3.22.16 \(\int \frac {560 x^7-x^9+e^{3 x} (320 x^4-x^6)+e^{2 x} (-38400 x^3+38400 x^4+1320 x^5-120 x^6-3 x^7)+e^x (-67200 x^4+67200 x^5+1560 x^6-120 x^7-3 x^8)+e^{30+15 x} (e^{3 x} x^3-240 x^4+x^6+e^{2 x} (-360 x^2+120 x^3+3 x^4)+e^x (28800 x-28800 x^2-600 x^3+120 x^4+3 x^5))+e^{20+10 x} (-38400 x^3+192000 x^4+1200 x^5-800 x^6-3 x^7+e^{3 x} (480 x^2-800 x^3-3 x^4)+e^{2 x} (-76800 x+230400 x^2+2520 x^3-2760 x^4-9 x^5)+e^x (-201600 x^2+508800 x^3+3240 x^4-2760 x^5-9 x^6))+e^{10+5 x} (89600 x^4-448000 x^5-1520 x^6+800 x^7+3 x^8+e^{3 x} (51200 x-256000 x^2-800 x^3+800 x^4+3 x^5)+e^{2 x} (268800 x^2-1036800 x^3-3480 x^4+2760 x^5+9 x^6)+e^x (393600 x^3-1315200 x^4-4200 x^5+2760 x^6+9 x^7))}{-1600 e^{3 x} x^3-4800 e^{2 x} x^4-4800 e^x x^5-1600 x^6+e^{30+15 x} (1600 e^{3 x}+4800 e^{2 x} x+4800 e^x x^2+1600 x^3)+e^{20+10 x} (-4800 e^{3 x} x-14400 e^{2 x} x^2-14400 e^x x^3-4800 x^4)+e^{10+5 x} (4800 e^{3 x} x^2+14400 e^{2 x} x^3+14400 e^x x^4+4800 x^5)} \, dx\)

Optimal. Leaf size=36 \[ x^2 \left (-\frac {x}{80}+\frac {3}{e^x+x}+\frac {4}{-e^{5 (2+x)}+x}\right )^2 \]

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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[(560*x^7 - x^9 + E^(3*x)*(320*x^4 - x^6) + E^(2*x)*(-38400*x^3 + 38400*x^4 + 1320*x^5 - 120*x^6 - 3*x^7) +
E^x*(-67200*x^4 + 67200*x^5 + 1560*x^6 - 120*x^7 - 3*x^8) + E^(30 + 15*x)*(E^(3*x)*x^3 - 240*x^4 + x^6 + E^(2
*x)*(-360*x^2 + 120*x^3 + 3*x^4) + E^x*(28800*x - 28800*x^2 - 600*x^3 + 120*x^4 + 3*x^5)) + E^(20 + 10*x)*(-38
400*x^3 + 192000*x^4 + 1200*x^5 - 800*x^6 - 3*x^7 + E^(3*x)*(480*x^2 - 800*x^3 - 3*x^4) + E^(2*x)*(-76800*x +
230400*x^2 + 2520*x^3 - 2760*x^4 - 9*x^5) + E^x*(-201600*x^2 + 508800*x^3 + 3240*x^4 - 2760*x^5 - 9*x^6)) + E^
(10 + 5*x)*(89600*x^4 - 448000*x^5 - 1520*x^6 + 800*x^7 + 3*x^8 + E^(3*x)*(51200*x - 256000*x^2 - 800*x^3 + 80
0*x^4 + 3*x^5) + E^(2*x)*(268800*x^2 - 1036800*x^3 - 3480*x^4 + 2760*x^5 + 9*x^6) + E^x*(393600*x^3 - 1315200*
x^4 - 4200*x^5 + 2760*x^6 + 9*x^7)))/(-1600*E^(3*x)*x^3 - 4800*E^(2*x)*x^4 - 4800*E^x*x^5 - 1600*x^6 + E^(30 +
15*x)*(1600*E^(3*x) + 4800*E^(2*x)*x + 4800*E^x*x^2 + 1600*x^3) + E^(20 + 10*x)*(-4800*E^(3*x)*x - 14400*E^(2
*x)*x^2 - 14400*E^x*x^3 - 4800*x^4) + E^(10 + 5*x)*(4800*E^(3*x)*x^2 + 14400*E^(2*x)*x^3 + 14400*E^x*x^4 + 480
0*x^5)),x]

[Out]

