^3)*log(x)^6 + 3*(x^7*e^3 + 6*x^6*e^3 + 12*x^5*e^3 + 8*x^4*e^
3)*log(x)^4 + 3*(x^8*e^3 + 6*x^7*e^3 + 12*x^6*e^3 + 8*x^5*e^3)*log(x)^2)*e^(3/(x + 3)) + 625*e^(12/(x + 3) + 1
2))

________________________________________________________________________________________

mupad [F]  time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int -\frac {{\mathrm {e}}^{\frac {4\,\left (3\,x+12\right )}{x+3}}\,\left (6\,x^5+52\,x^4+102\,x^3+36\,x^2\right )\,{\ln \relax (x)}^2+{\mathrm {e}}^{\frac {4\,\left (3\,x+12\right )}{x+3}}\,\left (8\,x^5+64\,x^4+168\,x^3+144\,x^2\right )\,\ln \relax (x)-{\mathrm {e}}^{\frac {5\,\left (3\,x+12\right )}{x+3}}\,\left (10\,x^3+60\,x^2+90\,x\right )+{\mathrm {e}}^{\frac {4\,\left (3\,x+12\right )}{x+3}}\,\left (10\,x^6+84\,x^5+186\,x^4+108\,x^3\right )}{{\mathrm {e}}^{\frac {3\,\left (3\,x+12\right )}{x+3}}\,\left (1250\,x^8+12500\,x^7+46250\,x^6+75000\,x^5+45000\,x^4\right )+{\ln \relax (x)}^8\,\left ({\mathrm {e}}^{\frac {3\,x+12}{x+3}}\,\left (25\,x^{10}+350\,x^9+2025\,x^8+6200\,x^7+10600\,x^6+9600\,x^5+3600\,x^4\right )+1440\,x^6+4560\,x^7+6160\,x^8+4600\,x^9+2050\,x^{10}+545\,x^{11}+80\,x^{12}+5\,x^{13}\right )+{\mathrm {e}}^{\frac {2\,\left (3\,x+12\right )}{x+3}}\,\left (250\,x^{11}+3000\,x^{10}+14250\,x^9+33500\,x^8+39000\,x^7+18000\,x^6\right )+{\ln \relax (x)}^{10}\,\left (x^{12}+16\,x^{11}+109\,x^{10}+410\,x^9+920\,x^8+1232\,x^7+912\,x^6+288\,x^5\right )+{\ln \relax (x)}^6\,\left ({\mathrm {e}}^{\frac {2\,\left (3\,x+12\right )}{x+3}}\,\left (250\,x^8+3000\,x^7+14250\,x^6+33500\,x^5+39000\,x^4+18000\,x^3\right )+{\mathrm {e}}^{\frac {3\,x+12}{x+3}}\,\left (100\,x^{11}+1400\,x^{10}+8100\,x^9+24800\,x^8+42400\,x^7+38400\,x^6+14400\,x^5\right )+2880\,x^7+9120\,x^8+12320\,x^9+9200\,x^{10}+4100\,x^{11}+1090\,x^{12}+160\,x^{13}+10\,x^{14}\right )+{\ln \relax (x)}^4\,\left ({\mathrm {e}}^{\frac {3\,\left (3\,x+12\right )}{x+3}}\,\left (1250\,x^6+12500\,x^5+46250\,x^4+75000\,x^3+45000\,x^2\right )+{\mathrm {e}}^{\frac {2\,\left (3\,x+12\right )}{x+3}}\,\left (750\,x^9+9000\,x^8+42750\,x^7+100500\,x^6+117000\,x^5+54000\,x^4\right )+{\mathrm {e}}^{\frac {3\,x+12}{x+3}}\,\left (150\,x^{12}+2100\,x^{11}+12150\,x^{10}+37200\,x^9+63600\,x^8+57600\,x^7+21600\,x^6\right )+2880\,x^8+9120\,x^9+12320\,x^{10}+9200\,x^{11}+4100\,x^{12}+1090\,x^{13}+160\,x^{14}+10\,x^{15}\right )+{\mathrm {e}}^{\frac {3\,x+12}{x+3}}\,\left (25\,x^{14}+350\,x^{13}+2025\,x^{12}+6200\,x^{11}+10600\,x^{10}+9600\,x^9+3600\,x^8\right )+{\mathrm {e}}^{\frac {4\,\left (3\,x+12\right )}{x+3}}\,\left (3125\,x^5+25000\,x^4+65625\,x^3+56250\,x^2\right )+{\ln \relax (x)}^2\,\left ({\mathrm {e}}^{\frac {3\,\left (3\,x+12\right )}{x+3}}\,\left (2500\,x^7+25000\,x^6+92500\,x^5+150000\,x^4+90000\,x^3\right )+{\mathrm {e}}^{\frac {2\,\left (3\,x+12\right )}{x+3}}\,\left (750\,x^{10}+9000\,x^9+42750\,x^8+100500\,x^7+117000\,x^6+54000\,x^5\right )+{\mathrm {e}}^{\frac {4\,\left (3\,x+12\right )}{x+3}}\,\left (3125\,x^4+25000\,x^3+65625\,x^2+56250\,x\right )+{\mathrm {e}}^{\frac {3\,x+12}{x+3}}\,\left (100\,x^{13}+1400\,x^{12}+8100\,x^{11}+24800\,x^{10}+42400\,x^9+38400\,x^8+14400\,x^7\right )+1440\,x^9+4560\,x^{10}+6160\,x^{11}+4600\,x^{12}+2050\,x^{13}+545\,x^{14}+80\,x^{15}+5\,x^{16}\right )+288\,x^{10}+912\,x^{11}+1232\,x^{12}+920\,x^{13}+410\,x^{14}+109\,x^{15}+16\,x^{16}+x^{17}+{\mathrm {e}}^{\frac {5\,\left (3\,x+12\right )}{x+3}}\,\left (3125\,x^2+18750\,x+28125\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp((4*(3*x + 12))/(x + 3))*(108*x^3 + 186*x^4 + 84*x^5 + 10*x^6) - exp((5*(3*x + 12))/(x + 3))*(90*x +
60*x^2 + 10*x^3) + exp((4*(3*x + 12))/(x + 3))*log(x)^2*(36*x^2 + 102*x^3 + 52*x^4 + 6*x^5) + exp((4*(3*x + 12
))/(x + 3))*log(x)*(144*x^2 + 168*x^3 + 64*x^4 + 8*x^5))/(exp((3*(3*x + 12))/(x + 3))*(45000*x^4 + 75000*x^5 +
46250*x^6 + 12500*x^7 + 1250*x^8) + log(x)^8*(exp((3*x + 12)/(x + 3))*(3600*x^4 + 9600*x^5 + 10600*x^6 + 6200
*x^7 + 2025*x^8 + 350*x^9 + 25*x^10) + 1440*x^6 + 4560*x^7 + 6160*x^8 + 4600*x^9 + 2050*x^10 + 545*x^11 + 80*x
^12 + 5*x^13) + exp((2*(3*x + 12))/(x + 3))*(18000*x^6 + 39000*x^7 + 33500*x^8 + 14250*x^9 + 3000*x^10 + 250*x
^11) + log(x)^10*(288*x^5 + 912*x^6 + 1232*x^7 + 920*x^8 + 410*x^9 + 109*x^10 + 16*x^11 + x^12) + log(x)^6*(ex
p((2*(3*x + 12))/(x + 3))*(18000*x^3 + 39000*x^4 + 33500*x^5 + 14250*x^6 + 3000*x^7 + 250*x^8) + exp((3*x + 12
)/(x + 3))*(14400*x^5 + 38400*x^6 + 42400*x^7 + 24800*x^8 + 8100*x^9 + 1400*x^10 + 100*x^11) + 2880*x^7 + 9120
*x^8 + 12320*x^9 + 9200*x^10 + 4100*x^11 + 1090*x^12 + 160*x^13 + 10*x^14) + log(x)^4*(exp((3*(3*x + 12))/(x +
3))*(45000*x^2 + 75000*x^3 + 46250*x^4 + 12500*x^5 + 1250*x^6) + exp((2*(3*x + 12))/(x + 3))*(54000*x^4 + 117
000*x^5 + 100500*x^6 + 42750*x^7 + 9000*x^8 + 750*x^9) + exp((3*x + 12)/(x + 3))*(21600*x^6 + 57600*x^7 + 6360
0*x^8 + 37200*x^9 + 12150*x^10 + 2100*x^11 + 150*x^12) + 2880*x^8 + 9120*x^9 + 12320*x^10 + 9200*x^11 + 4100*x
^12 + 1090*x^13 + 160*x^14 + 10*x^15) + exp((3*x + 12)/(x + 3))*(3600*x^8 + 9600*x^9 + 10600*x^10 + 6200*x^11
+ 2025*x^12 + 350*x^13 + 25*x^14) + exp((4*(3*x + 12))/(x + 3))*(56250*x^2 + 65625*x^3 + 25000*x^4 + 3125*x^5)
+ log(x)^2*(exp((3*(3*x + 12))/(x + 3))*(90000*x^3 + 150000*x^4 + 92500*x^5 + 25000*x^6 + 2500*x^7) + exp((2*
(3*x + 12))/(x + 3))*(54000*x^5 + 117000*x^6 + 100500*x^7 + 42750*x^8 + 9000*x^9 + 750*x^10) + exp((4*(3*x + 1
2))/(x + 3))*(56250*x + 65625*x^2 + 25000*x^3 + 3125*x^4) + exp((3*x + 12)/(x + 3))*(14400*x^7 + 38400*x^8 + 4
2400*x^9 + 24800*x^10 + 8100*x^11 + 1400*x^12 + 100*x^13) + 1440*x^9 + 4560*x^10 + 6160*x^11 + 4600*x^12 + 205
0*x^13 + 545*x^14 + 80*x^15 + 5*x^16) + 288*x^10 + 912*x^11 + 1232*x^12 + 920*x^13 + 410*x^14 + 109*x^15 + 16*
x^16 + x^17 + exp((5*(3*x + 12))/(x + 3))*(18750*x + 3125*x^2 + 28125)),x)

