∫ e−1−9x2+6x4−24x5+35x6−16x7−22x8+56x9−70x10+56x11−28x12+8x13−x14+e4x(−45x2+9x3+30x4−126x5+199x6−115x7−94x8+302x9−406x10+350x11−196x12+68x13−13x14+x15) __________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ 9x2−6x4+24x5−35x6+16x7+22x8−56x9+70x10−56x11+28x12−8x13+x14 (−6+6x2−32x3+60x4−48x5+14x6+e4x(513x3−108x4−513x5+2160x6−3339x7+1296x8+4112x9−10244x10+12684x11−7652x12−3481x13+14652x14−20265x15+18708x16−12573x17+6160x18−2134x19+492x20−67x21+4x22)) _______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________−27x3 +27x5 −108x6 +153x7 −36x8 −224x9 +492x10 −564x11 +284x12 +243x13 −720x14 +915x15 −792x16 +495x17 −220x18 +66x19 −12x20 +x21 dx

3.92.5 $\int \frac {e^{\frac {-1-9 x^2+6 x^4-24 x^5+35 x^6-16 x^7-22 x^8+56 x^9-70 x^{10}+56 x^{11}-28 x^{12}+8 x^{13}-x^{14}+e^{4 x} (-45 x^2+9 x^3+30 x^4-126 x^5+199 x^6-115 x^7-94 x^8+302 x^9-406 x^{10}+350 x^{11}-196 x^{12}+68 x^{13}-13 x^{14}+x^{15})}{9 x^2-6 x^4+24 x^5-35 x^6+16 x^7+22 x^8-56 x^9+70 x^{10}-56 x^{11}+28 x^{12}-8 x^{13}+x^{14}}} (-6+6 x^2-32 x^3+60 x^4-48 x^5+14 x^6+e^{4 x} (513 x^3-108 x^4-513 x^5+2160 x^6-3339 x^7+1296 x^8+4112 x^9-10244 x^{10}+12684 x^{11}-7652 x^{12}-3481 x^{13}+14652 x^{14}-20265 x^{15}+18708 x^{16}-12573 x^{17}+6160 x^{18}-2134 x^{19}+492 x^{20}-67 x^{21}+4 x^{22}))}{-27 x^3+27 x^5-108 x^6+153 x^7-36 x^8-224 x^9+492 x^{10}-564 x^{11}+284 x^{12}+243 x^{13}-720 x^{14}+915 x^{15}-792 x^{16}+495 x^{17}-220 x^{18}+66 x^{19}-12 x^{20}+x^{21}} \, dx$

Optimal. Leaf size=32 \[ e^{-1+e^{4 x} (-5+x)-\frac {1}{x^2 \left (3-(-1+x)^4 x^2\right )^2}} \]

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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[(E^((-1 - 9*x^2 + 6*x^4 - 24*x^5 + 35*x^6 - 16*x^7 - 22*x^8 + 56*x^9 - 70*x^10 + 56*x^11 - 28*x^12 + 8*x^1

3 - x^14 + E^(4*x)*(-45*x^2 + 9*x^3 + 30*x^4 - 126*x^5 + 199*x^6 - 115*x^7 - 94*x^8 + 302*x^9 - 406*x^10 + 350

*x^11 - 196*x^12 + 68*x^13 - 13*x^14 + x^15))/(9*x^2 - 6*x^4 + 24*x^5 - 35*x^6 + 16*x^7 + 22*x^8 - 56*x^9 + 70

*x^10 - 56*x^11 + 28*x^12 - 8*x^13 + x^14))*(-6 + 6*x^2 - 32*x^3 + 60*x^4 - 48*x^5 + 14*x^6 + E^(4*x)*(513*x^3

- 108*x^4 - 513*x^5 + 2160*x^6 - 3339*x^7 + 1296*x^8 + 4112*x^9 - 10244*x^10 + 12684*x^11 - 7652*x^12 - 3481*

x^13 + 14652*x^14 - 20265*x^15 + 18708*x^16 - 12573*x^17 + 6160*x^18 - 2134*x^19 + 492*x^20 - 67*x^21 + 4*x^22

)))/(-27*x^3 + 27*x^5 - 108*x^6 + 153*x^7 - 36*x^8 - 224*x^9 + 492*x^10 - 564*x^11 + 284*x^12 + 243*x^13 - 720

*x^14 + 915*x^15 - 792*x^16 + 495*x^17 - 220*x^18 + 66*x^19 - 12*x^20 + x^21),x]

[Out]

$Aborted

Rubi steps

Aborted

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Mathematica [B] time = 0.95, size = 217, normalized size = 6.78 \begin {gather*} e^{\frac {-1-9 \left (1+5 e^{4 x}\right ) x^2+9 e^{4 x} x^3+6 \left (1+5 e^{4 x}\right ) x^4-6 \left (4+21 e^{4 x}\right ) x^5+\left (35+199 e^{4 x}\right ) x^6-\left (16+115 e^{4 x}\right ) x^7-2 \left (11+47 e^{4 x}\right ) x^8+\left (56+302 e^{4 x}\right ) x^9-14 \left (5+29 e^{4 x}\right ) x^{10}+14 \left (4+25 e^{4 x}\right ) x^{11}-28 \left (1+7 e^{4 x}\right ) x^{12}+\left (8+68 e^{4 x}\right ) x^{13}-\left (1+13 e^{4 x}\right ) x^{14}+e^{4 x} x^{15}}{x^2 \left (-3+x^2-4 x^3+6 x^4-4 x^5+x^6\right )^2}} \end {gather*}

Antiderivative was successfully veriﬁed.

