3.17.21 $\int \frac{e^{\frac{-256x+512x^2+128x^3-646x^4-11x^5+320x^6+32x^7-64x^8-16x^9}{512-1024x-256x^2+1280x^3+22x^4-640x^5-64x^6+128x^7+32x^8}}(-65536+262144x-196608x^2-464896x^3+642560x^4+340480x^5-721920x^6-161536x^7+456711x^8+80384x^9-178368x^{10}-41984x^{11}+39584x^{12}+14336x^{13}-3072x^{14}-2048x^{15}-256x^{16})}{131072-524288x+393216x^2+917504x^3-1266688x^4-677888x^5+1436160x^6+323072x^7-917262x^8-161536x^9+359040x^{10}+84736x^{11}-79168x^{12}-28672x^{13}+6144x^{14}+4096x^{15}+512x^{16}}dx$

Optimal. Leaf size=33 $$e^{\frac{1}{2}(\frac{6}{5-16{(\frac{2-x}{x}-x)}^4}-x)}$$

________________________________________________________________________________________

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 = {} $$\begin{array}{c}\text{\$Aborted}\end{array}$$

Verification is not applicable to the result.

[In]

Int[(E^((-256*x + 512*x^2 + 128*x^3 - 646*x^4 - 11*x^5 + 320*x^6 + 32*x^7 - 64*x^8 - 16*x^9)/(512 - 1024*x - 2
56*x^2 + 1280*x^3 + 22*x^4 - 640*x^5 - 64*x^6 + 128*x^7 + 32*x^8))*(-65536 + 262144*x - 196608*x^2 - 464896*x^
3 + 642560*x^4 + 340480*x^5 - 721920*x^6 - 161536*x^7 + 456711*x^8 + 80384*x^9 - 178368*x^10 - 41984*x^11 + 39
584*x^12 + 14336*x^13 - 3072*x^14 - 2048*x^15 - 256*x^16))/(131072 - 524288*x + 393216*x^2 + 917504*x^3 - 1266
688*x^4 - 677888*x^5 + 1436160*x^6 + 323072*x^7 - 917262*x^8 - 161536*x^9 + 359040*x^10 + 84736*x^11 - 79168*x
^12 - 28672*x^13 + 6144*x^14 + 4096*x^15 + 512*x^16),x]

[Out]

$Aborted

Rubi steps

Aborted

________________________________________________________________________________________

Mathematica [A]  time = 0.13, size = 55, normalized size = 1.67 $$\begin{array}{c}{e}^{-\frac{x}{2}-\frac{3x^4}{256-512x-128x^2+640x^3+11x^4-320x^5-32x^6+64x^7+16x^8}}\end{array}$$

Antiderivative was successfully verified.

[In]

Integrate[(E^((-256*x + 512*x^2 + 128*x^3 - 646*x^4 - 11*x^5 + 320*x^6 + 32*x^7 - 64*x^8 - 16*x^9)/(512 - 1024
*x - 256*x^2 + 1280*x^3 + 22*x^4 - 640*x^5 - 64*x^6 + 128*x^7 + 32*x^8))*(-65536 + 262144*x - 196608*x^2 - 464
896*x^3 + 642560*x^4 + 340480*x^5 - 721920*x^6 - 161536*x^7 + 456711*x^8 + 80384*x^9 - 178368*x^10 - 41984*x^1
1 + 39584*x^12 + 14336*x^13 - 3072*x^14 - 2048*x^15 - 256*x^16))/(131072 - 524288*x + 393216*x^2 + 917504*x^3
- 1266688*x^4 - 677888*x^5 + 1436160*x^6 + 323072*x^7 - 917262*x^8 - 161536*x^9 + 359040*x^10 + 84736*x^11 - 7
9168*x^12 - 28672*x^13 + 6144*x^14 + 4096*x^15 + 512*x^16),x]

[Out]

E^(-1/2*x - (3*x^4)/(256 - 512*x - 128*x^2 + 640*x^3 + 11*x^4 - 320*x^5 - 32*x^6 + 64*x^7 + 16*x^8))

