3.85.80 \(\int \frac {e^{1+2 x} (-225-425 x-10 x^2+450 x^3+287 x^4-41 x^5-99 x^6-35 x^7-4 x^8)+e (1500-2700 x^2-900 x^3+1620 x^4+1080 x^5-144 x^6-324 x^7-108 x^8-12 x^9)}{-16000 x^4+28800 x^6+9600 x^7-17280 x^8-11520 x^9+1536 x^{10}+3456 x^{11}+1152 x^{12}+128 x^{13}+e^{6 x} (54 x^4+54 x^5+18 x^6+2 x^7)+e^{4 x} (-1080 x^4-720 x^5+528 x^6+648 x^7+216 x^8+24 x^9)+e^{2 x} (7200 x^4+2400 x^5-8640 x^6-5760 x^7+1632 x^8+2592 x^9+864 x^{10}+96 x^{11})} \, dx\)

Optimal. Leaf size=35 \[ \frac {e}{2 x \left (x+x \left (3+\frac {e^{2 x}}{x^2-\frac {5}{3+x}}\right )\right )^2} \]

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Rubi [F]  time = 6.53, 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 {e^{1+2 x} \left (-225-425 x-10 x^2+450 x^3+287 x^4-41 x^5-99 x^6-35 x^7-4 x^8\right )+e \left (1500-2700 x^2-900 x^3+1620 x^4+1080 x^5-144 x^6-324 x^7-108 x^8-12 x^9\right )}{-16000 x^4+28800 x^6+9600 x^7-17280 x^8-11520 x^9+1536 x^{10}+3456 x^{11}+1152 x^{12}+128 x^{13}+e^{6 x} \left (54 x^4+54 x^5+18 x^6+2 x^7\right )+e^{4 x} \left (-1080 x^4-720 x^5+528 x^6+648 x^7+216 x^8+24 x^9\right )+e^{2 x} \left (7200 x^4+2400 x^5-8640 x^6-5760 x^7+1632 x^8+2592 x^9+864 x^{10}+96 x^{11}\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^(1 + 2*x)*(-225 - 425*x - 10*x^2 + 450*x^3 + 287*x^4 - 41*x^5 - 99*x^6 - 35*x^7 - 4*x^8) + E*(1500 - 27
00*x^2 - 900*x^3 + 1620*x^4 + 1080*x^5 - 144*x^6 - 324*x^7 - 108*x^8 - 12*x^9))/(-16000*x^4 + 28800*x^6 + 9600
*x^7 - 17280*x^8 - 11520*x^9 + 1536*x^10 + 3456*x^11 + 1152*x^12 + 128*x^13 + E^(6*x)*(54*x^4 + 54*x^5 + 18*x^
6 + 2*x^7) + E^(4*x)*(-1080*x^4 - 720*x^5 + 528*x^6 + 648*x^7 + 216*x^8 + 24*x^9) + E^(2*x)*(7200*x^4 + 2400*x
^5 - 8640*x^6 - 5760*x^7 + 1632*x^8 + 2592*x^9 + 864*x^10 + 96*x^11)),x]

[Out]