[In]

Integrate[(E^((-1 - 9*x^2 + 6*x^4 - 24*x^5 + 35*x^6 - 16*x^7 - 22*x^8 + 56*x^9 - 70*x^10 + 56*x^11 - 28*x^12 +

8*x^13 - x^14 + E^(4*x)*(-45*x^2 + 9*x^3 + 30*x^4 - 126*x^5 + 199*x^6 - 115*x^7 - 94*x^8 + 302*x^9 - 406*x^10

+ 350*x^11 - 196*x^12 + 68*x^13 - 13*x^14 + x^15))/(9*x^2 - 6*x^4 + 24*x^5 - 35*x^6 + 16*x^7 + 22*x^8 - 56*x^

9 + 70*x^10 - 56*x^11 + 28*x^12 - 8*x^13 + x^14))*(-6 + 6*x^2 - 32*x^3 + 60*x^4 - 48*x^5 + 14*x^6 + E^(4*x)*(5

13*x^3 - 108*x^4 - 513*x^5 + 2160*x^6 - 3339*x^7 + 1296*x^8 + 4112*x^9 - 10244*x^10 + 12684*x^11 - 7652*x^12 -

3481*x^13 + 14652*x^14 - 20265*x^15 + 18708*x^16 - 12573*x^17 + 6160*x^18 - 2134*x^19 + 492*x^20 - 67*x^21 +

4*x^22)))/(-27*x^3 + 27*x^5 - 108*x^6 + 153*x^7 - 36*x^8 - 224*x^9 + 492*x^10 - 564*x^11 + 284*x^12 + 243*x^13

- 720*x^14 + 915*x^15 - 792*x^16 + 495*x^17 - 220*x^18 + 66*x^19 - 12*x^20 + x^21),x]

[Out]

E^((-1 - 9*(1 + 5*E^(4*x))*x^2 + 9*E^(4*x)*x^3 + 6*(1 + 5*E^(4*x))*x^4 - 6*(4 + 21*E^(4*x))*x^5 + (35 + 199*E^

(4*x))*x^6 - (16 + 115*E^(4*x))*x^7 - 2*(11 + 47*E^(4*x))*x^8 + (56 + 302*E^(4*x))*x^9 - 14*(5 + 29*E^(4*x))*x

^10 + 14*(4 + 25*E^(4*x))*x^11 - 28*(1 + 7*E^(4*x))*x^12 + (8 + 68*E^(4*x))*x^13 - (1 + 13*E^(4*x))*x^14 + E^(

4*x)*x^15)/(x^2*(-3 + x^2 - 4*x^3 + 6*x^4 - 4*x^5 + x^6)^2))

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fricas [B] time = 0.51, size = 199, normalized size = 6.22 \begin {gather*} e^{\left (-\frac {x^{14} - 8 \, x^{13} + 28 \, x^{12} - 56 \, x^{11} + 70 \, x^{10} - 56 \, x^{9} + 22 \, x^{8} + 16 \, x^{7} - 35 \, x^{6} + 24 \, x^{5} - 6 \, x^{4} + 9 \, x^{2} - {\left (x^{15} - 13 \, x^{14} + 68 \, x^{13} - 196 \, x^{12} + 350 \, x^{11} - 406 \, x^{10} + 302 \, x^{9} - 94 \, x^{8} - 115 \, x^{7} + 199 \, x^{6} - 126 \, x^{5} + 30 \, x^{4} + 9 \, x^{3} - 45 \, x^{2}\right )} e^{\left (4 \, x\right )} + 1}{x^{14} - 8 \, x^{13} + 28 \, x^{12} - 56 \, x^{11} + 70 \, x^{10} - 56 \, x^{9} + 22 \, x^{8} + 16 \, x^{7} - 35 \, x^{6} + 24 \, x^{5} - 6 \, x^{4} + 9 \, x^{2}}\right )} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x^22-67*x^21+492*x^20-2134*x^19+6160*x^18-12573*x^17+18708*x^16-20265*x^15+14652*x^14-3481*x^13-

7652*x^12+12684*x^11-10244*x^10+4112*x^9+1296*x^8-3339*x^7+2160*x^6-513*x^5-108*x^4+513*x^3)*exp(4*x)+14*x^6-4

8*x^5+60*x^4-32*x^3+6*x^2-6)*exp(((x^15-13*x^14+68*x^13-196*x^12+350*x^11-406*x^10+302*x^9-94*x^8-115*x^7+199*

x^6-126*x^5+30*x^4+9*x^3-45*x^2)*exp(4*x)-x^14+8*x^13-28*x^12+56*x^11-70*x^10+56*x^9-22*x^8-16*x^7+35*x^6-24*x

^5+6*x^4-9*x^2-1)/(x^14-8*x^13+28*x^12-56*x^11+70*x^10-56*x^9+22*x^8+16*x^7-35*x^6+24*x^5-6*x^4+9*x^2))/(x^21-