________________________________________________________________________________________

fricas [B]  time = 0.69, size = 89, normalized size = 2.70 $$\begin{array}{c}{e}^{(-\frac{16x^9+64x^8-32x^7-320x^6+11x^5+646x^4-128x^3-512x^2+256x}{2(16x^8+64x^7-32x^6-320x^5+11x^4+640x^3-128x^2-512x+256)})}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-256*x^16-2048*x^15-3072*x^14+14336*x^13+39584*x^12-41984*x^11-178368*x^10+80384*x^9+456711*x^8-161
536*x^7-721920*x^6+340480*x^5+642560*x^4-464896*x^3-196608*x^2+262144*x-65536)*exp((-16*x^9-64*x^8+32*x^7+320*
x^6-11*x^5-646*x^4+128*x^3+512*x^2-256*x)/(32*x^8+128*x^7-64*x^6-640*x^5+22*x^4+1280*x^3-256*x^2-1024*x+512))/
(512*x^16+4096*x^15+6144*x^14-28672*x^13-79168*x^12+84736*x^11+359040*x^10-161536*x^9-917262*x^8+323072*x^7+14
36160*x^6-677888*x^5-1266688*x^4+917504*x^3+393216*x^2-524288*x+131072),x, algorithm="fricas")

[Out]

e^(-1/2*(16*x^9 + 64*x^8 - 32*x^7 - 320*x^6 + 11*x^5 + 646*x^4 - 128*x^3 - 512*x^2 + 256*x)/(16*x^8 + 64*x^7 -
32*x^6 - 320*x^5 + 11*x^4 + 640*x^3 - 128*x^2 - 512*x + 256))

________________________________________________________________________________________

giac [B]  time = 1.21, size = 423, normalized size = 12.82 $$\begin{array}{c}{e}^{(-\frac{8x^9}{16x^8+64x^7-32x^6-320x^5+11x^4+640x^3-128x^2-512x+256}-\frac{32x^8}{16x^8+64x^7-32x^6-320x^5+11x^4+640x^3-128x^2-512x+256}+\frac{16x^7}{16x^8+64x^7-32x^6-320x^5+11x^4+640x^3-128x^2-512x+256}+\frac{160x^6}{16x^8+64x^7-32x^6-320x^5+11x^4+640x^3-128x^2-512x+256}-\frac{11x^5}{2(16x^8+64x^7-32x^6-320x^5+11x^4+640x^3-128x^2-512x+256)}-\frac{323x^4}{16x^8+64x^7-32x^6-320x^5+11x^4+640x^3-128x^2-512x+256}+\frac{64x^3}{16x^8+64x^7-32x^6-320x^5+11x^4+640x^3-128x^2-512x+256}+\frac{256x^2}{16x^8+64x^7-32x^6-320x^5+11x^4+640x^3-128x^2-512x+256}-\frac{128x}{16x^8+64x^7-32x^6-320x^5+11x^4+640x^3-128x^2-512x+256})}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-256*x^16-2048*x^15-3072*x^14+14336*x^13+39584*x^12-41984*x^11-178368*x^10+80384*x^9+456711*x^8-161
536*x^7-721920*x^6+340480*x^5+642560*x^4-464896*x^3-196608*x^2+262144*x-65536)*exp((-16*x^9-64*x^8+32*x^7+320*
x^6-11*x^5-646*x^4+128*x^3+512*x^2-256*x)/(32*x^8+128*x^7-64*x^6-640*x^5+22*x^4+1280*x^3-256*x^2-1024*x+512))/
(512*x^16+4096*x^15+6144*x^14-28672*x^13-79168*x^12+84736*x^11+359040*x^10-161536*x^9-917262*x^8+323072*x^7+14
36160*x^6-677888*x^5-1266688*x^4+917504*x^3+393216*x^2-524288*x+131072),x, algorithm="giac")

[Out]

