3.42.63 \(\int \frac {-4 e^{10 x}-80 e^{8 x} x-640 e^{6 x} x^2-2560 e^{4 x} x^3-5120 e^{2 x} x^4-4096 x^5+e^{\frac {65536 x^2+25 e^{8 x} x^2+400 e^{6 x} x^3-40960 x^4+6400 x^6+e^{4 x} (-2560 x^2+2400 x^4)+e^{2 x} (-20480 x^3+6400 x^5)}{e^{8 x}+16 e^{6 x} x+96 e^{4 x} x^2+256 e^{2 x} x^3+256 x^4}} (-1572864 x^4+6144 x^6+153600 x^8+e^{10 x} (6 x+150 x^3)+e^{8 x} (120 x^2+3000 x^4)+e^{6 x} (-14400 x^3+30720 x^4+24000 x^5)+e^{4 x} (-119040 x^4+245760 x^5+96000 x^6)+e^{2 x} (393216 x^3-1572864 x^4-238080 x^5+491520 x^6+192000 x^7))}{3 e^{10 x}+60 e^{8 x} x+480 e^{6 x} x^2+1920 e^{4 x} x^3+3840 e^{2 x} x^4+3072 x^5} \, dx\)

Optimal. Leaf size=37 \[ \left (e^{x^2 \left (-5+\frac {16}{\left (\frac {e^{2 x}}{4}+x\right )^2}\right )^2}-\frac {4}{3 x}\right ) x^2 \]

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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[(-4*E^(10*x) - 80*E^(8*x)*x - 640*E^(6*x)*x^2 - 2560*E^(4*x)*x^3 - 5120*E^(2*x)*x^4 - 4096*x^5 + E^((65536
*x^2 + 25*E^(8*x)*x^2 + 400*E^(6*x)*x^3 - 40960*x^4 + 6400*x^6 + E^(4*x)*(-2560*x^2 + 2400*x^4) + E^(2*x)*(-20
480*x^3 + 6400*x^5))/(E^(8*x) + 16*E^(6*x)*x + 96*E^(4*x)*x^2 + 256*E^(2*x)*x^3 + 256*x^4))*(-1572864*x^4 + 61
44*x^6 + 153600*x^8 + E^(10*x)*(6*x + 150*x^3) + E^(8*x)*(120*x^2 + 3000*x^4) + E^(6*x)*(-14400*x^3 + 30720*x^
4 + 24000*x^5) + E^(4*x)*(-119040*x^4 + 245760*x^5 + 96000*x^6) + E^(2*x)*(393216*x^3 - 1572864*x^4 - 238080*x
^5 + 491520*x^6 + 192000*x^7)))/(3*E^(10*x) + 60*E^(8*x)*x + 480*E^(6*x)*x^2 + 1920*E^(4*x)*x^3 + 3840*E^(2*x)
*x^4 + 3072*x^5),x]

[Out]

$Aborted

Rubi steps

Aborted

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Mathematica [A]  time = 0.68, size = 53, normalized size = 1.43 \begin {gather*} \frac {1}{3} \left (-4 x+3 e^{25 x^2+\frac {65536 x^2}{\left (e^{2 x}+4 x\right )^4}-\frac {2560 x^2}{\left (e^{2 x}+4 x\right )^2}} x^2\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-4*E^(10*x) - 80*E^(8*x)*x - 640*E^(6*x)*x^2 - 2560*E^(4*x)*x^3 - 5120*E^(2*x)*x^4 - 4096*x^5 + E^(
(65536*x^2 + 25*E^(8*x)*x^2 + 400*E^(6*x)*x^3 - 40960*x^4 + 6400*x^6 + E^(4*x)*(-2560*x^2 + 2400*x^4) + E^(2*x
)*(-20480*x^3 + 6400*x^5))/(E^(8*x) + 16*E^(6*x)*x + 96*E^(4*x)*x^2 + 256*E^(2*x)*x^3 + 256*x^4))*(-1572864*x^
4 + 6144*x^6 + 153600*x^8 + E^(10*x)*(6*x + 150*x^3) + E^(8*x)*(120*x^2 + 3000*x^4) + E^(6*x)*(-14400*x^3 + 30
720*x^4 + 24000*x^5) + E^(4*x)*(-119040*x^4 + 245760*x^5 + 96000*x^6) + E^(2*x)*(393216*x^3 - 1572864*x^4 - 23
8080*x^5 + 491520*x^6 + 192000*x^7)))/(3*E^(10*x) + 60*E^(8*x)*x + 480*E^(6*x)*x^2 + 1920*E^(4*x)*x^3 + 3840*E
^(2*x)*x^4 + 3072*x^5),x]

[Out]

(-4*x + 3*E^(25*x^2 + (65536*x^2)/(E^(2*x) + 4*x)^4 - (2560*x^2)/(E^(2*x) + 4*x)^2)*x^2)/3