12*x^20+66*x^19-220*x^18+495*x^17-792*x^16+915*x^15-720*x^14+243*x^13+284*x^12-564*x^11+492*x^10-224*x^9-36*x^

8+153*x^7-108*x^6+27*x^5-27*x^3),x, algorithm="fricas")

[Out]

e^(-(x^14 - 8*x^13 + 28*x^12 - 56*x^11 + 70*x^10 - 56*x^9 + 22*x^8 + 16*x^7 - 35*x^6 + 24*x^5 - 6*x^4 + 9*x^2

- (x^15 - 13*x^14 + 68*x^13 - 196*x^12 + 350*x^11 - 406*x^10 + 302*x^9 - 94*x^8 - 115*x^7 + 199*x^6 - 126*x^5

+ 30*x^4 + 9*x^3 - 45*x^2)*e^(4*x) + 1)/(x^14 - 8*x^13 + 28*x^12 - 56*x^11 + 70*x^10 - 56*x^9 + 22*x^8 + 16*x^

7 - 35*x^6 + 24*x^5 - 6*x^4 + 9*x^2))

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giac [B] time = 29.49, size = 1836, normalized size = 57.38 result too large to display

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x^22-67*x^21+492*x^20-2134*x^19+6160*x^18-12573*x^17+18708*x^16-20265*x^15+14652*x^14-3481*x^13-

7652*x^12+12684*x^11-10244*x^10+4112*x^9+1296*x^8-3339*x^7+2160*x^6-513*x^5-108*x^4+513*x^3)*exp(4*x)+14*x^6-4

8*x^5+60*x^4-32*x^3+6*x^2-6)*exp(((x^15-13*x^14+68*x^13-196*x^12+350*x^11-406*x^10+302*x^9-94*x^8-115*x^7+199*

x^6-126*x^5+30*x^4+9*x^3-45*x^2)*exp(4*x)-x^14+8*x^13-28*x^12+56*x^11-70*x^10+56*x^9-22*x^8-16*x^7+35*x^6-24*x

^5+6*x^4-9*x^2-1)/(x^14-8*x^13+28*x^12-56*x^11+70*x^10-56*x^9+22*x^8+16*x^7-35*x^6+24*x^5-6*x^4+9*x^2))/(x^21-

12*x^20+66*x^19-220*x^18+495*x^17-792*x^16+915*x^15-720*x^14+243*x^13+284*x^12-564*x^11+492*x^10-224*x^9-36*x^

8+153*x^7-108*x^6+27*x^5-27*x^3),x, algorithm="giac")

[Out]

e^(x^15*e^(4*x)/(x^14 - 8*x^13 + 28*x^12 - 56*x^11 + 70*x^10 - 56*x^9 + 22*x^8 + 16*x^7 - 35*x^6 + 24*x^5 - 6*

x^4 + 9*x^2) - 13*x^14*e^(4*x)/(x^14 - 8*x^13 + 28*x^12 - 56*x^11 + 70*x^10 - 56*x^9 + 22*x^8 + 16*x^7 - 35*x^

6 + 24*x^5 - 6*x^4 + 9*x^2) - x^14/(x^14 - 8*x^13 + 28*x^12 - 56*x^11 + 70*x^10 - 56*x^9 + 22*x^8 + 16*x^7 - 3

5*x^6 + 24*x^5 - 6*x^4 + 9*x^2) + 68*x^13*e^(4*x)/(x^14 - 8*x^13 + 28*x^12 - 56*x^11 + 70*x^10 - 56*x^9 + 22*x

^8 + 16*x^7 - 35*x^6 + 24*x^5 - 6*x^4 + 9*x^2) + 8*x^13/(x^14 - 8*x^13 + 28*x^12 - 56*x^11 + 70*x^10 - 56*x^9

+ 22*x^8 + 16*x^7 - 35*x^6 + 24*x^5 - 6*x^4 + 9*x^2) - 196*x^12*e^(4*x)/(x^14 - 8*x^13 + 28*x^12 - 56*x^11 + 7

0*x^10 - 56*x^9 + 22*x^8 + 16*x^7 - 35*x^6 + 24*x^5 - 6*x^4 + 9*x^2) - 28*x^12/(x^14 - 8*x^13 + 28*x^12 - 56*x

^11 + 70*x^10 - 56*x^9 + 22*x^8 + 16*x^7 - 35*x^6 + 24*x^5 - 6*x^4 + 9*x^2) + 350*x^11*e^(4*x)/(x^14 - 8*x^13

+ 28*x^12 - 56*x^11 + 70*x^10 - 56*x^9 + 22*x^8 + 16*x^7 - 35*x^6 + 24*x^5 - 6*x^4 + 9*x^2) + 56*x^11/(x^14 -

8*x^13 + 28*x^12 - 56*x^11 + 70*x^10 - 56*x^9 + 22*x^8 + 16*x^7 - 35*x^6 + 24*x^5 - 6*x^4 + 9*x^2) - 406*x^10*

e^(4*x)/(x^14 - 8*x^13 + 28*x^12 - 56*x^11 + 70*x^10 - 56*x^9 + 22*x^8 + 16*x^7 - 35*x^6 + 24*x^5 - 6*x^4 + 9*

x^2) - 70*x^10/(x^14 - 8*x^13 + 28*x^12 - 56*x^11 + 70*x^10 - 56*x^9 + 22*x^8 + 16*x^7 - 35*x^6 + 24*x^5 - 6*x