$Aborted

Rubi steps

Aborted

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Mathematica [B]  time = 0.54, size = 80, normalized size = 2.22 \begin {gather*} \frac {x^2 \left (e^{10+6 x} x-x \left (-560+x^2\right )-e^x \left (-320+x^2\right )+e^{5 (2+x)} \left (-240+x^2\right )\right )^2}{6400 \left (e^{10+6 x}-e^x x+e^{5 (2+x)} x-x^2\right )^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(560*x^7 - x^9 + E^(3*x)*(320*x^4 - x^6) + E^(2*x)*(-38400*x^3 + 38400*x^4 + 1320*x^5 - 120*x^6 - 3*
x^7) + E^x*(-67200*x^4 + 67200*x^5 + 1560*x^6 - 120*x^7 - 3*x^8) + E^(30 + 15*x)*(E^(3*x)*x^3 - 240*x^4 + x^6
+ E^(2*x)*(-360*x^2 + 120*x^3 + 3*x^4) + E^x*(28800*x - 28800*x^2 - 600*x^3 + 120*x^4 + 3*x^5)) + E^(20 + 10*x
)*(-38400*x^3 + 192000*x^4 + 1200*x^5 - 800*x^6 - 3*x^7 + E^(3*x)*(480*x^2 - 800*x^3 - 3*x^4) + E^(2*x)*(-7680
0*x + 230400*x^2 + 2520*x^3 - 2760*x^4 - 9*x^5) + E^x*(-201600*x^2 + 508800*x^3 + 3240*x^4 - 2760*x^5 - 9*x^6)
) + E^(10 + 5*x)*(89600*x^4 - 448000*x^5 - 1520*x^6 + 800*x^7 + 3*x^8 + E^(3*x)*(51200*x - 256000*x^2 - 800*x^
3 + 800*x^4 + 3*x^5) + E^(2*x)*(268800*x^2 - 1036800*x^3 - 3480*x^4 + 2760*x^5 + 9*x^6) + E^x*(393600*x^3 - 13
15200*x^4 - 4200*x^5 + 2760*x^6 + 9*x^7)))/(-1600*E^(3*x)*x^3 - 4800*E^(2*x)*x^4 - 4800*E^x*x^5 - 1600*x^6 + E
^(30 + 15*x)*(1600*E^(3*x) + 4800*E^(2*x)*x + 4800*E^x*x^2 + 1600*x^3) + E^(20 + 10*x)*(-4800*E^(3*x)*x - 1440
0*E^(2*x)*x^2 - 14400*E^x*x^3 - 4800*x^4) + E^(10 + 5*x)*(4800*E^(3*x)*x^2 + 14400*E^(2*x)*x^3 + 14400*E^x*x^4
+ 4800*x^5)),x]

[Out]

(x^2*(E^(10 + 6*x)*x - x*(-560 + x^2) - E^x*(-320 + x^2) + E^(5*(2 + x))*(-240 + x^2))^2)/(6400*(E^(10 + 6*x)
- E^x*x + E^(5*(2 + x))*x - x^2)^2)

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fricas [B]  time = 0.80, size = 239, normalized size = 6.64 \begin {gather*} \frac {x^{8} - 1120 \, x^{6} + x^{4} e^{\left (12 \, x + 20\right )} + 313600 \, x^{4} + {\left (x^{6} - 640 \, x^{4} + 102400 \, x^{2}\right )} e^{\left (2 \, x\right )} + 2 \, {\left (x^{5} - 240 \, x^{3}\right )} e^{\left (11 \, x + 20\right )} + {\left (x^{6} - 480 \, x^{4} + 57600 \, x^{2}\right )} e^{\left (10 \, x + 20\right )} - 2 \, {\left (x^{5} - 320 \, x^{3}\right )} e^{\left (7 \, x + 10\right )} - 4 \, {\left (x^{6} - 560 \, x^{4} + 38400 \, x^{2}\right )} e^{\left (6 \, x + 10\right )} - 2 \, {\left (x^{7} - 800 \, x^{5} + 134400 \, x^{3}\right )} e^{\left (5 \, x + 10\right )} + 2 \, {\left (x^{7} - 880 \, x^{5} + 179200 \, x^{3}\right )} e^{x}}{6400 \, {\left (x^{4} - 2 \, x^{3} e^{\left (5 \, x + 10\right )} + 2 \, x^{3} e^{x} + x^{2} e^{\left (2 \, x\right )} + x^{2} e^{\left (10 \, x + 20\right )} - 4 \, x^{2} e^{\left (6 \, x + 10\right )} + 2 \, x e^{\left (11 \, x + 20\right )} - 2 \, x e^{\left (7 \, x + 10\right )} + e^{\left (12 \, x + 20\right )}\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((x^3*exp(x)^3+(3*x^4+120*x^3-360*x^2)*exp(x)^2+(3*x^5+120*x^4-600*x^3-28800*x^2+28800*x)*exp(x)+x^6
-240*x^4)*exp(5*x+10)^3+((-3*x^4-800*x^3+480*x^2)*exp(x)^3+(-9*x^5-2760*x^4+2520*x^3+230400*x^2-76800*x)*exp(x
)^2+(-9*x^6-2760*x^5+3240*x^4+508800*x^3-201600*x^2)*exp(x)-3*x^7-800*x^6+1200*x^5+192000*x^4-38400*x^3)*exp(5
*x+10)^2+((3*x^5+800*x^4-800*x^3-256000*x^2+51200*x)*exp(x)^3+(9*x^6+2760*x^5-3480*x^4-1036800*x^3+268800*x^2)
*exp(x)^2+(9*x^7+2760*x^6-4200*x^5-1315200*x^4+393600*x^3)*exp(x)+3*x^8+800*x^7-1520*x^6-448000*x^5+89600*x^4)
*exp(5*x+10)+(-x^6+320*x^4)*exp(x)^3+(-3*x^7-120*x^6+1320*x^5+38400*x^4-38400*x^3)*exp(x)^2+(-3*x^8-120*x^7+15
60*x^6+67200*x^5-67200*x^4)*exp(x)-x^9+560*x^7)/((1600*exp(x)^3+4800*x*exp(x)^2+4800*exp(x)*x^2+1600*x^3)*exp(
5*x+10)^3+(-4800*x*exp(x)^3-14400*exp(x)^2*x^2-14400*exp(x)*x^3-4800*x^4)*exp(5*x+10)^2+(4800*x^2*exp(x)^3+144
00*exp(x)^2*x^3+14400*exp(x)*x^4+4800*x^5)*exp(5*x+10)-1600*x^3*exp(x)^3-4800*exp(x)^2*x^4-4800*x^5*exp(x)-160
0*x^6),x, algorithm="fricas")