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fricas [B]  time = 0.91, size = 115, normalized size = 3.11 \begin {gather*} x^{2} e^{\left (\frac {6400 \, x^{6} - 40960 \, x^{4} + 400 \, x^{3} e^{\left (6 \, x\right )} + 25 \, x^{2} e^{\left (8 \, x\right )} + 65536 \, x^{2} + 160 \, {\left (15 \, x^{4} - 16 \, x^{2}\right )} e^{\left (4 \, x\right )} + 1280 \, {\left (5 \, x^{5} - 16 \, x^{3}\right )} e^{\left (2 \, x\right )}}{256 \, x^{4} + 256 \, x^{3} e^{\left (2 \, x\right )} + 96 \, x^{2} e^{\left (4 \, x\right )} + 16 \, x e^{\left (6 \, x\right )} + e^{\left (8 \, x\right )}}\right )} - \frac {4}{3} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((150*x^3+6*x)*exp(x)^10+(3000*x^4+120*x^2)*exp(x)^8+(24000*x^5+30720*x^4-14400*x^3)*exp(x)^6+(9600
0*x^6+245760*x^5-119040*x^4)*exp(x)^4+(192000*x^7+491520*x^6-238080*x^5-1572864*x^4+393216*x^3)*exp(x)^2+15360
0*x^8+6144*x^6-1572864*x^4)*exp((25*x^2*exp(x)^8+400*x^3*exp(x)^6+(2400*x^4-2560*x^2)*exp(x)^4+(6400*x^5-20480
*x^3)*exp(x)^2+6400*x^6-40960*x^4+65536*x^2)/(exp(x)^8+16*x*exp(x)^6+96*x^2*exp(x)^4+256*exp(x)^2*x^3+256*x^4)
)-4*exp(x)^10-80*x*exp(x)^8-640*x^2*exp(x)^6-2560*x^3*exp(x)^4-5120*exp(x)^2*x^4-4096*x^5)/(3*exp(x)^10+60*x*e
xp(x)^8+480*x^2*exp(x)^6+1920*x^3*exp(x)^4+3840*exp(x)^2*x^4+3072*x^5),x, algorithm="fricas")

[Out]

x^2*e^((6400*x^6 - 40960*x^4 + 400*x^3*e^(6*x) + 25*x^2*e^(8*x) + 65536*x^2 + 160*(15*x^4 - 16*x^2)*e^(4*x) +
1280*(5*x^5 - 16*x^3)*e^(2*x))/(256*x^4 + 256*x^3*e^(2*x) + 96*x^2*e^(4*x) + 16*x*e^(6*x) + e^(8*x))) - 4/3*x

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giac [F(-2)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: TypeError} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((150*x^3+6*x)*exp(x)^10+(3000*x^4+120*x^2)*exp(x)^8+(24000*x^5+30720*x^4-14400*x^3)*exp(x)^6+(9600
0*x^6+245760*x^5-119040*x^4)*exp(x)^4+(192000*x^7+491520*x^6-238080*x^5-1572864*x^4+393216*x^3)*exp(x)^2+15360
0*x^8+6144*x^6-1572864*x^4)*exp((25*x^2*exp(x)^8+400*x^3*exp(x)^6+(2400*x^4-2560*x^2)*exp(x)^4+(6400*x^5-20480
*x^3)*exp(x)^2+6400*x^6-40960*x^4+65536*x^2)/(exp(x)^8+16*x*exp(x)^6+96*x^2*exp(x)^4+256*exp(x)^2*x^3+256*x^4)
)-4*exp(x)^10-80*x*exp(x)^8-640*x^2*exp(x)^6-2560*x^3*exp(x)^4-5120*exp(x)^2*x^4-4096*x^5)/(3*exp(x)^10+60*x*e
xp(x)^8+480*x^2*exp(x)^6+1920*x^3*exp(x)^4+3840*exp(x)^2*x^4+3072*x^5),x, algorithm="giac")

[Out]

Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,sageVARx):;OUTP
UT:Evaluation time: 1.02Unable to divide, perhaps due to rounding error%%%{-2894802230932904885589274625217197
69633174961

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maple [B]  time = 0.21, size = 107, normalized size = 2.89