^4 + 9*x^2) + 302*x^9*e^(4*x)/(x^14 - 8*x^13 + 28*x^12 - 56*x^11 + 70*x^10 - 56*x^9 + 22*x^8 + 16*x^7 - 35*x^6

+ 24*x^5 - 6*x^4 + 9*x^2) + 56*x^9/(x^14 - 8*x^13 + 28*x^12 - 56*x^11 + 70*x^10 - 56*x^9 + 22*x^8 + 16*x^7 -

35*x^6 + 24*x^5 - 6*x^4 + 9*x^2) - 94*x^8*e^(4*x)/(x^14 - 8*x^13 + 28*x^12 - 56*x^11 + 70*x^10 - 56*x^9 + 22*x

^8 + 16*x^7 - 35*x^6 + 24*x^5 - 6*x^4 + 9*x^2) - 22*x^8/(x^14 - 8*x^13 + 28*x^12 - 56*x^11 + 70*x^10 - 56*x^9

+ 22*x^8 + 16*x^7 - 35*x^6 + 24*x^5 - 6*x^4 + 9*x^2) - 115*x^7*e^(4*x)/(x^14 - 8*x^13 + 28*x^12 - 56*x^11 + 70

*x^10 - 56*x^9 + 22*x^8 + 16*x^7 - 35*x^6 + 24*x^5 - 6*x^4 + 9*x^2) - 16*x^7/(x^14 - 8*x^13 + 28*x^12 - 56*x^1

1 + 70*x^10 - 56*x^9 + 22*x^8 + 16*x^7 - 35*x^6 + 24*x^5 - 6*x^4 + 9*x^2) + 199*x^6*e^(4*x)/(x^14 - 8*x^13 + 2

8*x^12 - 56*x^11 + 70*x^10 - 56*x^9 + 22*x^8 + 16*x^7 - 35*x^6 + 24*x^5 - 6*x^4 + 9*x^2) + 35*x^6/(x^14 - 8*x^

13 + 28*x^12 - 56*x^11 + 70*x^10 - 56*x^9 + 22*x^8 + 16*x^7 - 35*x^6 + 24*x^5 - 6*x^4 + 9*x^2) - 126*x^5*e^(4*

x)/(x^14 - 8*x^13 + 28*x^12 - 56*x^11 + 70*x^10 - 56*x^9 + 22*x^8 + 16*x^7 - 35*x^6 + 24*x^5 - 6*x^4 + 9*x^2)

- 24*x^5/(x^14 - 8*x^13 + 28*x^12 - 56*x^11 + 70*x^10 - 56*x^9 + 22*x^8 + 16*x^7 - 35*x^6 + 24*x^5 - 6*x^4 + 9

*x^2) + 30*x^4*e^(4*x)/(x^14 - 8*x^13 + 28*x^12 - 56*x^11 + 70*x^10 - 56*x^9 + 22*x^8 + 16*x^7 - 35*x^6 + 24*x

^5 - 6*x^4 + 9*x^2) + 6*x^4/(x^14 - 8*x^13 + 28*x^12 - 56*x^11 + 70*x^10 - 56*x^9 + 22*x^8 + 16*x^7 - 35*x^6 +

24*x^5 - 6*x^4 + 9*x^2) + 9*x^3*e^(4*x)/(x^14 - 8*x^13 + 28*x^12 - 56*x^11 + 70*x^10 - 56*x^9 + 22*x^8 + 16*x

^7 - 35*x^6 + 24*x^5 - 6*x^4 + 9*x^2) - 45*x^2*e^(4*x)/(x^14 - 8*x^13 + 28*x^12 - 56*x^11 + 70*x^10 - 56*x^9 +

22*x^8 + 16*x^7 - 35*x^6 + 24*x^5 - 6*x^4 + 9*x^2) - 9*x^2/(x^14 - 8*x^13 + 28*x^12 - 56*x^11 + 70*x^10 - 56*

x^9 + 22*x^8 + 16*x^7 - 35*x^6 + 24*x^5 - 6*x^4 + 9*x^2) - 1/(x^14 - 8*x^13 + 28*x^12 - 56*x^11 + 70*x^10 - 56

*x^9 + 22*x^8 + 16*x^7 - 35*x^6 + 24*x^5 - 6*x^4 + 9*x^2))

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maple [B] time = 1.17, size = 218, normalized size = 6.81


method	result	size

risch	${\mathrm e}^{\frac {-1+56 x^{11}-28 x^{12}+8 x^{13}-x^{14}-16 x^{7}-22 x^{8}-70 x^{10}+56 x^{9}+35 x^{6}-24 x^{5}+6 x^{4}-9 x^{2}+9 x^{3} {\mathrm e}^{4 x}-45 x^{2} {\mathrm e}^{4 x}+{\mathrm e}^{4 x} x^{15}-13 \,{\mathrm e}^{4 x} x^{14}+68 \,{\mathrm e}^{4 x} x^{13}-196 \,{\mathrm e}^{4 x} x^{12}+350 \,{\mathrm e}^{4 x} x^{11}-406 \,{\mathrm e}^{4 x} x^{10}+302 \,{\mathrm e}^{4 x} x^{9}-94 \,{\mathrm e}^{4 x} x^{8}-115 \,{\mathrm e}^{4 x} x^{7}+199 \,{\mathrm e}^{4 x} x^{6}-126 \,{\mathrm e}^{4 x} x^{5}+30 x^{4} {\mathrm e}^{4 x}}{x^{2} \left (x^{6}-4 x^{5}+6 x^{4}-4 x^{3}+x^{2}-3\right )^{2}}}$	$218$

