3.36.24 \(\int \frac {e^{5 x} (-128-512 x-192 x^2)+e^{4 x} (-3072 x-5376 x^2-1536 x^3)+e^{2 x} (2304 x+6336 x^2-52224 x^3-34560 x^4)+e^{3 x} (192+896 x-20000 x^2-20608 x^3-3456 x^4)+e^x (-72-128 x+4804 x^2+10848 x^3-49184 x^4-21888 x^5+5184 x^6)}{324 x^2+900 x^3-13487 x^4-47536 x^5+197808 x^6+770240 x^7-1139360 x^8-4591872 x^9+3297024 x^{10}+5971968 x^{11}+1679616 x^{12}+e^{8 x} (1024 x^2+1024 x^3+256 x^4)+e^{7 x} (24576 x^3+24576 x^4+6144 x^5)+e^{6 x} (-3072 x^2-7168 x^3+253184 x^4+257024 x^5+64512 x^6)+e^{5 x} (-55296 x^3-129024 x^4+1460736 x^5+1529856 x^6+387072 x^7)+e^{4 x} (3456 x^2+10624 x^3-400544 x^4-959744 x^5+5150976 x^6+5667840 x^7+1451520 x^8)+e^{3 x} (41472 x^3+127488 x^4-1488768 x^5-3775488 x^6+11326464 x^7+13381632 x^8+3483648 x^9)+e^{2 x} (-1728 x^2-5568 x^3+177232 x^4+563520 x^5-2972352 x^6-8281600 x^7+15075072 x^8+19657728 x^9+5225472 x^{10})+e^x (-10368 x^3-33408 x^4+316896 x^5+1086336 x^6-2980224 x^7-9600000 x^8+10990080 x^9+16422912 x^{10}+4478976 x^{11})} \, dx\)

Optimal. Leaf size=39 \[ \frac {e^x}{4 x (2+x) \left (-x+\left (\frac {3}{4}+x-\left (e^x+3 x\right )^2\right )^2\right )} \]

________________________________________________________________________________________

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*x)*(-128 - 512*x - 192*x^2) + E^(4*x)*(-3072*x - 5376*x^2 - 1536*x^3) + E^(2*x)*(2304*x + 6336*x^2 -
52224*x^3 - 34560*x^4) + E^(3*x)*(192 + 896*x - 20000*x^2 - 20608*x^3 - 3456*x^4) + E^x*(-72 - 128*x + 4804*x
^2 + 10848*x^3 - 49184*x^4 - 21888*x^5 + 5184*x^6))/(324*x^2 + 900*x^3 - 13487*x^4 - 47536*x^5 + 197808*x^6 +
770240*x^7 - 1139360*x^8 - 4591872*x^9 + 3297024*x^10 + 5971968*x^11 + 1679616*x^12 + E^(8*x)*(1024*x^2 + 1024
*x^3 + 256*x^4) + E^(7*x)*(24576*x^3 + 24576*x^4 + 6144*x^5) + E^(6*x)*(-3072*x^2 - 7168*x^3 + 253184*x^4 + 25
7024*x^5 + 64512*x^6) + E^(5*x)*(-55296*x^3 - 129024*x^4 + 1460736*x^5 + 1529856*x^6 + 387072*x^7) + E^(4*x)*(
3456*x^2 + 10624*x^3 - 400544*x^4 - 959744*x^5 + 5150976*x^6 + 5667840*x^7 + 1451520*x^8) + E^(3*x)*(41472*x^3
+ 127488*x^4 - 1488768*x^5 - 3775488*x^6 + 11326464*x^7 + 13381632*x^8 + 3483648*x^9) + E^(2*x)*(-1728*x^2 -
5568*x^3 + 177232*x^4 + 563520*x^5 - 2972352*x^6 - 8281600*x^7 + 15075072*x^8 + 19657728*x^9 + 5225472*x^10) +
E^x*(-10368*x^3 - 33408*x^4 + 316896*x^5 + 1086336*x^6 - 2980224*x^7 - 9600000*x^8 + 10990080*x^9 + 16422912*
x^10 + 4478976*x^11)),x]

[Out]