e^(-8*x^9/(16*x^8 + 64*x^7 - 32*x^6 - 320*x^5 + 11*x^4 + 640*x^3 - 128*x^2 - 512*x + 256) - 32*x^8/(16*x^8 + 6
4*x^7 - 32*x^6 - 320*x^5 + 11*x^4 + 640*x^3 - 128*x^2 - 512*x + 256) + 16*x^7/(16*x^8 + 64*x^7 - 32*x^6 - 320*
x^5 + 11*x^4 + 640*x^3 - 128*x^2 - 512*x + 256) + 160*x^6/(16*x^8 + 64*x^7 - 32*x^6 - 320*x^5 + 11*x^4 + 640*x
^3 - 128*x^2 - 512*x + 256) - 11/2*x^5/(16*x^8 + 64*x^7 - 32*x^6 - 320*x^5 + 11*x^4 + 640*x^3 - 128*x^2 - 512*
x + 256) - 323*x^4/(16*x^8 + 64*x^7 - 32*x^6 - 320*x^5 + 11*x^4 + 640*x^3 - 128*x^2 - 512*x + 256) + 64*x^3/(1
6*x^8 + 64*x^7 - 32*x^6 - 320*x^5 + 11*x^4 + 640*x^3 - 128*x^2 - 512*x + 256) + 256*x^2/(16*x^8 + 64*x^7 - 32*
x^6 - 320*x^5 + 11*x^4 + 640*x^3 - 128*x^2 - 512*x + 256) - 128*x/(16*x^8 + 64*x^7 - 32*x^6 - 320*x^5 + 11*x^4
+ 640*x^3 - 128*x^2 - 512*x + 256))

________________________________________________________________________________________

maple [A]  time = 0.43, size = 87, normalized size = 2.64

method	result	size
gosper	${\mathrm{e}}^{-\frac{x(16x^8+64x^7-32x^6-320x^5+11x^4+646x^3-128x^2-512x+256)}{2(16x^8+64x^7-32x^6-320x^5+11x^4+640x^3-128x^2-512x+256)}}$	$87$
risch	${\mathrm{e}}^{-\frac{x(16x^8+64x^7-32x^6-320x^5+11x^4+646x^3-128x^2-512x+256)}{2(16x^8+64x^7-32x^6-320x^5+11x^4+640x^3-128x^2-512x+256)}}$	$87$
norman	$\frac{-512x{\mathrm{e}}^{\frac{-16x^9-64x^8+32x^7+320x^6-11x^5-646x^4+128x^3+512x^2-256x}{32x^8+128x^7-64x^6-640x^5+22x^4+1280x^3-256x^2-1024x+512}}-128x^2{\mathrm{e}}^{\frac{-16x^9-64x^8+32x^7+320x^6-11x^5-646x^4+128x^3+512x^2-256x}{32x^8+128x^7-64x^6-640x^5+22x^4+1280x^3-256x^2-1024x+512}}+640x^3{\mathrm{e}}^{\frac{-16x^9-64x^8+32x^7+320x^6-11x^5-646x^4+128x^3+512x^2-256x}{32x^8+128x^7-64x^6-640x^5+22x^4+1280x^3-256x^2-1024x+512}}+11x^4{\mathrm{e}}^{\frac{-16x^9-64x^8+32x^7+320x^6-11x^5-646x^4+128x^3+512x^2-256x}{32x^8+128x^7-64x^6-640x^5+22x^4+1280x^3-256x^2-1024x+512}}-320x^5{\mathrm{e}}^{\frac{-16x^9-64x^8+32x^7+320x^6-11x^5-646x^4+128x^3+512x^2-256x}{32x^8+128x^7-64x^6-640x^5+22x^4+1280x^3-256x^2-1024x+512}}-32x^6{\mathrm{e}}^{\frac{-16x^9-64x^8+32x^7+320x^6-11x^5-646x^4+128x^3+512x^2-256x}{32x^8+128x^7-64x^6-640x^5+22x^4+1280x^3-256x^2-1024x+512}}+64x^7{\mathrm{e}}^{\frac{-16x^9-64x^8+32x^7+320x^6-11x^5-646x^4+128x^3+512x^2-256x}{32x^8+128x^7-64x^6-640x^5+22x^4+1280x^3-256x^2-1024x+512}}+16x^8{\mathrm{e}}^{\frac{-16x^9-64x^8+32x^7+320x^6-11x^5-646x^4+128x^3+512x^2-256x}{32x^8+128x^7-64x^6-640x^5+22x^4+1280x^3-256x^2-1024x+512}}+256{\mathrm{e}}^{\frac{-16x^9-64x^8+32x^7+320x^6-11x^5-646x^4+128x^3+512x^2-256x}{32x^8+128x^7-64x^6-640x^5+22x^4+1280x^3-256x^2-1024x+512}}}{16x^8+64x^7-32x^6-320x^5+11x^4+640x^3-128x^2-512x+256}$	$877$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-256*x^16-2048*x^15-3072*x^14+14336*x^13+39584*x^12-41984*x^11-178368*x^10+80384*x^9+456711*x^8-161536*x^
7-721920*x^6+340480*x^5+642560*x^4-464896*x^3-196608*x^2+262144*x-65536)*exp((-16*x^9-64*x^8+32*x^7+320*x^6-11
*x^5-646*x^4+128*x^3+512*x^2-256*x)/(32*x^8+128*x^7-64*x^6-640*x^5+22*x^4+1280*x^3-256*x^2-1024*x+512))/(512*x
^16+4096*x^15+6144*x^14-28672*x^13-79168*x^12+84736*x^11+359040*x^10-161536*x^9-917262*x^8+323072*x^7+1436160*
x^6-677888*x^5-1266688*x^4+917504*x^3+393216*x^2-524288*x+131072),x,method=_RETURNVERBOSE)