1320*E*Defer[Int][(-20 + 3*E^(2*x) + E^(2*x)*x + 12*x^2 + 4*x^3)^(-3), x] - (3500*E*Defer[Int][1/(x^3*(-20 + 3
*E^(2*x) + E^(2*x)*x + 12*x^2 + 4*x^3)^3), x])/3 - (4900*E*Defer[Int][1/(x^2*(-20 + 3*E^(2*x) + E^(2*x)*x + 12
*x^2 + 4*x^3)^3), x])/9 + (48100*E*Defer[Int][1/(x*(-20 + 3*E^(2*x) + E^(2*x)*x + 12*x^2 + 4*x^3)^3), x])/27 -
660*E*Defer[Int][x/(-20 + 3*E^(2*x) + E^(2*x)*x + 12*x^2 + 4*x^3)^3, x] - 876*E*Defer[Int][x^2/(-20 + 3*E^(2*
x) + E^(2*x)*x + 12*x^2 + 4*x^3)^3, x] - 120*E*Defer[Int][x^3/(-20 + 3*E^(2*x) + E^(2*x)*x + 12*x^2 + 4*x^3)^3
, x] + 144*E*Defer[Int][x^4/(-20 + 3*E^(2*x) + E^(2*x)*x + 12*x^2 + 4*x^3)^3, x] + 64*E*Defer[Int][x^5/(-20 +
3*E^(2*x) + E^(2*x)*x + 12*x^2 + 4*x^3)^3, x] + 8*E*Defer[Int][x^6/(-20 + 3*E^(2*x) + E^(2*x)*x + 12*x^2 + 4*x
^3)^3, x] + (500*E*Defer[Int][1/((3 + x)*(-20 + 3*E^(2*x) + E^(2*x)*x + 12*x^2 + 4*x^3)^3), x])/27 + (49*E*Def
er[Int][(-20 + 3*E^(2*x) + E^(2*x)*x + 12*x^2 + 4*x^3)^(-2), x])/2 - (75*E*Defer[Int][1/(x^4*(-20 + 3*E^(2*x)
+ E^(2*x)*x + 12*x^2 + 4*x^3)^2), x])/2 - (175*E*Defer[Int][1/(x^3*(-20 + 3*E^(2*x) + E^(2*x)*x + 12*x^2 + 4*x
^3)^2), x])/3 + (160*E*Defer[Int][1/(x^2*(-20 + 3*E^(2*x) + E^(2*x)*x + 12*x^2 + 4*x^3)^2), x])/9 + (1865*E*De
fer[Int][1/(x*(-20 + 3*E^(2*x) + E^(2*x)*x + 12*x^2 + 4*x^3)^2), x])/27 - 15*E*Defer[Int][x/(-20 + 3*E^(2*x) +
E^(2*x)*x + 12*x^2 + 4*x^3)^2, x] - (23*E*Defer[Int][x^2/(-20 + 3*E^(2*x) + E^(2*x)*x + 12*x^2 + 4*x^3)^2, x]
)/2 - 2*E*Defer[Int][x^3/(-20 + 3*E^(2*x) + E^(2*x)*x + 12*x^2 + 4*x^3)^2, x] + (25*E*Defer[Int][1/((3 + x)*(-
20 + 3*E^(2*x) + E^(2*x)*x + 12*x^2 + 4*x^3)^2), x])/27