$Aborted

Rubi steps

Aborted

________________________________________________________________________________________

Mathematica [B]  time = 0.21, size = 83, normalized size = 2.13 \begin {gather*} \frac {4 e^x}{x (2+x) \left (9+16 e^{4 x}+8 x+192 e^{3 x} x-200 x^2-288 x^3+1296 x^4+48 e^x x \left (-3-4 x+36 x^2\right )+8 e^{2 x} \left (-3-4 x+108 x^2\right )\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^(5*x)*(-128 - 512*x - 192*x^2) + E^(4*x)*(-3072*x - 5376*x^2 - 1536*x^3) + E^(2*x)*(2304*x + 6336
*x^2 - 52224*x^3 - 34560*x^4) + E^(3*x)*(192 + 896*x - 20000*x^2 - 20608*x^3 - 3456*x^4) + E^x*(-72 - 128*x +
4804*x^2 + 10848*x^3 - 49184*x^4 - 21888*x^5 + 5184*x^6))/(324*x^2 + 900*x^3 - 13487*x^4 - 47536*x^5 + 197808*
x^6 + 770240*x^7 - 1139360*x^8 - 4591872*x^9 + 3297024*x^10 + 5971968*x^11 + 1679616*x^12 + E^(8*x)*(1024*x^2
+ 1024*x^3 + 256*x^4) + E^(7*x)*(24576*x^3 + 24576*x^4 + 6144*x^5) + E^(6*x)*(-3072*x^2 - 7168*x^3 + 253184*x^
4 + 257024*x^5 + 64512*x^6) + E^(5*x)*(-55296*x^3 - 129024*x^4 + 1460736*x^5 + 1529856*x^6 + 387072*x^7) + E^(
4*x)*(3456*x^2 + 10624*x^3 - 400544*x^4 - 959744*x^5 + 5150976*x^6 + 5667840*x^7 + 1451520*x^8) + E^(3*x)*(414
72*x^3 + 127488*x^4 - 1488768*x^5 - 3775488*x^6 + 11326464*x^7 + 13381632*x^8 + 3483648*x^9) + E^(2*x)*(-1728*
x^2 - 5568*x^3 + 177232*x^4 + 563520*x^5 - 2972352*x^6 - 8281600*x^7 + 15075072*x^8 + 19657728*x^9 + 5225472*x
^10) + E^x*(-10368*x^3 - 33408*x^4 + 316896*x^5 + 1086336*x^6 - 2980224*x^7 - 9600000*x^8 + 10990080*x^9 + 164
22912*x^10 + 4478976*x^11)),x]

[Out]

(4*E^x)/(x*(2 + x)*(9 + 16*E^(4*x) + 8*x + 192*E^(3*x)*x - 200*x^2 - 288*x^3 + 1296*x^4 + 48*E^x*x*(-3 - 4*x +
36*x^2) + 8*E^(2*x)*(-3 - 4*x + 108*x^2)))