[Out]

1/6400*(x^8 - 1120*x^6 + x^4*e^(12*x + 20) + 313600*x^4 + (x^6 - 640*x^4 + 102400*x^2)*e^(2*x) + 2*(x^5 - 240*
x^3)*e^(11*x + 20) + (x^6 - 480*x^4 + 57600*x^2)*e^(10*x + 20) - 2*(x^5 - 320*x^3)*e^(7*x + 10) - 4*(x^6 - 560
*x^4 + 38400*x^2)*e^(6*x + 10) - 2*(x^7 - 800*x^5 + 134400*x^3)*e^(5*x + 10) + 2*(x^7 - 880*x^5 + 179200*x^3)*
e^x)/(x^4 - 2*x^3*e^(5*x + 10) + 2*x^3*e^x + x^2*e^(2*x) + x^2*e^(10*x + 20) - 4*x^2*e^(6*x + 10) + 2*x*e^(11*
x + 20) - 2*x*e^(7*x + 10) + e^(12*x + 20))

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giac [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(((x^3*exp(x)^3+(3*x^4+120*x^3-360*x^2)*exp(x)^2+(3*x^5+120*x^4-600*x^3-28800*x^2+28800*x)*exp(x)+x^6
-240*x^4)*exp(5*x+10)^3+((-3*x^4-800*x^3+480*x^2)*exp(x)^3+(-9*x^5-2760*x^4+2520*x^3+230400*x^2-76800*x)*exp(x
)^2+(-9*x^6-2760*x^5+3240*x^4+508800*x^3-201600*x^2)*exp(x)-3*x^7-800*x^6+1200*x^5+192000*x^4-38400*x^3)*exp(5
*x+10)^2+((3*x^5+800*x^4-800*x^3-256000*x^2+51200*x)*exp(x)^3+(9*x^6+2760*x^5-3480*x^4-1036800*x^3+268800*x^2)
*exp(x)^2+(9*x^7+2760*x^6-4200*x^5-1315200*x^4+393600*x^3)*exp(x)+3*x^8+800*x^7-1520*x^6-448000*x^5+89600*x^4)
*exp(5*x+10)+(-x^6+320*x^4)*exp(x)^3+(-3*x^7-120*x^6+1320*x^5+38400*x^4-38400*x^3)*exp(x)^2+(-3*x^8-120*x^7+15
60*x^6+67200*x^5-67200*x^4)*exp(x)-x^9+560*x^7)/((1600*exp(x)^3+4800*x*exp(x)^2+4800*exp(x)*x^2+1600*x^3)*exp(
5*x+10)^3+(-4800*x*exp(x)^3-14400*exp(x)^2*x^2-14400*exp(x)*x^3-4800*x^4)*exp(5*x+10)^2+(4800*x^2*exp(x)^3+144
00*exp(x)^2*x^3+14400*exp(x)*x^4+4800*x^5)*exp(5*x+10)-1600*x^3*exp(x)^3-4800*exp(x)^2*x^4-4800*x^5*exp(x)-160
0*x^6),x, algorithm="giac")