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e \left (5-3 x^2-x^3\right ) \left (12 \left (-5+3 x^2+x^3\right )^2+e^{2 x} \left (-45-85 x-29 x^2+30 x^3+23 x^4+4 x^5\right )\right )}{2 x^4 \left (e^{2 x} (3+x)+4 \left (-5+3 x^2+x^3\right )\right )^3} \, dx\\ &=\frac {1}{2} e \int \frac {\left (5-3 x^2-x^3\right ) \left (12 \left (-5+3 x^2+x^3\right )^2+e^{2 x} \left (-45-85 x-29 x^2+30 x^3+23 x^4+4 x^5\right )\right )}{x^4 \left (e^{2 x} (3+x)+4 \left (-5+3 x^2+x^3\right )\right )^3} \, dx\\ &=\frac {1}{2} e \int \left (\frac {8 \left (-5+3 x^2+x^3\right )^2 \left (-35-28 x+6 x^2+10 x^3+2 x^4\right )}{x^3 (3+x) \left (-20+3 e^{2 x}+e^{2 x} x+12 x^2+4 x^3\right )^3}-\frac {225+425 x+10 x^2-450 x^3-287 x^4+41 x^5+99 x^6+35 x^7+4 x^8}{x^4 (3+x) \left (-20+3 e^{2 x}+e^{2 x} x+12 x^2+4 x^3\right )^2}\right ) \, dx\\ &=-\left (\frac {1}{2} e \int \frac {225+425 x+10 x^2-450 x^3-287 x^4+41 x^5+99 x^6+35 x^7+4 x^8}{x^4 (3+x) \left (-20+3 e^{2 x}+e^{2 x} x+12 x^2+4 x^3\right )^2} \, dx\right )+(4 e) \int \frac {\left (-5+3 x^2+x^3\right )^2 \left (-35-28 x+6 x^2+10 x^3+2 x^4\right )}{x^3 (3+x) \left (-20+3 e^{2 x}+e^{2 x} x+12 x^2+4 x^3\right )^3} \, dx\\ &=-\left (\frac {1}{2} e \int \left (-\frac {49}{\left (-20+3 e^{2 x}+e^{2 x} x+12 x^2+4 x^3\right )^2}+\frac {75}{x^4 \left (-20+3 e^{2 x}+e^{2 x} x+12 x^2+4 x^3\right )^2}+\frac {350}{3 x^3 \left (-20+3 e^{2 x}+e^{2 x} x+12 x^2+4 x^3\right )^2}-\frac {320}{9 x^2 \left (-20+3 e^{2 x}+e^{2 x} x+12 x^2+4 x^3\right )^2}-\frac {3730}{27 x \left (-20+3 e^{2 x}+e^{2 x} x+12 x^2+4 x^3\right )^2}+\frac {30 x}{\left (-20+3 e^{2 x}+e^{2 x} x+12 x^2+4 x^3\right )^2}+\frac {23 x^2}{\left (-20+3 e^{2 x}+e^{2 x} x+12 x^2+4 x^3\right )^2}+\frac {4 x^3}{\left (-20+3 e^{2 x}+e^{2 x} x+12 x^2+4 x^3\right )^2}-\frac {50}{27 (3+x) \left (-20+3 e^{2 x}+e^{2 x} x+12 x^2+4 x^3\right )^2}\right ) \, dx\right )+(4 e) \int \left (\frac {330}{\left (-20+3 e^{2 x}+e^{2 x} x+12 x^2+4 x^3\right )^3}-\frac {875}{3 x^3 \left (-20+3 e^{2 x}+e^{2 x} x+12 x^2+4 x^3\right )^3}-\frac {1225}{9 x^2 \left (-20+3 e^{2 x}+e^{2 x} x+12 x^2+4 x^3\right )^3}+\frac {12025}{27 x \left (-20+3 e^{2 x}+e^{2 x} x+12 x^2+4 x^3\right )^3}-\frac {165 x}{\left (-20+3 e^{2 x}+e^{2 x} x+12 x^2+4 x^3\right )^3}-\frac {219 x^2}{\left (-20+3 e^{2 x}+e^{2 x} x+12 x^2+4 x^3\right )^3}-\frac {30 x^3}{\left (-20+3 e^{2 x}+e^{2 x} x+12 x^2+4 x^3\right )^3}+\frac {36 x^4}{\left (-20+3 e^{2 x}+e^{2 x} x+12 x^2+4 x^3\right )^3}+\frac {16 x^5}{\left (-20+3 e^{2 x}+e^{2 x} x+12 x^2+4 x^3\right )^3}+\frac {2 x^6}{\left (-20+3 e^{2 x}+e^{2 x} x+12 x^2+4 x^3\right )^3}+\frac {125}{27 (3+x) \left (-20+3 e^{2 x}+e^{2 x} x+12 x^2+4 x^3\right )^3}\right ) \, dx\\ &=\frac {1}{27} (25 e) \int \frac {1}{(3+x) \left (-20+3 e^{2 x}+e^{2 x} x+12 x^2+4 x^3\right )^2} \, dx-(2 e) \int \frac {x^3}{\left (-20+3 e^{2 x}+e^{2 x} x+12 x^2+4 x^3\right )^2} \, dx+(8 e) \int \frac {x^6}{\left (-20+3 e^{2 x}+e^{2 x} x+12 x^2+4 x^3\right )^3} \, dx-\frac {1}{2} (23 e) \int \frac {x^2}{\left (-20+3 e^{2 x}+e^{2 x} x+12 x^2+4 x^3\right )^2} \, dx-(15 e) \int \frac {x}{\left (-20+3 e^{2 x}+e^{2 x} x+12 x^2+4 x^3\right )^2} \, dx+\frac {1}{9} (160 e) \int \frac {1}{x^2 \left (-20+3 e^{2 x}+e^{2 x} x+12 x^2+4 x^3\right )^2} \, dx+\frac {1}{27} (500 e) \int \frac {1}{(3+x) \left (-20+3 e^{2 x}+e^{2 x} x+12 x^2+4 x^3\right )^3} \, dx+\frac {1}{2} (49 e) \int \frac {1}{\left (-20+3 e^{2 x}+e^{2 x} x+12 x^2+4 x^3\right )^2} \, dx-\frac {1}{2} (75 e) \int \frac {1}{x^4 \left (-20+3 e^{2 x}+e^{2 x} x+12 x^2+4 x^3\right )^2} \, dx-\frac {1}{3} (175 e) \int \frac {1}{x^3 \left (-20+3 e^{2 x}+e^{2 x} x+12 x^2+4 x^3\right )^2} \, dx+(64 e) \int \frac {x^5}{\left (-20+3 e^{2 x}+e^{2 x} x+12 x^2+4 x^3\right )^3} \, dx+\frac {1}{27} (1865 e) \int \frac {1}{x \left (-20+3 e^{2 x}+e^{2 x} x+12 x^2+4 x^3\right )^2} \, dx-(120 e) \int \frac {x^3}{\left (-20+3 e^{2 x}+e^{2 x} x+12 x^2+4 x^3\right )^3} \, dx+(144 e) \int \frac {x^4}{\left (-20+3 e^{2 x}+e^{2 x} x+12 x^2+4 x^3\right )^3} \, dx-\frac {1}{9} (4900 e) \int \frac {1}{x^2 \left (-20+3 e^{2 x}+e^{2 x} x+12 x^2+4 x^3\right )^3} \, dx-(660 e) \int \frac {x}{\left (-20+3 e^{2 x}+e^{2 x} x+12 x^2+4 x^3\right )^3} \, dx-(876 e) \int \frac {x^2}{\left (-20+3 e^{2 x}+e^{2 x} x+12 x^2+4 x^3\right )^3} \, dx-\frac {1}{3} (3500 e) \int \frac {1}{x^3 \left (-20+3 e^{2 x}+e^{2 x} x+12 x^2+4 x^3\right )^3} \, dx+(1320 e) \int \frac {1}{\left (-20+3 e^{2 x}+e^{2 x} x+12 x^2+4 x^3\right )^3} \, dx+\frac {1}{27} (48100 e) \int \frac {1}{x \left (-20+3 e^{2 x}+e^{2 x} x+12 x^2+4 x^3\right )^3} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.07, size = 44, normalized size = 1.26 \begin {gather*} \frac {e \left (-5+3 x^2+x^3\right )^2}{2 x^3 \left (e^{2 x} (3+x)+4 \left (-5+3 x^2+x^3\right )\right )^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^(1 + 2*x)*(-225 - 425*x - 10*x^2 + 450*x^3 + 287*x^4 - 41*x^5 - 99*x^6 - 35*x^7 - 4*x^8) + E*(150
0 - 2700*x^2 - 900*x^3 + 1620*x^4 + 1080*x^5 - 144*x^6 - 324*x^7 - 108*x^8 - 12*x^9))/(-16000*x^4 + 28800*x^6
+ 9600*x^7 - 17280*x^8 - 11520*x^9 + 1536*x^10 + 3456*x^11 + 1152*x^12 + 128*x^13 + E^(6*x)*(54*x^4 + 54*x^5 +
18*x^6 + 2*x^7) + E^(4*x)*(-1080*x^4 - 720*x^5 + 528*x^6 + 648*x^7 + 216*x^8 + 24*x^9) + E^(2*x)*(7200*x^4 +
2400*x^5 - 8640*x^6 - 5760*x^7 + 1632*x^8 + 2592*x^9 + 864*x^10 + 96*x^11)),x]