________________________________________________________________________________________

fricas [B]  time = 0.65, size = 113, normalized size = 2.90 \begin {gather*} \frac {4 \, e^{x}}{1296 \, x^{6} + 2304 \, x^{5} - 776 \, x^{4} - 392 \, x^{3} + 25 \, x^{2} + 16 \, {\left (x^{2} + 2 \, x\right )} e^{\left (4 \, x\right )} + 192 \, {\left (x^{3} + 2 \, x^{2}\right )} e^{\left (3 \, x\right )} + 8 \, {\left (108 \, x^{4} + 212 \, x^{3} - 11 \, x^{2} - 6 \, x\right )} e^{\left (2 \, x\right )} + 48 \, {\left (36 \, x^{5} + 68 \, x^{4} - 11 \, x^{3} - 6 \, x^{2}\right )} e^{x} + 18 \, x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-192*x^2-512*x-128)*exp(x)^5+(-1536*x^3-5376*x^2-3072*x)*exp(x)^4+(-3456*x^4-20608*x^3-20000*x^2+8
96*x+192)*exp(x)^3+(-34560*x^4-52224*x^3+6336*x^2+2304*x)*exp(x)^2+(5184*x^6-21888*x^5-49184*x^4+10848*x^3+480
4*x^2-128*x-72)*exp(x))/((256*x^4+1024*x^3+1024*x^2)*exp(x)^8+(6144*x^5+24576*x^4+24576*x^3)*exp(x)^7+(64512*x
^6+257024*x^5+253184*x^4-7168*x^3-3072*x^2)*exp(x)^6+(387072*x^7+1529856*x^6+1460736*x^5-129024*x^4-55296*x^3)
*exp(x)^5+(1451520*x^8+5667840*x^7+5150976*x^6-959744*x^5-400544*x^4+10624*x^3+3456*x^2)*exp(x)^4+(3483648*x^9
[phone]*x^8+11326464*x^7-3775488*x^6-1488768*x^5+127488*x^4+41472*x^3)*exp(x)^3+(5225472*x^10+19657728*x^9+1
5075072*x^8-8281600*x^7-2972352*x^6+563520*x^5+177232*x^4-5568*x^3-1728*x^2)*exp(x)^2+(4478976*x^11+16422912*x
^10+10990080*x^9-9600000*x^8-2980224*x^7+1086336*x^6+316896*x^5-33408*x^4-10368*x^3)*exp(x)+1679616*x^12+59719
68*x^11+3297024*x^10-4591872*x^9-1139360*x^8+770240*x^7+197808*x^6-47536*x^5-13487*x^4+900*x^3+324*x^2),x, alg
orithm="fricas")

[Out]

4*e^x/(1296*x^6 + 2304*x^5 - 776*x^4 - 392*x^3 + 25*x^2 + 16*(x^2 + 2*x)*e^(4*x) + 192*(x^3 + 2*x^2)*e^(3*x) +
8*(108*x^4 + 212*x^3 - 11*x^2 - 6*x)*e^(2*x) + 48*(36*x^5 + 68*x^4 - 11*x^3 - 6*x^2)*e^x + 18*x)

________________________________________________________________________________________

giac [B]  time = 4.11, size = 131, normalized size = 3.36 \begin {gather*} \frac {8 \, e^{x}}{1296 \, x^{6} + 1728 \, x^{5} e^{x} + 2304 \, x^{5} + 864 \, x^{4} e^{\left (2 \, x\right )} + 3264 \, x^{4} e^{x} - 776 \, x^{4} + 192 \, x^{3} e^{\left (3 \, x\right )} + 1696 \, x^{3} e^{\left (2 \, x\right )} - 528 \, x^{3} e^{x} - 392 \, x^{3} + 16 \, x^{2} e^{\left (4 \, x\right )} + 384 \, x^{2} e^{\left (3 \, x\right )} - 88 \, x^{2} e^{\left (2 \, x\right )} - 288 \, x^{2} e^{x} + 25 \, x^{2} + 32 \, x e^{\left (4 \, x\right )} - 48 \, x e^{\left (2 \, x\right )} + 18 \, x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-192*x^2-512*x-128)*exp(x)^5+(-1536*x^3-5376*x^2-3072*x)*exp(x)^4+(-3456*x^4-20608*x^3-20000*x^2+8
96*x+192)*exp(x)^3+(-34560*x^4-52224*x^3+6336*x^2+2304*x)*exp(x)^2+(5184*x^6-21888*x^5-49184*x^4+10848*x^3+480
4*x^2-128*x-72)*exp(x))/((256*x^4+1024*x^3+1024*x^2)*exp(x)^8+(6144*x^5+24576*x^4+24576*x^3)*exp(x)^7+(64512*x
^6+257024*x^5+253184*x^4-7168*x^3-3072*x^2)*exp(x)^6+(387072*x^7+1529856*x^6+1460736*x^5-129024*x^4-55296*x^3)
*exp(x)^5+(1451520*x^8+5667840*x^7+5150976*x^6-959744*x^5-400544*x^4+10624*x^3+3456*x^2)*exp(x)^4+(3483648*x^9
[phone]*x^8+11326464*x^7-3775488*x^6-1488768*x^5+127488*x^4+41472*x^3)*exp(x)^3+(5225472*x^10+19657728*x^9+1
5075072*x^8-8281600*x^7-2972352*x^6+563520*x^5+177232*x^4-5568*x^3-1728*x^2)*exp(x)^2+(4478976*x^11+16422912*x
^10+10990080*x^9-9600000*x^8-2980224*x^7+1086336*x^6+316896*x^5-33408*x^4-10368*x^3)*exp(x)+1679616*x^12+59719
68*x^11+3297024*x^10-4591872*x^9-1139360*x^8+770240*x^7+197808*x^6-47536*x^5-13487*x^4+900*x^3+324*x^2),x, alg
orithm="giac")