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int(((4*x^22-67*x^21+492*x^20-2134*x^19+6160*x^18-12573*x^17+18708*x^16-20265*x^15+14652*x^14-3481*x^13-7652*x

^12+12684*x^11-10244*x^10+4112*x^9+1296*x^8-3339*x^7+2160*x^6-513*x^5-108*x^4+513*x^3)*exp(4*x)+14*x^6-48*x^5+

60*x^4-32*x^3+6*x^2-6)*exp(((x^15-13*x^14+68*x^13-196*x^12+350*x^11-406*x^10+302*x^9-94*x^8-115*x^7+199*x^6-12

6*x^5+30*x^4+9*x^3-45*x^2)*exp(4*x)-x^14+8*x^13-28*x^12+56*x^11-70*x^10+56*x^9-22*x^8-16*x^7+35*x^6-24*x^5+6*x

^4-9*x^2-1)/(x^14-8*x^13+28*x^12-56*x^11+70*x^10-56*x^9+22*x^8+16*x^7-35*x^6+24*x^5-6*x^4+9*x^2))/(x^21-12*x^2

0+66*x^19-220*x^18+495*x^17-792*x^16+915*x^15-720*x^14+243*x^13+284*x^12-564*x^11+492*x^10-224*x^9-36*x^8+153*

x^7-108*x^6+27*x^5-27*x^3),x,method=_RETURNVERBOSE)

[Out]

exp((-1+56*x^11-28*x^12+8*x^13-x^14-16*x^7-22*x^8-70*x^10+56*x^9+35*x^6-24*x^5+6*x^4-9*x^2+9*x^3*exp(4*x)-45*x

^2*exp(4*x)+exp(4*x)*x^15-13*exp(4*x)*x^14+68*exp(4*x)*x^13-196*exp(4*x)*x^12+350*exp(4*x)*x^11-406*exp(4*x)*x

^10+302*exp(4*x)*x^9-94*exp(4*x)*x^8-115*exp(4*x)*x^7+199*exp(4*x)*x^6-126*exp(4*x)*x^5+30*x^4*exp(4*x))/x^2/(

x^6-4*x^5+6*x^4-4*x^3+x^2-3)^2)

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maxima [B] time = 9.88, size = 470, normalized size = 14.69 \begin {gather*} e^{\left (-\frac {x^{4}}{3 \, {\left (x^{12} - 8 \, x^{11} + 28 \, x^{10} - 56 \, x^{9} + 70 \, x^{8} - 56 \, x^{7} + 22 \, x^{6} + 16 \, x^{5} - 35 \, x^{4} + 24 \, x^{3} - 6 \, x^{2} + 9\right )}} + \frac {x^{4}}{9 \, {\left (x^{6} - 4 \, x^{5} + 6 \, x^{4} - 4 \, x^{3} + x^{2} - 3\right )}} + \frac {4 \, x^{3}}{3 \, {\left (x^{12} - 8 \, x^{11} + 28 \, x^{10} - 56 \, x^{9} + 70 \, x^{8} - 56 \, x^{7} + 22 \, x^{6} + 16 \, x^{5} - 35 \, x^{4} + 24 \, x^{3} - 6 \, x^{2} + 9\right )}} - \frac {4 \, x^{3}}{9 \, {\left (x^{6} - 4 \, x^{5} + 6 \, x^{4} - 4 \, x^{3} + x^{2} - 3\right )}} + x e^{\left (4 \, x\right )} - \frac {2 \, x^{2}}{x^{12} - 8 \, x^{11} + 28 \, x^{10} - 56 \, x^{9} + 70 \, x^{8} - 56 \, x^{7} + 22 \, x^{6} + 16 \, x^{5} - 35 \, x^{4} + 24 \, x^{3} - 6 \, x^{2} + 9} + \frac {2 \, x^{2}}{3 \, {\left (x^{6} - 4 \, x^{5} + 6 \, x^{4} - 4 \, x^{3} + x^{2} - 3\right )}} + \frac {4 \, x}{3 \, {\left (x^{12} - 8 \, x^{11} + 28 \, x^{10} - 56 \, x^{9} + 70 \, x^{8} - 56 \, x^{7} + 22 \, x^{6} + 16 \, x^{5} - 35 \, x^{4} + 24 \, x^{3} - 6 \, x^{2} + 9\right )}} - \frac {4 \, x}{9 \, {\left (x^{6} - 4 \, x^{5} + 6 \, x^{4} - 4 \, x^{3} + x^{2} - 3\right )}} - \frac {1}{3 \, {\left (x^{12} - 8 \, x^{11} + 28 \, x^{10} - 56 \, x^{9} + 70 \, x^{8} - 56 \, x^{7} + 22 \, x^{6} + 16 \, x^{5} - 35 \, x^{4} + 24 \, x^{3} - 6 \, x^{2} + 9\right )}} + \frac {1}{9 \, {\left (x^{6} - 4 \, x^{5} + 6 \, x^{4} - 4 \, x^{3} + x^{2} - 3\right )}} - \frac {1}{9 \, x^{2}} - 5 \, e^{\left (4 \, x\right )} - 1\right )} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x^22-67*x^21+492*x^20-2134*x^19+6160*x^18-12573*x^17+18708*x^16-20265*x^15+14652*x^14-3481*x^13-