[Out]

exp(-1/2*x*(16*x^8+64*x^7-32*x^6-320*x^5+11*x^4+646*x^3-128*x^2-512*x+256)/(16*x^8+64*x^7-32*x^6-320*x^5+11*x^
4+640*x^3-128*x^2-512*x+256))

________________________________________________________________________________________

maxima [B]  time = 26.12, size = 52, normalized size = 1.58 $$\begin{array}{c}{e}^{(-\frac{3x^4}{16x^8+64x^7-32x^6-320x^5+11x^4+640x^3-128x^2-512x+256}-\frac{1}{2}x)}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-256*x^16-2048*x^15-3072*x^14+14336*x^13+39584*x^12-41984*x^11-178368*x^10+80384*x^9+456711*x^8-161
536*x^7-721920*x^6+340480*x^5+642560*x^4-464896*x^3-196608*x^2+262144*x-65536)*exp((-16*x^9-64*x^8+32*x^7+320*
x^6-11*x^5-646*x^4+128*x^3+512*x^2-256*x)/(32*x^8+128*x^7-64*x^6-640*x^5+22*x^4+1280*x^3-256*x^2-1024*x+512))/
(512*x^16+4096*x^15+6144*x^14-28672*x^13-79168*x^12+84736*x^11+359040*x^10-161536*x^9-917262*x^8+323072*x^7+14
36160*x^6-677888*x^5-1266688*x^4+917504*x^3+393216*x^2-524288*x+131072),x, algorithm="maxima")

[Out]

e^(-3*x^4/(16*x^8 + 64*x^7 - 32*x^6 - 320*x^5 + 11*x^4 + 640*x^3 - 128*x^2 - 512*x + 256) - 1/2*x)

________________________________________________________________________________________

mupad [B]  time = 0.51, size = 431, normalized size = 13.06 $$\begin{array}{c}{\mathrm{e}}^{-\frac{128x}{16x^8+64x^7-32x^6-320x^5+11x^4+640x^3-128x^2-512x+256}}{\mathrm{e}}^{-\frac{8x^9}{16x^8+64x^7-32x^6-320x^5+11x^4+640x^3-128x^2-512x+256}}{\mathrm{e}}^{\frac{16x^7}{16x^8+64x^7-32x^6-320x^5+11x^4+640x^3-128x^2-512x+256}}{\mathrm{e}}^{-\frac{32x^8}{16x^8+64x^7-32x^6-320x^5+11x^4+640x^3-128x^2-512x+256}}{\mathrm{e}}^{\frac{64x^3}{16x^8+64x^7-32x^6-320x^5+11x^4+640x^3-128x^2-512x+256}}{\mathrm{e}}^{\frac{160x^6}{16x^8+64x^7-32x^6-320x^5+11x^4+640x^3-128x^2-512x+256}}{\mathrm{e}}^{\frac{256x^2}{16x^8+64x^7-32x^6-320x^5+11x^4+640x^3-128x^2-512x+256}}{\mathrm{e}}^{-\frac{323x^4}{16x^8+64x^7-32x^6-320x^5+11x^4+640x^3-128x^2-512x+256}}{\mathrm{e}}^{-\frac{11x^5}{32x^8+128x^7-64x^6-640x^5+22x^4+1280x^3-256x^2-1024x+512}}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(-(256*x - 512*x^2 - 128*x^3 + 646*x^4 + 11*x^5 - 320*x^6 - 32*x^7 + 64*x^8 + 16*x^9)/(1280*x^3 - 256
*x^2 - 1024*x + 22*x^4 - 640*x^5 - 64*x^6 + 128*x^7 + 32*x^8 + 512))*(196608*x^2 - 262144*x + 464896*x^3 - 642
560*x^4 - 340480*x^5 + 721920*x^6 + 161536*x^7 - 456711*x^8 - 80384*x^9 + 178368*x^10 + 41984*x^11 - 39584*x^1
2 - 14336*x^13 + 3072*x^14 + 2048*x^15 + 256*x^16 + 65536))/(393216*x^2 - 524288*x + 917504*x^3 - 1266688*x^4
- 677888*x^5 + 1436160*x^6 + 323072*x^7 - 917262*x^8 - 161536*x^9 + 359040*x^10 + 84736*x^11 - 79168*x^12 - 28
672*x^13 + 6144*x^14 + 4096*x^15 + 512*x^16 + 131072),x)