[Out]

(E*(-5 + 3*x^2 + x^3)^2)/(2*x^3*(E^(2*x)*(3 + x) + 4*(-5 + 3*x^2 + x^3))^2)

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fricas [B]  time = 0.66, size = 118, normalized size = 3.37 \begin {gather*} \frac {{\left (x^{6} + 6 \, x^{5} + 9 \, x^{4} - 10 \, x^{3} - 30 \, x^{2} + 25\right )} e^{3}}{2 \, {\left (16 \, {\left (x^{9} + 6 \, x^{8} + 9 \, x^{7} - 10 \, x^{6} - 30 \, x^{5} + 25 \, x^{3}\right )} e^{2} + {\left (x^{5} + 6 \, x^{4} + 9 \, x^{3}\right )} e^{\left (4 \, x + 2\right )} + 8 \, {\left (x^{7} + 6 \, x^{6} + 9 \, x^{5} - 5 \, x^{4} - 15 \, x^{3}\right )} e^{\left (2 \, x + 2\right )}\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-4*x^8-35*x^7-99*x^6-41*x^5+287*x^4+450*x^3-10*x^2-425*x-225)*exp(1)*exp(x)^2+(-12*x^9-108*x^8-324
*x^7-144*x^6+1080*x^5+1620*x^4-900*x^3-2700*x^2+1500)*exp(1))/((2*x^7+18*x^6+54*x^5+54*x^4)*exp(x)^6+(24*x^9+2
16*x^8+648*x^7+528*x^6-720*x^5-1080*x^4)*exp(x)^4+(96*x^11+864*x^10+2592*x^9+1632*x^8-5760*x^7-8640*x^6+2400*x
^5+7200*x^4)*exp(x)^2+128*x^13+1152*x^12+3456*x^11+1536*x^10-11520*x^9-17280*x^8+9600*x^7+28800*x^6-16000*x^4)
,x, algorithm="fricas")

[Out]

1/2*(x^6 + 6*x^5 + 9*x^4 - 10*x^3 - 30*x^2 + 25)*e^3/(16*(x^9 + 6*x^8 + 9*x^7 - 10*x^6 - 30*x^5 + 25*x^3)*e^2
+ (x^5 + 6*x^4 + 9*x^3)*e^(4*x + 2) + 8*(x^7 + 6*x^6 + 9*x^5 - 5*x^4 - 15*x^3)*e^(2*x + 2))

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giac [B]  time = 0.22, size = 145, normalized size = 4.14 \begin {gather*} \frac {x^{6} e + 6 \, x^{5} e + 9 \, x^{4} e - 10 \, x^{3} e - 30 \, x^{2} e + 25 \, e}{2 \, {\left (16 \, x^{9} + 96 \, x^{8} + 8 \, x^{7} e^{\left (2 \, x\right )} + 144 \, x^{7} + 48 \, x^{6} e^{\left (2 \, x\right )} - 160 \, x^{6} + x^{5} e^{\left (4 \, x\right )} + 72 \, x^{5} e^{\left (2 \, x\right )} - 480 \, x^{5} + 6 \, x^{4} e^{\left (4 \, x\right )} - 40 \, x^{4} e^{\left (2 \, x\right )} + 9 \, x^{3} e^{\left (4 \, x\right )} - 120 \, x^{3} e^{\left (2 \, x\right )} + 400 \, x^{3}\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-4*x^8-35*x^7-99*x^6-41*x^5+287*x^4+450*x^3-10*x^2-425*x-225)*exp(1)*exp(x)^2+(-12*x^9-108*x^8-324
*x^7-144*x^6+1080*x^5+1620*x^4-900*x^3-2700*x^2+1500)*exp(1))/((2*x^7+18*x^6+54*x^5+54*x^4)*exp(x)^6+(24*x^9+2
16*x^8+648*x^7+528*x^6-720*x^5-1080*x^4)*exp(x)^4+(96*x^11+864*x^10+2592*x^9+1632*x^8-5760*x^7-8640*x^6+2400*x
^5+7200*x^4)*exp(x)^2+128*x^13+1152*x^12+3456*x^11+1536*x^10-11520*x^9-17280*x^8+9600*x^7+28800*x^6-16000*x^4)
,x, algorithm="giac")

[Out]

1/2*(x^6*e + 6*x^5*e + 9*x^4*e - 10*x^3*e - 30*x^2*e + 25*e)/(16*x^9 + 96*x^8 + 8*x^7*e^(2*x) + 144*x^7 + 48*x
^6*e^(2*x) - 160*x^6 + x^5*e^(4*x) + 72*x^5*e^(2*x) - 480*x^5 + 6*x^4*e^(4*x) - 40*x^4*e^(2*x) + 9*x^3*e^(4*x)
- 120*x^3*e^(2*x) + 400*x^3)