[Out]

Timed out

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maple [B]  time = 0.24, size = 153, normalized size = 4.25

method	result	size
risch	\(\frac {x^{4}}{6400}-\frac {x^{2} \left (3 x^{2} {\mathrm e}^{10 x +20}+3 x \,{\mathrm e}^{11 x +20}-360 \,{\mathrm e}^{10 x +20}-10 \,{\mathrm e}^{5 x +10} x^{3}-14 x^{2} {\mathrm e}^{6 x +10}-4 x \,{\mathrm e}^{7 x +10}+1680 \,{\mathrm e}^{5 x +10} x +960 \,{\mathrm e}^{6 x +10}+7 x^{4}+11 \,{\mathrm e}^{x} x^{3}+4 \,{\mathrm e}^{2 x} x^{2}-1960 x^{2}-2240 \,{\mathrm e}^{x} x -640 \,{\mathrm e}^{2 x}\right )}{40 \left ({\mathrm e}^{5 x +10} x +{\mathrm e}^{6 x +10}-x^{2}-{\mathrm e}^{x} x \right )^{2}}\)	\(153\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((x^3*exp(x)^3+(3*x^4+120*x^3-360*x^2)*exp(x)^2+(3*x^5+120*x^4-600*x^3-28800*x^2+28800*x)*exp(x)+x^6-240*x
^4)*exp(5*x+10)^3+((-3*x^4-800*x^3+480*x^2)*exp(x)^3+(-9*x^5-2760*x^4+2520*x^3+230400*x^2-76800*x)*exp(x)^2+(-
9*x^6-2760*x^5+3240*x^4+508800*x^3-201600*x^2)*exp(x)-3*x^7-800*x^6+1200*x^5+192000*x^4-38400*x^3)*exp(5*x+10)
^2+((3*x^5+800*x^4-800*x^3-256000*x^2+51200*x)*exp(x)^3+(9*x^6+2760*x^5-3480*x^4-1036800*x^3+268800*x^2)*exp(x
)^2+(9*x^7+2760*x^6-4200*x^5-1315200*x^4+393600*x^3)*exp(x)+3*x^8+800*x^7-1520*x^6-448000*x^5+89600*x^4)*exp(5
*x+10)+(-x^6+320*x^4)*exp(x)^3+(-3*x^7-120*x^6+1320*x^5+38400*x^4-38400*x^3)*exp(x)^2+(-3*x^8-120*x^7+1560*x^6
+67200*x^5-67200*x^4)*exp(x)-x^9+560*x^7)/((1600*exp(x)^3+4800*x*exp(x)^2+4800*exp(x)*x^2+1600*x^3)*exp(5*x+10
)^3+(-4800*x*exp(x)^3-14400*exp(x)^2*x^2-14400*exp(x)*x^3-4800*x^4)*exp(5*x+10)^2+(4800*x^2*exp(x)^3+14400*exp
(x)^2*x^3+14400*exp(x)*x^4+4800*x^5)*exp(5*x+10)-1600*x^3*exp(x)^3-4800*exp(x)^2*x^4-4800*x^5*exp(x)-1600*x^6)
,x,method=_RETURNVERBOSE)

[Out]

1/6400*x^4-1/40*x^2*(3*x^2*exp(10*x+20)+3*x*exp(11*x+20)-360*exp(10*x+20)-10*exp(5*x+10)*x^3-14*x^2*exp(6*x+10
)-4*x*exp(7*x+10)+1680*exp(5*x+10)*x+960*exp(6*x+10)+7*x^4+11*exp(x)*x^3+4*exp(2*x)*x^2-1960*x^2-2240*exp(x)*x
-640*exp(2*x))/(exp(5*x+10)*x+exp(6*x+10)-x^2-exp(x)*x)^2