[Out]

8*e^x/(1296*x^6 + 1728*x^5*e^x + 2304*x^5 + 864*x^4*e^(2*x) + 3264*x^4*e^x - 776*x^4 + 192*x^3*e^(3*x) + 1696*
x^3*e^(2*x) - 528*x^3*e^x - 392*x^3 + 16*x^2*e^(4*x) + 384*x^2*e^(3*x) - 88*x^2*e^(2*x) - 288*x^2*e^x + 25*x^2
+ 32*x*e^(4*x) - 48*x*e^(2*x) + 18*x)

________________________________________________________________________________________

maple [B]  time = 0.11, size = 89, normalized size = 2.28

method	result	size
risch	\(\frac {4 \,{\mathrm e}^{x}}{x \left (2+x \right ) \left (1296 x^{4}+1728 \,{\mathrm e}^{x} x^{3}+864 \,{\mathrm e}^{2 x} x^{2}+192 x \,{\mathrm e}^{3 x}+16 \,{\mathrm e}^{4 x}-288 x^{3}-192 \,{\mathrm e}^{x} x^{2}-32 x \,{\mathrm e}^{2 x}-200 x^{2}-144 \,{\mathrm e}^{x} x -24 \,{\mathrm e}^{2 x}+8 x +9\right )}\)	\(89\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-192*x^2-512*x-128)*exp(x)^5+(-1536*x^3-5376*x^2-3072*x)*exp(x)^4+(-3456*x^4-20608*x^3-20000*x^2+896*x+1
92)*exp(x)^3+(-34560*x^4-52224*x^3+6336*x^2+2304*x)*exp(x)^2+(5184*x^6-21888*x^5-49184*x^4+10848*x^3+4804*x^2-
128*x-72)*exp(x))/((256*x^4+1024*x^3+1024*x^2)*exp(x)^8+(6144*x^5+24576*x^4+24576*x^3)*exp(x)^7+(64512*x^6+257
024*x^5+253184*x^4-7168*x^3-3072*x^2)*exp(x)^6+(387072*x^7+1529856*x^6+1460736*x^5-129024*x^4-55296*x^3)*exp(x
)^5+(1451520*x^8+5667840*x^7+5150976*x^6-959744*x^5-400544*x^4+10624*x^3+3456*x^2)*exp(x)^4+(3483648*x^9+13381
632*x^8+11326464*x^7-3775488*x^6-1488768*x^5+127488*x^4+41472*x^3)*exp(x)^3+(5225472*x^10+19657728*x^9+1507507
2*x^8-8281600*x^7-2972352*x^6+563520*x^5+177232*x^4-5568*x^3-1728*x^2)*exp(x)^2+(4478976*x^11+16422912*x^10+10
990080*x^9-9600000*x^8-2980224*x^7+1086336*x^6+316896*x^5-33408*x^4-10368*x^3)*exp(x)+1679616*x^12+5971968*x^1
1+3297024*x^10-4591872*x^9-1139360*x^8+770240*x^7+197808*x^6-47536*x^5-13487*x^4+900*x^3+324*x^2),x,method=_RE
TURNVERBOSE)

[Out]

4/x/(2+x)*exp(x)/(1296*x^4+1728*exp(x)*x^3+864*exp(2*x)*x^2+192*x*exp(3*x)+16*exp(4*x)-288*x^3-192*exp(x)*x^2-
32*x*exp(2*x)-200*x^2-144*exp(x)*x-24*exp(2*x)+8*x+9)