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maple [A]  time = 0.08, size = 59, normalized size = 1.69

method	result	size
risch	\(\frac {{\mathrm e} \left (x^{6}+6 x^{5}+9 x^{4}-10 x^{3}-30 x^{2}+25\right )}{2 x^{3} \left (x \,{\mathrm e}^{2 x}+4 x^{3}+3 \,{\mathrm e}^{2 x}+12 x^{2}-20\right )^{2}}\)	\(59\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-4*x^8-35*x^7-99*x^6-41*x^5+287*x^4+450*x^3-10*x^2-425*x-225)*exp(1)*exp(x)^2+(-12*x^9-108*x^8-324*x^7-1
44*x^6+1080*x^5+1620*x^4-900*x^3-2700*x^2+1500)*exp(1))/((2*x^7+18*x^6+54*x^5+54*x^4)*exp(x)^6+(24*x^9+216*x^8
+648*x^7+528*x^6-720*x^5-1080*x^4)*exp(x)^4+(96*x^11+864*x^10+2592*x^9+1632*x^8-5760*x^7-8640*x^6+2400*x^5+720
0*x^4)*exp(x)^2+128*x^13+1152*x^12+3456*x^11+1536*x^10-11520*x^9-17280*x^8+9600*x^7+28800*x^6-16000*x^4),x,met
hod=_RETURNVERBOSE)

[Out]

1/2*exp(1)*(x^6+6*x^5+9*x^4-10*x^3-30*x^2+25)/x^3/(x*exp(2*x)+4*x^3+3*exp(2*x)+12*x^2-20)^2

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maxima [B]  time = 0.71, size = 123, normalized size = 3.51 \begin {gather*} \frac {x^{6} e + 6 \, x^{5} e + 9 \, x^{4} e - 10 \, x^{3} e - 30 \, x^{2} e + 25 \, e}{2 \, {\left (16 \, x^{9} + 96 \, x^{8} + 144 \, x^{7} - 160 \, x^{6} - 480 \, x^{5} + 400 \, x^{3} + {\left (x^{5} + 6 \, x^{4} + 9 \, x^{3}\right )} e^{\left (4 \, x\right )} + 8 \, {\left (x^{7} + 6 \, x^{6} + 9 \, x^{5} - 5 \, x^{4} - 15 \, x^{3}\right )} e^{\left (2 \, x\right )}\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-4*x^8-35*x^7-99*x^6-41*x^5+287*x^4+450*x^3-10*x^2-425*x-225)*exp(1)*exp(x)^2+(-12*x^9-108*x^8-324
*x^7-144*x^6+1080*x^5+1620*x^4-900*x^3-2700*x^2+1500)*exp(1))/((2*x^7+18*x^6+54*x^5+54*x^4)*exp(x)^6+(24*x^9+2
16*x^8+648*x^7+528*x^6-720*x^5-1080*x^4)*exp(x)^4+(96*x^11+864*x^10+2592*x^9+1632*x^8-5760*x^7-8640*x^6+2400*x
^5+7200*x^4)*exp(x)^2+128*x^13+1152*x^12+3456*x^11+1536*x^10-11520*x^9-17280*x^8+9600*x^7+28800*x^6-16000*x^4)
,x, algorithm="maxima")

[Out]

1/2*(x^6*e + 6*x^5*e + 9*x^4*e - 10*x^3*e - 30*x^2*e + 25*e)/(16*x^9 + 96*x^8 + 144*x^7 - 160*x^6 - 480*x^5 +
400*x^3 + (x^5 + 6*x^4 + 9*x^3)*e^(4*x) + 8*(x^7 + 6*x^6 + 9*x^5 - 5*x^4 - 15*x^3)*e^(2*x))