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maxima [B]  time = 4.08, size = 260, normalized size = 7.22 \begin {gather*} \frac {x^{8} - 1120 \, x^{6} + x^{4} e^{\left (12 \, x + 20\right )} + 313600 \, x^{4} + 2 \, {\left (x^{5} e^{20} - 240 \, x^{3} e^{20}\right )} e^{\left (11 \, x\right )} + {\left (x^{6} e^{20} - 480 \, x^{4} e^{20} + 57600 \, x^{2} e^{20}\right )} e^{\left (10 \, x\right )} - 2 \, {\left (x^{5} e^{10} - 320 \, x^{3} e^{10}\right )} e^{\left (7 \, x\right )} - 4 \, {\left (x^{6} e^{10} - 560 \, x^{4} e^{10} + 38400 \, x^{2} e^{10}\right )} e^{\left (6 \, x\right )} - 2 \, {\left (x^{7} e^{10} - 800 \, x^{5} e^{10} + 134400 \, x^{3} e^{10}\right )} e^{\left (5 \, x\right )} + {\left (x^{6} - 640 \, x^{4} + 102400 \, x^{2}\right )} e^{\left (2 \, x\right )} + 2 \, {\left (x^{7} - 880 \, x^{5} + 179200 \, x^{3}\right )} e^{x}}{6400 \, {\left (x^{4} - 2 \, x^{3} e^{\left (5 \, x + 10\right )} + 2 \, x^{3} e^{x} + x^{2} e^{\left (2 \, x\right )} + x^{2} e^{\left (10 \, x + 20\right )} - 4 \, x^{2} e^{\left (6 \, x + 10\right )} + 2 \, x e^{\left (11 \, x + 20\right )} - 2 \, x e^{\left (7 \, x + 10\right )} + e^{\left (12 \, x + 20\right )}\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((x^3*exp(x)^3+(3*x^4+120*x^3-360*x^2)*exp(x)^2+(3*x^5+120*x^4-600*x^3-28800*x^2+28800*x)*exp(x)+x^6
-240*x^4)*exp(5*x+10)^3+((-3*x^4-800*x^3+480*x^2)*exp(x)^3+(-9*x^5-2760*x^4+2520*x^3+230400*x^2-76800*x)*exp(x
)^2+(-9*x^6-2760*x^5+3240*x^4+508800*x^3-201600*x^2)*exp(x)-3*x^7-800*x^6+1200*x^5+192000*x^4-38400*x^3)*exp(5
*x+10)^2+((3*x^5+800*x^4-800*x^3-256000*x^2+51200*x)*exp(x)^3+(9*x^6+2760*x^5-3480*x^4-1036800*x^3+268800*x^2)
*exp(x)^2+(9*x^7+2760*x^6-4200*x^5-1315200*x^4+393600*x^3)*exp(x)+3*x^8+800*x^7-1520*x^6-448000*x^5+89600*x^4)
*exp(5*x+10)+(-x^6+320*x^4)*exp(x)^3+(-3*x^7-120*x^6+1320*x^5+38400*x^4-38400*x^3)*exp(x)^2+(-3*x^8-120*x^7+15
60*x^6+67200*x^5-67200*x^4)*exp(x)-x^9+560*x^7)/((1600*exp(x)^3+4800*x*exp(x)^2+4800*exp(x)*x^2+1600*x^3)*exp(
5*x+10)^3+(-4800*x*exp(x)^3-14400*exp(x)^2*x^2-14400*exp(x)*x^3-4800*x^4)*exp(5*x+10)^2+(4800*x^2*exp(x)^3+144
00*exp(x)^2*x^3+14400*exp(x)*x^4+4800*x^5)*exp(5*x+10)-1600*x^3*exp(x)^3-4800*exp(x)^2*x^4-4800*x^5*exp(x)-160
0*x^6),x, algorithm="maxima")

[Out]

1/6400*(x^8 - 1120*x^6 + x^4*e^(12*x + 20) + 313600*x^4 + 2*(x^5*e^20 - 240*x^3*e^20)*e^(11*x) + (x^6*e^20 - 4
80*x^4*e^20 + 57600*x^2*e^20)*e^(10*x) - 2*(x^5*e^10 - 320*x^3*e^10)*e^(7*x) - 4*(x^6*e^10 - 560*x^4*e^10 + 38
400*x^2*e^10)*e^(6*x) - 2*(x^7*e^10 - 800*x^5*e^10 + 134400*x^3*e^10)*e^(5*x) + (x^6 - 640*x^4 + 102400*x^2)*e
^(2*x) + 2*(x^7 - 880*x^5 + 179200*x^3)*e^x)/(x^4 - 2*x^3*e^(5*x + 10) + 2*x^3*e^x + x^2*e^(2*x) + x^2*e^(10*x
+ 20) - 4*x^2*e^(6*x + 10) + 2*x*e^(11*x + 20) - 2*x*e^(7*x + 10) + e^(12*x + 20))