________________________________________________________________________________________

maxima [B]  time = 0.81, size = 113, normalized size = 2.90 \begin {gather*} \frac {4 \, e^{x}}{1296 \, x^{6} + 2304 \, x^{5} - 776 \, x^{4} - 392 \, x^{3} + 25 \, x^{2} + 16 \, {\left (x^{2} + 2 \, x\right )} e^{\left (4 \, x\right )} + 192 \, {\left (x^{3} + 2 \, x^{2}\right )} e^{\left (3 \, x\right )} + 8 \, {\left (108 \, x^{4} + 212 \, x^{3} - 11 \, x^{2} - 6 \, x\right )} e^{\left (2 \, x\right )} + 48 \, {\left (36 \, x^{5} + 68 \, x^{4} - 11 \, x^{3} - 6 \, x^{2}\right )} e^{x} + 18 \, x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-192*x^2-512*x-128)*exp(x)^5+(-1536*x^3-5376*x^2-3072*x)*exp(x)^4+(-3456*x^4-20608*x^3-20000*x^2+8
96*x+192)*exp(x)^3+(-34560*x^4-52224*x^3+6336*x^2+2304*x)*exp(x)^2+(5184*x^6-21888*x^5-49184*x^4+10848*x^3+480
4*x^2-128*x-72)*exp(x))/((256*x^4+1024*x^3+1024*x^2)*exp(x)^8+(6144*x^5+24576*x^4+24576*x^3)*exp(x)^7+(64512*x
^6+257024*x^5+253184*x^4-7168*x^3-3072*x^2)*exp(x)^6+(387072*x^7+1529856*x^6+1460736*x^5-129024*x^4-55296*x^3)
*exp(x)^5+(1451520*x^8+5667840*x^7+5150976*x^6-959744*x^5-400544*x^4+10624*x^3+3456*x^2)*exp(x)^4+(3483648*x^9
[phone]*x^8+11326464*x^7-3775488*x^6-1488768*x^5+127488*x^4+41472*x^3)*exp(x)^3+(5225472*x^10+19657728*x^9+1
5075072*x^8-8281600*x^7-2972352*x^6+563520*x^5+177232*x^4-5568*x^3-1728*x^2)*exp(x)^2+(4478976*x^11+16422912*x
^10+10990080*x^9-9600000*x^8-2980224*x^7+1086336*x^6+316896*x^5-33408*x^4-10368*x^3)*exp(x)+1679616*x^12+59719
68*x^11+3297024*x^10-4591872*x^9-1139360*x^8+770240*x^7+197808*x^6-47536*x^5-13487*x^4+900*x^3+324*x^2),x, alg
orithm="maxima")

[Out]

4*e^x/(1296*x^6 + 2304*x^5 - 776*x^4 - 392*x^3 + 25*x^2 + 16*(x^2 + 2*x)*e^(4*x) + 192*(x^3 + 2*x^2)*e^(3*x) +
8*(108*x^4 + 212*x^3 - 11*x^2 - 6*x)*e^(2*x) + 48*(36*x^5 + 68*x^4 - 11*x^3 - 6*x^2)*e^x + 18*x)