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mupad [F]  time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int -\frac {\mathrm {e}\,\left (12\,x^9+108\,x^8+324\,x^7+144\,x^6-1080\,x^5-1620\,x^4+900\,x^3+2700\,x^2-1500\right )+{\mathrm {e}}^{2\,x}\,\mathrm {e}\,\left (4\,x^8+35\,x^7+99\,x^6+41\,x^5-287\,x^4-450\,x^3+10\,x^2+425\,x+225\right )}{{\mathrm {e}}^{4\,x}\,\left (24\,x^9+216\,x^8+648\,x^7+528\,x^6-720\,x^5-1080\,x^4\right )+{\mathrm {e}}^{2\,x}\,\left (96\,x^{11}+864\,x^{10}+2592\,x^9+1632\,x^8-5760\,x^7-8640\,x^6+2400\,x^5+7200\,x^4\right )+{\mathrm {e}}^{6\,x}\,\left (2\,x^7+18\,x^6+54\,x^5+54\,x^4\right )-16000\,x^4+28800\,x^6+9600\,x^7-17280\,x^8-11520\,x^9+1536\,x^{10}+3456\,x^{11}+1152\,x^{12}+128\,x^{13}} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(1)*(2700*x^2 + 900*x^3 - 1620*x^4 - 1080*x^5 + 144*x^6 + 324*x^7 + 108*x^8 + 12*x^9 - 1500) + exp(2*
x)*exp(1)*(425*x + 10*x^2 - 450*x^3 - 287*x^4 + 41*x^5 + 99*x^6 + 35*x^7 + 4*x^8 + 225))/(exp(4*x)*(528*x^6 -
720*x^5 - 1080*x^4 + 648*x^7 + 216*x^8 + 24*x^9) + exp(2*x)*(7200*x^4 + 2400*x^5 - 8640*x^6 - 5760*x^7 + 1632*
x^8 + 2592*x^9 + 864*x^10 + 96*x^11) + exp(6*x)*(54*x^4 + 54*x^5 + 18*x^6 + 2*x^7) - 16000*x^4 + 28800*x^6 + 9
600*x^7 - 17280*x^8 - 11520*x^9 + 1536*x^10 + 3456*x^11 + 1152*x^12 + 128*x^13),x)

[Out]

int(-(exp(1)*(2700*x^2 + 900*x^3 - 1620*x^4 - 1080*x^5 + 144*x^6 + 324*x^7 + 108*x^8 + 12*x^9 - 1500) + exp(2*
x)*exp(1)*(425*x + 10*x^2 - 450*x^3 - 287*x^4 + 41*x^5 + 99*x^6 + 35*x^7 + 4*x^8 + 225))/(exp(4*x)*(528*x^6 -
720*x^5 - 1080*x^4 + 648*x^7 + 216*x^8 + 24*x^9) + exp(2*x)*(7200*x^4 + 2400*x^5 - 8640*x^6 - 5760*x^7 + 1632*
x^8 + 2592*x^9 + 864*x^10 + 96*x^11) + exp(6*x)*(54*x^4 + 54*x^5 + 18*x^6 + 2*x^7) - 16000*x^4 + 28800*x^6 + 9
600*x^7 - 17280*x^8 - 11520*x^9 + 1536*x^10 + 3456*x^11 + 1152*x^12 + 128*x^13), x)

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sympy [B]  time = 0.75, size = 126, normalized size = 3.60 \begin {gather*} \frac {e x^{6} + 6 e x^{5} + 9 e x^{4} - 10 e x^{3} - 30 e x^{2} + 25 e}{32 x^{9} + 192 x^{8} + 288 x^{7} - 320 x^{6} - 960 x^{5} + 800 x^{3} + \left (2 x^{5} + 12 x^{4} + 18 x^{3}\right ) e^{4 x} + \left (16 x^{7} + 96 x^{6} + 144 x^{5} - 80 x^{4} - 240 x^{3}\right ) e^{2 x}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-4*x**8-35*x**7-99*x**6-41*x**5+287*x**4+450*x**3-10*x**2-425*x-225)*exp(1)*exp(x)**2+(-12*x**9-10
8*x**8-324*x**7-144*x**6+1080*x**5+1620*x**4-900*x**3-2700*x**2+1500)*exp(1))/((2*x**7+18*x**6+54*x**5+54*x**4
)*exp(x)**6+(24*x**9+216*x**8+648*x**7+528*x**6-720*x**5-1080*x**4)*exp(x)**4+(96*x**11+864*x**10+2592*x**9+16
32*x**8-5760*x**7-8640*x**6+2400*x**5+7200*x**4)*exp(x)**2+128*x**13+1152*x**12+3456*x**11+1536*x**10-11520*x*
*9-17280*x**8+9600*x**7+28800*x**6-16000*x**4),x)

[Out]

(E*x**6 + 6*E*x**5 + 9*E*x**4 - 10*E*x**3 - 30*E*x**2 + 25*E)/(32*x**9 + 192*x**8 + 288*x**7 - 320*x**6 - 960*
x**5 + 800*x**3 + (2*x**5 + 12*x**4 + 18*x**3)*exp(4*x) + (16*x**7 + 96*x**6 + 144*x**5 - 80*x**4 - 240*x**3)*
exp(2*x))

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