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mupad [B]  time = 4.70, size = 2084, normalized size = 57.89 result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(2*x)*(38400*x^3 - 38400*x^4 - 1320*x^5 + 120*x^6 + 3*x^7) - exp(3*x)*(320*x^4 - x^6) + exp(10*x + 20)
*(exp(3*x)*(800*x^3 - 480*x^2 + 3*x^4) + exp(2*x)*(76800*x - 230400*x^2 - 2520*x^3 + 2760*x^4 + 9*x^5) + exp(x
)*(201600*x^2 - 508800*x^3 - 3240*x^4 + 2760*x^5 + 9*x^6) + 38400*x^3 - 192000*x^4 - 1200*x^5 + 800*x^6 + 3*x^
7) + exp(x)*(67200*x^4 - 67200*x^5 - 1560*x^6 + 120*x^7 + 3*x^8) - exp(15*x + 30)*(exp(x)*(28800*x - 28800*x^2
- 600*x^3 + 120*x^4 + 3*x^5) + x^3*exp(3*x) + exp(2*x)*(120*x^3 - 360*x^2 + 3*x^4) - 240*x^4 + x^6) - 560*x^7
+ x^9 - exp(5*x + 10)*(exp(2*x)*(268800*x^2 - 1036800*x^3 - 3480*x^4 + 2760*x^5 + 9*x^6) + exp(3*x)*(51200*x
- 256000*x^2 - 800*x^3 + 800*x^4 + 3*x^5) + exp(x)*(393600*x^3 - 1315200*x^4 - 4200*x^5 + 2760*x^6 + 9*x^7) +
89600*x^4 - 448000*x^5 - 1520*x^6 + 800*x^7 + 3*x^8))/(4800*x^5*exp(x) + exp(10*x + 20)*(4800*x*exp(3*x) + 144
00*x^3*exp(x) + 14400*x^2*exp(2*x) + 4800*x^4) - exp(15*x + 30)*(1600*exp(3*x) + 4800*x*exp(2*x) + 4800*x^2*ex
p(x) + 1600*x^3) + 1600*x^3*exp(3*x) + 4800*x^4*exp(2*x) - exp(5*x + 10)*(14400*x^4*exp(x) + 4800*x^2*exp(3*x)
+ 14400*x^3*exp(2*x) + 4800*x^5) + 1600*x^6),x)

[Out]