[Out]

int(-(exp((4*(3*x + 12))/(x + 3))*(108*x^3 + 186*x^4 + 84*x^5 + 10*x^6) - exp((5*(3*x + 12))/(x + 3))*(90*x +
60*x^2 + 10*x^3) + exp((4*(3*x + 12))/(x + 3))*log(x)^2*(36*x^2 + 102*x^3 + 52*x^4 + 6*x^5) + exp((4*(3*x + 12
))/(x + 3))*log(x)*(144*x^2 + 168*x^3 + 64*x^4 + 8*x^5))/(exp((3*(3*x + 12))/(x + 3))*(45000*x^4 + 75000*x^5 +
46250*x^6 + 12500*x^7 + 1250*x^8) + log(x)^8*(exp((3*x + 12)/(x + 3))*(3600*x^4 + 9600*x^5 + 10600*x^6 + 6200
*x^7 + 2025*x^8 + 350*x^9 + 25*x^10) + 1440*x^6 + 4560*x^7 + 6160*x^8 + 4600*x^9 + 2050*x^10 + 545*x^11 + 80*x
^12 + 5*x^13) + exp((2*(3*x + 12))/(x + 3))*(18000*x^6 + 39000*x^7 + 33500*x^8 + 14250*x^9 + 3000*x^10 + 250*x
^11) + log(x)^10*(288*x^5 + 912*x^6 + 1232*x^7 + 920*x^8 + 410*x^9 + 109*x^10 + 16*x^11 + x^12) + log(x)^6*(ex
p((2*(3*x + 12))/(x + 3))*(18000*x^3 + 39000*x^4 + 33500*x^5 + 14250*x^6 + 3000*x^7 + 250*x^8) + exp((3*x + 12
)/(x + 3))*(14400*x^5 + 38400*x^6 + 42400*x^7 + 24800*x^8 + 8100*x^9 + 1400*x^10 + 100*x^11) + 2880*x^7 + 9120
*x^8 + 12320*x^9 + 9200*x^10 + 4100*x^11 + 1090*x^12 + 160*x^13 + 10*x^14) + log(x)^4*(exp((3*(3*x + 12))/(x +
3))*(45000*x^2 + 75000*x^3 + 46250*x^4 + 12500*x^5 + 1250*x^6) + exp((2*(3*x + 12))/(x + 3))*(54000*x^4 + 117
000*x^5 + 100500*x^6 + 42750*x^7 + 9000*x^8 + 750*x^9) + exp((3*x + 12)/(x + 3))*(21600*x^6 + 57600*x^7 + 6360
0*x^8 + 37200*x^9 + 12150*x^10 + 2100*x^11 + 150*x^12) + 2880*x^8 + 9120*x^9 + 12320*x^10 + 9200*x^11 + 4100*x
^12 + 1090*x^13 + 160*x^14 + 10*x^15) + exp((3*x + 12)/(x + 3))*(3600*x^8 + 9600*x^9 + 10600*x^10 + 6200*x^11
+ 2025*x^12 + 350*x^13 + 25*x^14) + exp((4*(3*x + 12))/(x + 3))*(56250*x^2 + 65625*x^3 + 25000*x^4 + 3125*x^5)
+ log(x)^2*(exp((3*(3*x + 12))/(x + 3))*(90000*x^3 + 150000*x^4 + 92500*x^5 + 25000*x^6 + 2500*x^7) + exp((2*
(3*x + 12))/(x + 3))*(54000*x^5 + 117000*x^6 + 100500*x^7 + 42750*x^8 + 9000*x^9 + 750*x^10) + exp((4*(3*x + 1
2))/(x + 3))*(56250*x + 65625*x^2 + 25000*x^3 + 3125*x^4) + exp((3*x + 12)/(x + 3))*(14400*x^7 + 38400*x^8 + 4
2400*x^9 + 24800*x^10 + 8100*x^11 + 1400*x^12 + 100*x^13) + 1440*x^9 + 4560*x^10 + 6160*x^11 + 4600*x^12 + 205
0*x^13 + 545*x^14 + 80*x^15 + 5*x^16) + 288*x^10 + 912*x^11 + 1232*x^12 + 920*x^13 + 410*x^14 + 109*x^15 + 16*
x^16 + x^17 + exp((5*(3*x + 12))/(x + 3))*(18750*x + 3125*x^2 + 28125)), x)