[Out]

exp(-(128*x)/(640*x^3 - 128*x^2 - 512*x + 11*x^4 - 320*x^5 - 32*x^6 + 64*x^7 + 16*x^8 + 256))*exp(-(8*x^9)/(64
0*x^3 - 128*x^2 - 512*x + 11*x^4 - 320*x^5 - 32*x^6 + 64*x^7 + 16*x^8 + 256))*exp((16*x^7)/(640*x^3 - 128*x^2
- 512*x + 11*x^4 - 320*x^5 - 32*x^6 + 64*x^7 + 16*x^8 + 256))*exp(-(32*x^8)/(640*x^3 - 128*x^2 - 512*x + 11*x^
4 - 320*x^5 - 32*x^6 + 64*x^7 + 16*x^8 + 256))*exp((64*x^3)/(640*x^3 - 128*x^2 - 512*x + 11*x^4 - 320*x^5 - 32
*x^6 + 64*x^7 + 16*x^8 + 256))*exp((160*x^6)/(640*x^3 - 128*x^2 - 512*x + 11*x^4 - 320*x^5 - 32*x^6 + 64*x^7 +
16*x^8 + 256))*exp((256*x^2)/(640*x^3 - 128*x^2 - 512*x + 11*x^4 - 320*x^5 - 32*x^6 + 64*x^7 + 16*x^8 + 256))
*exp(-(323*x^4)/(640*x^3 - 128*x^2 - 512*x + 11*x^4 - 320*x^5 - 32*x^6 + 64*x^7 + 16*x^8 + 256))*exp(-(11*x^5)
/(1280*x^3 - 256*x^2 - 1024*x + 22*x^4 - 640*x^5 - 64*x^6 + 128*x^7 + 32*x^8 + 512))

________________________________________________________________________________________

sympy [B]  time = 1.56, size = 85, normalized size = 2.58 $$\begin{array}{c}{e}^{\frac{-16x^9-64x^8+32x^7+320x^6-11x^5-646x^4+128x^3+512x^2-256x}{32x^8+128x^7-64x^6-640x^5+22x^4+1280x^3-256x^2-1024x+512}}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-256*x**16-2048*x**15-3072*x**14+14336*x**13+39584*x**12-41984*x**11-178368*x**10+80384*x**9+456711
*x**8-161536*x**7-721920*x**6+340480*x**5+642560*x**4-464896*x**3-196608*x**2+262144*x-65536)*exp((-16*x**9-64
*x**8+32*x**7+320*x**6-11*x**5-646*x**4+128*x**3+512*x**2-256*x)/(32*x**8+128*x**7-64*x**6-640*x**5+22*x**4+12
80*x**3-256*x**2-1024*x+512))/(512*x**16+4096*x**15+6144*x**14-28672*x**13-79168*x**12+84736*x**11+359040*x**1
0-161536*x**9-917262*x**8+323072*x**7+1436160*x**6-677888*x**5-1266688*x**4+917504*x**3+393216*x**2-524288*x+1
31072),x)

[Out]

exp((-16*x**9 - 64*x**8 + 32*x**7 + 320*x**6 - 11*x**5 - 646*x**4 + 128*x**3 + 512*x**2 - 256*x)/(32*x**8 + 12
8*x**7 - 64*x**6 - 640*x**5 + 22*x**4 + 1280*x**3 - 256*x**2 - 1024*x + 512))

________________________________________________________________________________________