7652*x^12+12684*x^11-10244*x^10+4112*x^9+1296*x^8-3339*x^7+2160*x^6-513*x^5-108*x^4+513*x^3)*exp(4*x)+14*x^6-4

8*x^5+60*x^4-32*x^3+6*x^2-6)*exp(((x^15-13*x^14+68*x^13-196*x^12+350*x^11-406*x^10+302*x^9-94*x^8-115*x^7+199*

x^6-126*x^5+30*x^4+9*x^3-45*x^2)*exp(4*x)-x^14+8*x^13-28*x^12+56*x^11-70*x^10+56*x^9-22*x^8-16*x^7+35*x^6-24*x

^5+6*x^4-9*x^2-1)/(x^14-8*x^13+28*x^12-56*x^11+70*x^10-56*x^9+22*x^8+16*x^7-35*x^6+24*x^5-6*x^4+9*x^2))/(x^21-

12*x^20+66*x^19-220*x^18+495*x^17-792*x^16+915*x^15-720*x^14+243*x^13+284*x^12-564*x^11+492*x^10-224*x^9-36*x^

8+153*x^7-108*x^6+27*x^5-27*x^3),x, algorithm="maxima")

[Out]

e^(-1/3*x^4/(x^12 - 8*x^11 + 28*x^10 - 56*x^9 + 70*x^8 - 56*x^7 + 22*x^6 + 16*x^5 - 35*x^4 + 24*x^3 - 6*x^2 +

9) + 1/9*x^4/(x^6 - 4*x^5 + 6*x^4 - 4*x^3 + x^2 - 3) + 4/3*x^3/(x^12 - 8*x^11 + 28*x^10 - 56*x^9 + 70*x^8 - 56

*x^7 + 22*x^6 + 16*x^5 - 35*x^4 + 24*x^3 - 6*x^2 + 9) - 4/9*x^3/(x^6 - 4*x^5 + 6*x^4 - 4*x^3 + x^2 - 3) + x*e^

(4*x) - 2*x^2/(x^12 - 8*x^11 + 28*x^10 - 56*x^9 + 70*x^8 - 56*x^7 + 22*x^6 + 16*x^5 - 35*x^4 + 24*x^3 - 6*x^2

+ 9) + 2/3*x^2/(x^6 - 4*x^5 + 6*x^4 - 4*x^3 + x^2 - 3) + 4/3*x/(x^12 - 8*x^11 + 28*x^10 - 56*x^9 + 70*x^8 - 56

*x^7 + 22*x^6 + 16*x^5 - 35*x^4 + 24*x^3 - 6*x^2 + 9) - 4/9*x/(x^6 - 4*x^5 + 6*x^4 - 4*x^3 + x^2 - 3) - 1/3/(x

^12 - 8*x^11 + 28*x^10 - 56*x^9 + 70*x^8 - 56*x^7 + 22*x^6 + 16*x^5 - 35*x^4 + 24*x^3 - 6*x^2 + 9) + 1/9/(x^6

- 4*x^5 + 6*x^4 - 4*x^3 + x^2 - 3) - 1/9/x^2 - 5*e^(4*x) - 1)

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mupad [B] time = 8.41, size = 1862, normalized size = 58.19 result too large to display

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(-(9*x^2 - 6*x^4 + 24*x^5 - 35*x^6 + 16*x^7 + 22*x^8 - 56*x^9 + 70*x^10 - 56*x^11 + 28*x^12 - 8*x^13

+ x^14 + exp(4*x)*(45*x^2 - 9*x^3 - 30*x^4 + 126*x^5 - 199*x^6 + 115*x^7 + 94*x^8 - 302*x^9 + 406*x^10 - 350*x

^11 + 196*x^12 - 68*x^13 + 13*x^14 - x^15) + 1)/(9*x^2 - 6*x^4 + 24*x^5 - 35*x^6 + 16*x^7 + 22*x^8 - 56*x^9 +

70*x^10 - 56*x^11 + 28*x^12 - 8*x^13 + x^14))*(exp(4*x)*(513*x^3 - 108*x^4 - 513*x^5 + 2160*x^6 - 3339*x^7 + 1

296*x^8 + 4112*x^9 - 10244*x^10 + 12684*x^11 - 7652*x^12 - 3481*x^13 + 14652*x^14 - 20265*x^15 + 18708*x^16 -

12573*x^17 + 6160*x^18 - 2134*x^19 + 492*x^20 - 67*x^21 + 4*x^22) + 6*x^2 - 32*x^3 + 60*x^4 - 48*x^5 + 14*x^6

- 6))/(27*x^3 - 27*x^5 + 108*x^6 - 153*x^7 + 36*x^8 + 224*x^9 - 492*x^10 + 564*x^11 - 284*x^12 - 243*x^13 + 72