________________________________________________________________________________________

mupad [F]  time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int -\frac {{\mathrm {e}}^{5\,x}\,\left (192\,x^2+512\,x+128\right )+{\mathrm {e}}^{4\,x}\,\left (1536\,x^3+5376\,x^2+3072\,x\right )+{\mathrm {e}}^{3\,x}\,\left (3456\,x^4+20608\,x^3+20000\,x^2-896\,x-192\right )-{\mathrm {e}}^{2\,x}\,\left (-34560\,x^4-52224\,x^3+6336\,x^2+2304\,x\right )+{\mathrm {e}}^x\,\left (-5184\,x^6+21888\,x^5+49184\,x^4-10848\,x^3-4804\,x^2+128\,x+72\right )}{{\mathrm {e}}^{6\,x}\,\left (64512\,x^6+257024\,x^5+253184\,x^4-7168\,x^3-3072\,x^2\right )+{\mathrm {e}}^{5\,x}\,\left (387072\,x^7+1529856\,x^6+1460736\,x^5-129024\,x^4-55296\,x^3\right )+{\mathrm {e}}^{4\,x}\,\left (1451520\,x^8+5667840\,x^7+5150976\,x^6-959744\,x^5-400544\,x^4+10624\,x^3+3456\,x^2\right )+{\mathrm {e}}^{3\,x}\,\left (3483648\,x^9+13381632\,x^8+11326464\,x^7-3775488\,x^6-1488768\,x^5+127488\,x^4+41472\,x^3\right )+{\mathrm {e}}^x\,\left (4478976\,x^{11}[phone]\,x^{10}[phone]\,x^9-9600000\,x^8-2980224\,x^7+1086336\,x^6+316896\,x^5-33408\,x^4-10368\,x^3\right )+{\mathrm {e}}^{8\,x}\,\left (256\,x^4+1024\,x^3+1024\,x^2\right )+{\mathrm {e}}^{7\,x}\,\left (6144\,x^5+24576\,x^4+24576\,x^3\right )+324\,x^2+900\,x^3-13487\,x^4-47536\,x^5+197808\,x^6+770240\,x^7-1139360\,x^8-4591872\,x^9+3297024\,x^{10}+5971968\,x^{11}+1679616\,x^{12}+{\mathrm {e}}^{2\,x}\,\left (5225472\,x^{10}[phone]\,x^9+15075072\,x^8-8281600\,x^7-2972352\,x^6+563520\,x^5+177232\,x^4-5568\,x^3-1728\,x^2\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(5*x)*(512*x + 192*x^2 + 128) + exp(4*x)*(3072*x + 5376*x^2 + 1536*x^3) + exp(3*x)*(20000*x^2 - 896*x
+ 20608*x^3 + 3456*x^4 - 192) - exp(2*x)*(2304*x + 6336*x^2 - 52224*x^3 - 34560*x^4) + exp(x)*(128*x - 4804*x
^2 - 10848*x^3 + 49184*x^4 + 21888*x^5 - 5184*x^6 + 72))/(exp(6*x)*(253184*x^4 - 7168*x^3 - 3072*x^2 + 257024*
x^5 + 64512*x^6) + exp(5*x)*(1460736*x^5 - 129024*x^4 - 55296*x^3 + 1529856*x^6 + 387072*x^7) + exp(4*x)*(3456
*x^2 + 10624*x^3 - 400544*x^4 - 959744*x^5 + 5150976*x^6 + 5667840*x^7 + 1451520*x^8) + exp(3*x)*(41472*x^3 +
127488*x^4 - 1488768*x^5 - 3775488*x^6 + 11326464*x^7 + 13381632*x^8 + 3483648*x^9) + exp(x)*(316896*x^5 - 334
08*x^4 - 10368*x^3 + 1086336*x^6 - 2980224*x^7 - 9600000*x^8 + 10990080*x^9 + 16422912*x^10 + 4478976*x^11) +
exp(8*x)*(1024*x^2 + 1024*x^3 + 256*x^4) + exp(7*x)*(24576*x^3 + 24576*x^4 + 6144*x^5) + 324*x^2 + 900*x^3 - 1
3487*x^4 - 47536*x^5 + 197808*x^6 + 770240*x^7 - 1139360*x^8 - 4591872*x^9 + 3297024*x^10 + 5971968*x^11 + 167
9616*x^12 + exp(2*x)*(177232*x^4 - 5568*x^3 - 1728*x^2 + 563520*x^5 - 2972352*x^6 - 8281600*x^7 + 15075072*x^8
+ 19657728*x^9 + 5225472*x^10)),x)

[Out]