(x^2*((7*x^6)/40 - 49*x^4 - 24*exp(12*x)*exp(20) - x^8/6400 + 96*x^2*exp(20)*exp(6*x - 10) + 48*x^3*exp(20)*ex
p(5*x - 10) - (7*x^3*exp(20)*exp(7*x - 10))/20 - (7*x^4*exp(20)*exp(6*x - 10))/10 - (7*x^5*exp(20)*exp(5*x - 1
0))/20 + (x^5*exp(20)*exp(7*x - 10))/3200 + (x^6*exp(20)*exp(6*x - 10))/1600 + (x^7*exp(20)*exp(5*x - 10))/320
0 - 24*x^2*exp(20)*exp(2*x - 20) + (7*x^4*exp(20)*exp(2*x - 20))/40 - (x^6*exp(20)*exp(2*x - 20))/6400 - 18*x^
5*exp(30)*exp(7*x - 10) - 36*x^6*exp(30)*exp(6*x - 10) - 18*x^7*exp(30)*exp(5*x - 10) + 9*x^4*exp(30)*exp(4*x
- 20) - 9*x^5*exp(30)*exp(3*x - 20) + 9*x^6*exp(30)*exp(2*x - 20) - (3*x^5*exp(30)*exp(5*x - 20))/40 - (x^5*ex
p(30)*exp(3*x - 30))/6400 + 9*x^3*exp(40)*exp(5*x - 30) + 9*x^6*exp(40)*exp(2*x - 30) - 16*x^2*exp(40)*exp(2*x
- 40) + 9*x^7*exp(50)*exp(5*x - 30) - 48*x*exp(11*x)*exp(20) + 9*exp(12*x)*exp(50)*exp(4*x - 20) + 16*exp(6*x
)*exp(50)*exp(2*x - 40) + 48*x*exp(20)*exp(7*x - 10) + 25*x^2*exp(6*x)*exp(10) + 25*x^3*exp(5*x)*exp(10) + (x^
6*exp(6*x)*exp(10))/6400 + (x^7*exp(5*x)*exp(10))/6400 - 24*x^2*exp(10*x)*exp(20) + 9*x^6*exp(6*x)*exp(20) + 9
*x^7*exp(5*x)*exp(20) + (7*x^2*exp(12*x)*exp(20))/40 + (7*x^3*exp(11*x)*exp(20))/20 + (7*x^4*exp(10*x)*exp(20)
)/40 - (x^4*exp(12*x)*exp(20))/6400 - (x^5*exp(11*x)*exp(20))/3200 - (x^6*exp(10*x)*exp(20))/6400 + 9*x^4*exp(
12*x)*exp(30) + 18*x^5*exp(11*x)*exp(30) + 9*x^6*exp(10*x)*exp(30) + (x^2*exp(18*x)*exp(30))/6400 + (3*x^3*exp
(17*x)*exp(30))/6400 + (3*x^4*exp(16*x)*exp(30))/6400 + (x^5*exp(15*x)*exp(30))/6400 - 25*x^3*exp(x - 10)*exp(
10) - (x^7*exp(x - 10)*exp(10))/6400 - 9*x^7*exp(x - 10)*exp(20) - 48*x^3*exp(x - 20)*exp(20) + (7*x^5*exp(x -
20)*exp(20))/20 - (x^7*exp(x - 20)*exp(20))/3200 + 18*x^7*exp(x - 20)*exp(30) + (x^5*exp(x - 30)*exp(30))/10
- 9*x^7*exp(x - 30)*exp(40) - 32*x^3*exp(x - 40)*exp(40) + 18*x*exp(11*x)*exp(50)*exp(4*x - 20) - 9*x*exp(12*x
)*exp(50)*exp(3*x - 20) - (3*x*exp(12*x)*exp(50)*exp(5*x - 20))/40 - 9*x*exp(6*x)*exp(50)*exp(5*x - 30) + 16*x
*exp(5*x)*exp(50)*exp(2*x - 40) - 16*x*exp(x - 10)*exp(50)*exp(2*x - 40) - (x^3*exp(12*x)*exp(x - 10)*exp(30))
/6400 - (x^4*exp(11*x)*exp(x - 10)*exp(30))/3200 - (x^5*exp(10*x)*exp(x - 10)*exp(30))/6400 + (x^5*exp(6*x)*ex
p(x - 20)*exp(30))/3200 + (x^6*exp(5*x)*exp(x - 20)*exp(30))/3200 + (x^2*exp(11*x)*exp(x - 30)*exp(50))/5 + (x
^3*exp(10*x)*exp(x - 30)*exp(50))/10 + 32*x^2*exp(5*x)*exp(x - 40)*exp(50) - 9*x^3*exp(12*x)*exp(x - 30)*exp(6
0) - 18*x^4*exp(11*x)*exp(x - 30)*exp(60) - 9*x^5*exp(10*x)*exp(x - 30)*exp(60) - (x^6*exp(x - 10)*exp(x - 20)
*exp(30))/3200 - 32*x^2*exp(x - 10)*exp(x - 40)*exp(50) + (x^4*exp(x - 20)*exp(x - 30)*exp(50))/5 - 18*x^6*exp
(x - 20)*exp(x - 30)*exp(60) - 18*x*exp(50)*exp(7*x - 10)*exp(4*x - 20) - (x^3*exp(6*x)*exp(30)*exp(7*x - 10))
/3200 - (x^4*exp(5*x)*exp(30)*exp(7*x - 10))/3200 - (x^4*exp(6*x)*exp(30)*exp(6*x - 10))/1600 - (x^5*exp(5*x)*
exp(30)*exp(6*x - 10))/1600 - (x^5*exp(6*x)*exp(30)*exp(5*x - 10))/3200 - (x^6*exp(5*x)*exp(30)*exp(5*x - 10))
/3200 + (x^4*exp(6*x)*exp(30)*exp(2*x - 20))/6400 + (x^5*exp(5*x)*exp(30)*exp(2*x - 20))/6400 + 9*x^2*exp(10*x
)*exp(50)*exp(4*x - 20) - 18*x^2*exp(11*x)*exp(50)*exp(3*x - 20) - 9*x^3*exp(10*x)*exp(50)*exp(3*x - 20) - (3*
x^2*exp(11*x)*exp(50)*exp(5*x - 20))/20 - (3*x^3*exp(10*x)*exp(50)*exp(5*x - 20))/40 - 9*x^2*exp(5*x)*exp(50)*
exp(5*x - 30) + 9*x^2*exp(12*x)*exp(60)*exp(2*x - 30) + 18*x^3*exp(11*x)*exp(60)*exp(2*x - 30) + 9*x^4*exp(10*
x)*exp(60)*exp(2*x - 30) - 9*x^5*exp(6*x)*exp(60)*exp(5*x - 30) - 9*x^6*exp(5*x)*exp(60)*exp(5*x - 30) + (x^4*
exp(x - 10)*exp(30)*exp(7*x - 10))/3200 + (x^5*exp(x - 10)*exp(30)*exp(6*x - 10))/1600 + (x^6*exp(x - 10)*exp(
30)*exp(5*x - 10))/3200 + 9*x^2*exp(x - 10)*exp(50)*exp(5*x - 30) + 18*x^3*exp(x - 20)*exp(50)*exp(4*x - 20) -
18*x^4*exp(x - 20)*exp(50)*exp(3*x - 20) - (x^2*exp(x - 30)*exp(50)*exp(7*x - 10))/5 - (2*x^3*exp(x - 30)*exp
(50)*exp(6*x - 10))/5 - (3*x^4*exp(x - 20)*exp(50)*exp(5*x - 20))/20 - (x^4*exp(x - 30)*exp(50)*exp(5*x - 10))
/5 + (x^3*exp(x - 30)*exp(50)*exp(2*x - 20))/10 + 18*x^4*exp(x - 30)*exp(60)*exp(7*x - 10) + 36*x^5*exp(x - 30
)*exp(60)*exp(6*x - 10) + 9*x^6*exp(x - 10)*exp(60)*exp(5*x - 30) + 18*x^6*exp(x - 30)*exp(60)*exp(5*x - 10) +
18*x^5*exp(x - 20)*exp(60)*exp(2*x - 30) - 9*x^5*exp(x - 30)*exp(60)*exp(2*x - 20) + (x*exp(12*x)*exp(x - 30)
*exp(50))/10 + 32*x*exp(6*x)*exp(x - 40)*exp(50) - 36*x^2*exp(50)*exp(6*x - 10)*exp(4*x - 20) + 18*x^2*exp(50)
*exp(7*x - 10)*exp(3*x - 20) - 18*x^3*exp(50)*exp(5*x - 10)*exp(4*x - 20) + 36*x^3*exp(50)*exp(6*x - 10)*exp(3
*x - 20) + 18*x^4*exp(50)*exp(5*x - 10)*exp(3*x - 20) + (3*x^2*exp(50)*exp(7*x - 10)*exp(5*x - 20))/20 + (3*x^
3*exp(50)*exp(6*x - 10)*exp(5*x - 20))/10 + (3*x^4*exp(50)*exp(5*x - 10)*exp(5*x - 20))/20 + 9*x^2*exp(50)*exp
(2*x - 20)*exp(4*x - 20) - 9*x^3*exp(50)*exp(2*x - 20)*exp(3*x - 20) - (3*x^3*exp(50)*exp(2*x - 20)*exp(5*x -
20))/40 - 18*x^3*exp(60)*exp(7*x - 10)*exp(2*x - 30) - 36*x^4*exp(60)*exp(6*x - 10)*exp(2*x - 30) - 18*x^5*exp
(60)*exp(5*x - 10)*exp(2*x - 30) + 9*x^4*exp(60)*exp(2*x - 20)*exp(2*x - 30)))/((exp(6*x)*exp(10) - x^2 + x*ex
p(5*x)*exp(10) - x*exp(x - 10)*exp(10))*(exp(12*x)*exp(20) + x^4 - 4*x^2*exp(20)*exp(6*x - 10) - 2*x^3*exp(20)
*exp(5*x - 10) + x^2*exp(20)*exp(2*x - 20) + 2*x*exp(11*x)*exp(20) - 2*x*exp(20)*exp(7*x - 10) + x^2*exp(10*x)
*exp(20) + 2*x^3*exp(x - 20)*exp(20)))