0*x^14 - 915*x^15 + 792*x^16 - 495*x^17 + 220*x^18 - 66*x^19 + 12*x^20 - x^21),x)

[Out]

exp((6*x^4)/(9*x^2 - 6*x^4 + 24*x^5 - 35*x^6 + 16*x^7 + 22*x^8 - 56*x^9 + 70*x^10 - 56*x^11 + 28*x^12 - 8*x^13

+ x^14))*exp(-(9*x^2)/(9*x^2 - 6*x^4 + 24*x^5 - 35*x^6 + 16*x^7 + 22*x^8 - 56*x^9 + 70*x^10 - 56*x^11 + 28*x^

12 - 8*x^13 + x^14))*exp(-x^14/(9*x^2 - 6*x^4 + 24*x^5 - 35*x^6 + 16*x^7 + 22*x^8 - 56*x^9 + 70*x^10 - 56*x^11

+ 28*x^12 - 8*x^13 + x^14))*exp((8*x^13)/(9*x^2 - 6*x^4 + 24*x^5 - 35*x^6 + 16*x^7 + 22*x^8 - 56*x^9 + 70*x^1

0 - 56*x^11 + 28*x^12 - 8*x^13 + x^14))*exp(-(16*x^7)/(9*x^2 - 6*x^4 + 24*x^5 - 35*x^6 + 16*x^7 + 22*x^8 - 56*

x^9 + 70*x^10 - 56*x^11 + 28*x^12 - 8*x^13 + x^14))*exp(-(24*x^5)/(9*x^2 - 6*x^4 + 24*x^5 - 35*x^6 + 16*x^7 +

22*x^8 - 56*x^9 + 70*x^10 - 56*x^11 + 28*x^12 - 8*x^13 + x^14))*exp(-(22*x^8)/(9*x^2 - 6*x^4 + 24*x^5 - 35*x^6

+ 16*x^7 + 22*x^8 - 56*x^9 + 70*x^10 - 56*x^11 + 28*x^12 - 8*x^13 + x^14))*exp(-(28*x^12)/(9*x^2 - 6*x^4 + 24

*x^5 - 35*x^6 + 16*x^7 + 22*x^8 - 56*x^9 + 70*x^10 - 56*x^11 + 28*x^12 - 8*x^13 + x^14))*exp((35*x^6)/(9*x^2 -

6*x^4 + 24*x^5 - 35*x^6 + 16*x^7 + 22*x^8 - 56*x^9 + 70*x^10 - 56*x^11 + 28*x^12 - 8*x^13 + x^14))*exp((56*x^

9)/(9*x^2 - 6*x^4 + 24*x^5 - 35*x^6 + 16*x^7 + 22*x^8 - 56*x^9 + 70*x^10 - 56*x^11 + 28*x^12 - 8*x^13 + x^14))

*exp((56*x^11)/(9*x^2 - 6*x^4 + 24*x^5 - 35*x^6 + 16*x^7 + 22*x^8 - 56*x^9 + 70*x^10 - 56*x^11 + 28*x^12 - 8*x

^13 + x^14))*exp(-(70*x^10)/(9*x^2 - 6*x^4 + 24*x^5 - 35*x^6 + 16*x^7 + 22*x^8 - 56*x^9 + 70*x^10 - 56*x^11 +

28*x^12 - 8*x^13 + x^14))*exp(-1/(9*x^2 - 6*x^4 + 24*x^5 - 35*x^6 + 16*x^7 + 22*x^8 - 56*x^9 + 70*x^10 - 56*x^

11 + 28*x^12 - 8*x^13 + x^14))*exp((9*x^3*exp(4*x))/(9*x^2 - 6*x^4 + 24*x^5 - 35*x^6 + 16*x^7 + 22*x^8 - 56*x^

9 + 70*x^10 - 56*x^11 + 28*x^12 - 8*x^13 + x^14))*exp((x^15*exp(4*x))/(9*x^2 - 6*x^4 + 24*x^5 - 35*x^6 + 16*x^

7 + 22*x^8 - 56*x^9 + 70*x^10 - 56*x^11 + 28*x^12 - 8*x^13 + x^14))*exp(-(13*x^14*exp(4*x))/(9*x^2 - 6*x^4 + 2

4*x^5 - 35*x^6 + 16*x^7 + 22*x^8 - 56*x^9 + 70*x^10 - 56*x^11 + 28*x^12 - 8*x^13 + x^14))*exp((30*x^4*exp(4*x)

)/(9*x^2 - 6*x^4 + 24*x^5 - 35*x^6 + 16*x^7 + 22*x^8 - 56*x^9 + 70*x^10 - 56*x^11 + 28*x^12 - 8*x^13 + x^14))*

exp(-(45*x^2*exp(4*x))/(9*x^2 - 6*x^4 + 24*x^5 - 35*x^6 + 16*x^7 + 22*x^8 - 56*x^9 + 70*x^10 - 56*x^11 + 28*x^

12 - 8*x^13 + x^14))*exp((68*x^13*exp(4*x))/(9*x^2 - 6*x^4 + 24*x^5 - 35*x^6 + 16*x^7 + 22*x^8 - 56*x^9 + 70*x

^10 - 56*x^11 + 28*x^12 - 8*x^13 + x^14))*exp(-(94*x^8*exp(4*x))/(9*x^2 - 6*x^4 + 24*x^5 - 35*x^6 + 16*x^7 + 2