________________________________________________________________________________________

sympy [B]  time = 16.83, size = 1035, normalized size = 34.50 result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-6*x**5-52*x**4-102*x**3-36*x**2)*exp((3*x+12)/(3+x))**4*ln(x)**2+(-8*x**5-64*x**4-168*x**3-144*x*
*2)*exp((3*x+12)/(3+x))**4*ln(x)+(10*x**3+60*x**2+90*x)*exp((3*x+12)/(3+x))**5+(-10*x**6-84*x**5-186*x**4-108*
x**3)*exp((3*x+12)/(3+x))**4)/((x**12+16*x**11+109*x**10+410*x**9+920*x**8+1232*x**7+912*x**6+288*x**5)*ln(x)*
*10+((25*x**10+350*x**9+2025*x**8+6200*x**7+10600*x**6+9600*x**5+3600*x**4)*exp((3*x+12)/(3+x))+5*x**13+80*x**
12+545*x**11+2050*x**10+4600*x**9+6160*x**8+4560*x**7+1440*x**6)*ln(x)**8+((250*x**8+3000*x**7+14250*x**6+3350
0*x**5+39000*x**4+18000*x**3)*exp((3*x+12)/(3+x))**2+(100*x**11+1400*x**10+8100*x**9+24800*x**8+42400*x**7+384
00*x**6+14400*x**5)*exp((3*x+12)/(3+x))+10*x**14+160*x**13+1090*x**12+4100*x**11+9200*x**10+12320*x**9+9120*x*
*8+2880*x**7)*ln(x)**6+((1250*x**6+12500*x**5+46250*x**4+75000*x**3+45000*x**2)*exp((3*x+12)/(3+x))**3+(750*x*
*9+9000*x**8+42750*x**7+100500*x**6+117000*x**5+54000*x**4)*exp((3*x+12)/(3+x))**2+(150*x**12+2100*x**11+12150
*x**10+37200*x**9+63600*x**8+57600*x**7+21600*x**6)*exp((3*x+12)/(3+x))+10*x**15+160*x**14+1090*x**13+4100*x**
12+9200*x**11+12320*x**10+9120*x**9+2880*x**8)*ln(x)**4+((3125*x**4+25000*x**3+65625*x**2+56250*x)*exp((3*x+12
)/(3+x))**4+(2500*x**7+25000*x**6+92500*x**5+150000*x**4+90000*x**3)*exp((3*x+12)/(3+x))**3+(750*x**10+9000*x*
*9+42750*x**8+100500*x**7+117000*x**6+54000*x**5)*exp((3*x+12)/(3+x))**2+(100*x**13+1400*x**12+8100*x**11+2480
0*x**10+42400*x**9+38400*x**8+14400*x**7)*exp((3*x+12)/(3+x))+5*x**16+80*x**15+545*x**14+2050*x**13+4600*x**12
+6160*x**11+4560*x**10+1440*x**9)*ln(x)**2+(3125*x**2+18750*x+28125)*exp((3*x+12)/(3+x))**5+(3125*x**5+25000*x
**4+65625*x**3+56250*x**2)*exp((3*x+12)/(3+x))**4+(1250*x**8+12500*x**7+46250*x**6+75000*x**5+45000*x**4)*exp(
(3*x+12)/(3+x))**3+(250*x**11+3000*x**10+14250*x**9+33500*x**8+39000*x**7+18000*x**6)*exp((3*x+12)/(3+x))**2+(
25*x**14+350*x**13+2025*x**12+6200*x**11+10600*x**10+9600*x**9+3600*x**8)*exp((3*x+12)/(3+x))+x**17+16*x**16+1
09*x**15+410*x**14+920*x**13+1232*x**12+912*x**11+288*x**10),x)