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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(((x**3*exp(x)**3+(3*x**4+120*x**3-360*x**2)*exp(x)**2+(3*x**5+120*x**4-600*x**3-28800*x**2+28800*x)*
exp(x)+x**6-240*x**4)*exp(5*x+10)**3+((-3*x**4-800*x**3+480*x**2)*exp(x)**3+(-9*x**5-2760*x**4+2520*x**3+23040
0*x**2-76800*x)*exp(x)**2+(-9*x**6-2760*x**5+3240*x**4+508800*x**3-201600*x**2)*exp(x)-3*x**7-800*x**6+1200*x*
*5+192000*x**4-38400*x**3)*exp(5*x+10)**2+((3*x**5+800*x**4-800*x**3-256000*x**2+51200*x)*exp(x)**3+(9*x**6+27
60*x**5-3480*x**4-1036800*x**3+268800*x**2)*exp(x)**2+(9*x**7+2760*x**6-4200*x**5-1315200*x**4+393600*x**3)*ex
p(x)+3*x**8+800*x**7-1520*x**6-448000*x**5+89600*x**4)*exp(5*x+10)+(-x**6+320*x**4)*exp(x)**3+(-3*x**7-120*x**
6+1320*x**5+38400*x**4-38400*x**3)*exp(x)**2+(-3*x**8-120*x**7+1560*x**6+67200*x**5-67200*x**4)*exp(x)-x**9+56
0*x**7)/((1600*exp(x)**3+4800*x*exp(x)**2+4800*exp(x)*x**2+1600*x**3)*exp(5*x+10)**3+(-4800*x*exp(x)**3-14400*
exp(x)**2*x**2-14400*exp(x)*x**3-4800*x**4)*exp(5*x+10)**2+(4800*x**2*exp(x)**3+14400*exp(x)**2*x**3+14400*exp
(x)*x**4+4800*x**5)*exp(5*x+10)-1600*x**3*exp(x)**3-4800*exp(x)**2*x**4-4800*x**5*exp(x)-1600*x**6),x)

[Out]

Timed out

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