int(-(exp(5*x)*(512*x + 192*x^2 + 128) + exp(4*x)*(3072*x + 5376*x^2 + 1536*x^3) + exp(3*x)*(20000*x^2 - 896*x
+ 20608*x^3 + 3456*x^4 - 192) - exp(2*x)*(2304*x + 6336*x^2 - 52224*x^3 - 34560*x^4) + exp(x)*(128*x - 4804*x
^2 - 10848*x^3 + 49184*x^4 + 21888*x^5 - 5184*x^6 + 72))/(exp(6*x)*(253184*x^4 - 7168*x^3 - 3072*x^2 + 257024*
x^5 + 64512*x^6) + exp(5*x)*(1460736*x^5 - 129024*x^4 - 55296*x^3 + 1529856*x^6 + 387072*x^7) + exp(4*x)*(3456
*x^2 + 10624*x^3 - 400544*x^4 - 959744*x^5 + 5150976*x^6 + 5667840*x^7 + 1451520*x^8) + exp(3*x)*(41472*x^3 +
127488*x^4 - 1488768*x^5 - 3775488*x^6 + 11326464*x^7 + 13381632*x^8 + 3483648*x^9) + exp(x)*(316896*x^5 - 334
08*x^4 - 10368*x^3 + 1086336*x^6 - 2980224*x^7 - 9600000*x^8 + 10990080*x^9 + 16422912*x^10 + 4478976*x^11) +
exp(8*x)*(1024*x^2 + 1024*x^3 + 256*x^4) + exp(7*x)*(24576*x^3 + 24576*x^4 + 6144*x^5) + 324*x^2 + 900*x^3 - 1
3487*x^4 - 47536*x^5 + 197808*x^6 + 770240*x^7 - 1139360*x^8 - 4591872*x^9 + 3297024*x^10 + 5971968*x^11 + 167
9616*x^12 + exp(2*x)*(177232*x^4 - 5568*x^3 - 1728*x^2 + 563520*x^5 - 2972352*x^6 - 8281600*x^7 + 15075072*x^8
+ 19657728*x^9 + 5225472*x^10)), x)

________________________________________________________________________________________

sympy [B]  time = 0.81, size = 109, normalized size = 2.79 \begin {gather*} \frac {4 e^{x}}{1296 x^{6} + 2304 x^{5} - 776 x^{4} - 392 x^{3} + 25 x^{2} + 18 x + \left (16 x^{2} + 32 x\right ) e^{4 x} + \left (192 x^{3} + 384 x^{2}\right ) e^{3 x} + \left (864 x^{4} + 1696 x^{3} - 88 x^{2} - 48 x\right ) e^{2 x} + \left (1728 x^{5} + 3264 x^{4} - 528 x^{3} - 288 x^{2}\right ) e^{x}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-192*x**2-512*x-128)*exp(x)**5+(-1536*x**3-5376*x**2-3072*x)*exp(x)**4+(-3456*x**4-20608*x**3-2000
0*x**2+896*x+192)*exp(x)**3+(-34560*x**4-52224*x**3+6336*x**2+2304*x)*exp(x)**2+(5184*x**6-21888*x**5-49184*x*
*4+10848*x**3+4804*x**2-128*x-72)*exp(x))/((256*x**4+1024*x**3+1024*x**2)*exp(x)**8+(6144*x**5+24576*x**4+2457
6*x**3)*exp(x)**7+(64512*x**6+257024*x**5+253184*x**4-7168*x**3-3072*x**2)*exp(x)**6+(387072*x**7+1529856*x**6
+1460736*x**5-129024*x**4-55296*x**3)*exp(x)**5+(1451520*x**8+5667840*x**7+5150976*x**6-959744*x**5-400544*x**
4+10624*x**3+3456*x**2)*exp(x)**4+(3483648*x**9+13381632*x**8+11326464*x**7-3775488*x**6-1488768*x**5+127488*x
**4+41472*x**3)*exp(x)**3+(5225472*x**10+19657728*x**9+15075072*x**8-8281600*x**7-2972352*x**6+563520*x**5+177
232*x**4-5568*x**3-1728*x**2)*exp(x)**2+(4478976*x**11+16422912*x**10+10990080*x**9-9600000*x**8-2980224*x**7+
1086336*x**6+316896*x**5-33408*x**4-10368*x**3)*exp(x)+1679616*x**12+5971968*x**11+3297024*x**10-4591872*x**9-
1139360*x**8+770240*x**7+197808*x**6-47536*x**5-13487*x**4+900*x**3+324*x**2),x)

[Out]

4*exp(x)/(1296*x**6 + 2304*x**5 - 776*x**4 - 392*x**3 + 25*x**2 + 18*x + (16*x**2 + 32*x)*exp(4*x) + (192*x**3
+ 384*x**2)*exp(3*x) + (864*x**4 + 1696*x**3 - 88*x**2 - 48*x)*exp(2*x) + (1728*x**5 + 3264*x**4 - 528*x**3 -
288*x**2)*exp(x))

________________________________________________________________________________________