[Out]

x**2/625 + (-x**14 - 4*x**13*log(x)**2 - 8*x**13 - 6*x**12*log(x)**4 - 32*x**12*log(x)**2 - 24*x**12 - 4*x**11
*log(x)**6 - 48*x**11*log(x)**4 - 96*x**11*log(x)**2 - 32*x**11 - x**10*log(x)**8 - 32*x**10*log(x)**6 - 144*x
**10*log(x)**4 - 128*x**10*log(x)**2 - 16*x**10 - 8*x**9*log(x)**8 - 96*x**9*log(x)**6 - 192*x**9*log(x)**4 -
64*x**9*log(x)**2 - 24*x**8*log(x)**8 - 128*x**8*log(x)**6 - 96*x**8*log(x)**4 - 32*x**7*log(x)**8 - 64*x**7*l
og(x)**6 - 16*x**6*log(x)**8 + (-500*x**5 - 500*x**4*log(x)**2 - 1000*x**4 - 1000*x**3*log(x)**2)*exp(3*(3*x +
12)/(x + 3)) + (-150*x**8 - 300*x**7*log(x)**2 - 600*x**7 - 150*x**6*log(x)**4 - 1200*x**6*log(x)**2 - 600*x*
*6 - 600*x**5*log(x)**4 - 1200*x**5*log(x)**2 - 600*x**4*log(x)**4)*exp(2*(3*x + 12)/(x + 3)) + (-20*x**11 - 6
0*x**10*log(x)**2 - 120*x**10 - 60*x**9*log(x)**4 - 360*x**9*log(x)**2 - 240*x**9 - 20*x**8*log(x)**6 - 360*x*
*8*log(x)**4 - 720*x**8*log(x)**2 - 160*x**8 - 120*x**7*log(x)**6 - 720*x**7*log(x)**4 - 480*x**7*log(x)**2 -
240*x**6*log(x)**6 - 480*x**6*log(x)**4 - 160*x**5*log(x)**6)*exp((3*x + 12)/(x + 3)))/(625*x**12 + 2500*x**11
*log(x)**2 + 5000*x**11 + 3750*x**10*log(x)**4 + 20000*x**10*log(x)**2 + 15000*x**10 + 2500*x**9*log(x)**6 + 3
0000*x**9*log(x)**4 + 60000*x**9*log(x)**2 + 20000*x**9 + 625*x**8*log(x)**8 + 20000*x**8*log(x)**6 + 90000*x*
*8*log(x)**4 + 80000*x**8*log(x)**2 + 10000*x**8 + 5000*x**7*log(x)**8 + 60000*x**7*log(x)**6 + 120000*x**7*lo
g(x)**4 + 40000*x**7*log(x)**2 + 15000*x**6*log(x)**8 + 80000*x**6*log(x)**6 + 60000*x**6*log(x)**4 + 20000*x*
*5*log(x)**8 + 40000*x**5*log(x)**6 + 10000*x**4*log(x)**8 + (312500*x**3 + 312500*x**2*log(x)**2 + 625000*x**
2 + 625000*x*log(x)**2)*exp(3*(3*x + 12)/(x + 3)) + (93750*x**6 + 187500*x**5*log(x)**2 + 375000*x**5 + 93750*
x**4*log(x)**4 + 750000*x**4*log(x)**2 + 375000*x**4 + 375000*x**3*log(x)**4 + 750000*x**3*log(x)**2 + 375000*
x**2*log(x)**4)*exp(2*(3*x + 12)/(x + 3)) + (12500*x**9 + 37500*x**8*log(x)**2 + 75000*x**8 + 37500*x**7*log(x
)**4 + 225000*x**7*log(x)**2 + 150000*x**7 + 12500*x**6*log(x)**6 + 225000*x**6*log(x)**4 + 450000*x**6*log(x)
**2 + 100000*x**6 + 75000*x**5*log(x)**6 + 450000*x**5*log(x)**4 + 300000*x**5*log(x)**2 + 150000*x**4*log(x)*
*6 + 300000*x**4*log(x)**4 + 100000*x**3*log(x)**6)*exp((3*x + 12)/(x + 3)) + 390625*exp(4*(3*x + 12)/(x + 3))
)

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