2*x^8 - 56*x^9 + 70*x^10 - 56*x^11 + 28*x^12 - 8*x^13 + x^14))*exp(-(115*x^7*exp(4*x))/(9*x^2 - 6*x^4 + 24*x^5

- 35*x^6 + 16*x^7 + 22*x^8 - 56*x^9 + 70*x^10 - 56*x^11 + 28*x^12 - 8*x^13 + x^14))*exp(-(126*x^5*exp(4*x))/(

9*x^2 - 6*x^4 + 24*x^5 - 35*x^6 + 16*x^7 + 22*x^8 - 56*x^9 + 70*x^10 - 56*x^11 + 28*x^12 - 8*x^13 + x^14))*exp

((199*x^6*exp(4*x))/(9*x^2 - 6*x^4 + 24*x^5 - 35*x^6 + 16*x^7 + 22*x^8 - 56*x^9 + 70*x^10 - 56*x^11 + 28*x^12

- 8*x^13 + x^14))*exp(-(196*x^12*exp(4*x))/(9*x^2 - 6*x^4 + 24*x^5 - 35*x^6 + 16*x^7 + 22*x^8 - 56*x^9 + 70*x^

10 - 56*x^11 + 28*x^12 - 8*x^13 + x^14))*exp((302*x^9*exp(4*x))/(9*x^2 - 6*x^4 + 24*x^5 - 35*x^6 + 16*x^7 + 22

*x^8 - 56*x^9 + 70*x^10 - 56*x^11 + 28*x^12 - 8*x^13 + x^14))*exp((350*x^11*exp(4*x))/(9*x^2 - 6*x^4 + 24*x^5

- 35*x^6 + 16*x^7 + 22*x^8 - 56*x^9 + 70*x^10 - 56*x^11 + 28*x^12 - 8*x^13 + x^14))*exp(-(406*x^10*exp(4*x))/(

9*x^2 - 6*x^4 + 24*x^5 - 35*x^6 + 16*x^7 + 22*x^8 - 56*x^9 + 70*x^10 - 56*x^11 + 28*x^12 - 8*x^13 + x^14))

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sympy [B] time = 7.20, size = 196, normalized size = 6.12 \begin {gather*} e^{\frac {- x^{14} + 8 x^{13} - 28 x^{12} + 56 x^{11} - 70 x^{10} + 56 x^{9} - 22 x^{8} - 16 x^{7} + 35 x^{6} - 24 x^{5} + 6 x^{4} - 9 x^{2} + \left (x^{15} - 13 x^{14} + 68 x^{13} - 196 x^{12} + 350 x^{11} - 406 x^{10} + 302 x^{9} - 94 x^{8} - 115 x^{7} + 199 x^{6} - 126 x^{5} + 30 x^{4} + 9 x^{3} - 45 x^{2}\right ) e^{4 x} - 1}{x^{14} - 8 x^{13} + 28 x^{12} - 56 x^{11} + 70 x^{10} - 56 x^{9} + 22 x^{8} + 16 x^{7} - 35 x^{6} + 24 x^{5} - 6 x^{4} + 9 x^{2}}} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x**22-67*x**21+492*x**20-2134*x**19+6160*x**18-12573*x**17+18708*x**16-20265*x**15+14652*x**14-3

481*x**13-7652*x**12+12684*x**11-10244*x**10+4112*x**9+1296*x**8-3339*x**7+2160*x**6-513*x**5-108*x**4+513*x**

3)*exp(4*x)+14*x**6-48*x**5+60*x**4-32*x**3+6*x**2-6)*exp(((x**15-13*x**14+68*x**13-196*x**12+350*x**11-406*x*

*10+302*x**9-94*x**8-115*x**7+199*x**6-126*x**5+30*x**4+9*x**3-45*x**2)*exp(4*x)-x**14+8*x**13-28*x**12+56*x**

11-70*x**10+56*x**9-22*x**8-16*x**7+35*x**6-24*x**5+6*x**4-9*x**2-1)/(x**14-8*x**13+28*x**12-56*x**11+70*x**10

-56*x**9+22*x**8+16*x**7-35*x**6+24*x**5-6*x**4+9*x**2))/(x**21-12*x**20+66*x**19-220*x**18+495*x**17-792*x**1

6+915*x**15-720*x**14+243*x**13+284*x**12-564*x**11+492*x**10-224*x**9-36*x**8+153*x**7-108*x**6+27*x**5-27*x*

*3),x)

[Out]

exp((-x**14 + 8*x**13 - 28*x**12 + 56*x**11 - 70*x**10 + 56*x**9 - 22*x**8 - 16*x**7 + 35*x**6 - 24*x**5 + 6*x

**4 - 9*x**2 + (x**15 - 13*x**14 + 68*x**13 - 196*x**12 + 350*x**11 - 406*x**10 + 302*x**9 - 94*x**8 - 115*x**

7 + 199*x**6 - 126*x**5 + 30*x**4 + 9*x**3 - 45*x**2)*exp(4*x) - 1)/(x**14 - 8*x**13 + 28*x**12 - 56*x**11 + 7

0*x**10 - 56*x**9 + 22*x**8 + 16*x**7 - 35*x**6 + 24*x**5 - 6*x**4 + 9*x**2))

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