method	result	size
risch	\(-\frac {4 x}{3}+x^{2} {\mathrm e}^{\frac {x^{2} \left (6400 \,{\mathrm e}^{2 x} x^{3}+6400 x^{4}+2400 x^{2} {\mathrm e}^{4 x}-20480 x \,{\mathrm e}^{2 x}+400 x \,{\mathrm e}^{6 x}-40960 x^{2}+25 \,{\mathrm e}^{8 x}-2560 \,{\mathrm e}^{4 x}+65536\right )}{{\mathrm e}^{8 x}+16 x \,{\mathrm e}^{6 x}+96 x^{2} {\mathrm e}^{4 x}+256 \,{\mathrm e}^{2 x} x^{3}+256 x^{4}}}\)	\(107\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((150*x^3+6*x)*exp(x)^10+(3000*x^4+120*x^2)*exp(x)^8+(24000*x^5+30720*x^4-14400*x^3)*exp(x)^6+(96000*x^6+
245760*x^5-119040*x^4)*exp(x)^4+(192000*x^7+491520*x^6-238080*x^5-1572864*x^4+393216*x^3)*exp(x)^2+153600*x^8+
6144*x^6-1572864*x^4)*exp((25*x^2*exp(x)^8+400*x^3*exp(x)^6+(2400*x^4-2560*x^2)*exp(x)^4+(6400*x^5-20480*x^3)*
exp(x)^2+6400*x^6-40960*x^4+65536*x^2)/(exp(x)^8+16*x*exp(x)^6+96*x^2*exp(x)^4+256*exp(x)^2*x^3+256*x^4))-4*ex
p(x)^10-80*x*exp(x)^8-640*x^2*exp(x)^6-2560*x^3*exp(x)^4-5120*exp(x)^2*x^4-4096*x^5)/(3*exp(x)^10+60*x*exp(x)^
8+480*x^2*exp(x)^6+1920*x^3*exp(x)^4+3840*exp(x)^2*x^4+3072*x^5),x,method=_RETURNVERBOSE)

[Out]

-4/3*x+x^2*exp(x^2*(6400*exp(2*x)*x^3+6400*x^4+2400*x^2*exp(4*x)-20480*x*exp(2*x)+400*x*exp(6*x)-40960*x^2+25*
exp(8*x)-2560*exp(4*x)+65536)/(exp(8*x)+16*x*exp(6*x)+96*x^2*exp(4*x)+256*exp(2*x)*x^3+256*x^4))

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maxima [B]  time = 55.12, size = 222, normalized size = 6.00 \begin {gather*} \frac {1}{3} \, {\left (3 \, x^{2} e^{\left (25 \, x^{2} + \frac {4096 \, e^{\left (4 \, x\right )}}{256 \, x^{4} + 256 \, x^{3} e^{\left (2 \, x\right )} + 96 \, x^{2} e^{\left (4 \, x\right )} + 16 \, x e^{\left (6 \, x\right )} + e^{\left (8 \, x\right )}} + \frac {320 \, e^{\left (2 \, x\right )}}{4 \, x + e^{\left (2 \, x\right )}} + \frac {4096}{16 \, x^{2} + 8 \, x e^{\left (2 \, x\right )} + e^{\left (4 \, x\right )}}\right )} - 4 \, x e^{\left (\frac {160 \, e^{\left (4 \, x\right )}}{16 \, x^{2} + 8 \, x e^{\left (2 \, x\right )} + e^{\left (4 \, x\right )}} + \frac {8192 \, e^{\left (2 \, x\right )}}{64 \, x^{3} + 48 \, x^{2} e^{\left (2 \, x\right )} + 12 \, x e^{\left (4 \, x\right )} + e^{\left (6 \, x\right )}} + 160\right )}\right )} e^{\left (-\frac {160 \, e^{\left (4 \, x\right )}}{16 \, x^{2} + 8 \, x e^{\left (2 \, x\right )} + e^{\left (4 \, x\right )}} - \frac {8192 \, e^{\left (2 \, x\right )}}{64 \, x^{3} + 48 \, x^{2} e^{\left (2 \, x\right )} + 12 \, x e^{\left (4 \, x\right )} + e^{\left (6 \, x\right )}} - 160\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((150*x^3+6*x)*exp(x)^10+(3000*x^4+120*x^2)*exp(x)^8+(24000*x^5+30720*x^4-14400*x^3)*exp(x)^6+(9600
0*x^6+245760*x^5-119040*x^4)*exp(x)^4+(192000*x^7+491520*x^6-238080*x^5-1572864*x^4+393216*x^3)*exp(x)^2+15360
0*x^8+6144*x^6-1572864*x^4)*exp((25*x^2*exp(x)^8+400*x^3*exp(x)^6+(2400*x^4-2560*x^2)*exp(x)^4+(6400*x^5-20480
*x^3)*exp(x)^2+6400*x^6-40960*x^4+65536*x^2)/(exp(x)^8+16*x*exp(x)^6+96*x^2*exp(x)^4+256*exp(x)^2*x^3+256*x^4)
)-4*exp(x)^10-80*x*exp(x)^8-640*x^2*exp(x)^6-2560*x^3*exp(x)^4-5120*exp(x)^2*x^4-4096*x^5)/(3*exp(x)^10+60*x*e
xp(x)^8+480*x^2*exp(x)^6+1920*x^3*exp(x)^4+3840*exp(x)^2*x^4+3072*x^5),x, algorithm="maxima")

[Out]

1/3*(3*x^2*e^(25*x^2 + 4096*e^(4*x)/(256*x^4 + 256*x^3*e^(2*x) + 96*x^2*e^(4*x) + 16*x*e^(6*x) + e^(8*x)) + 32
0*e^(2*x)/(4*x + e^(2*x)) + 4096/(16*x^2 + 8*x*e^(2*x) + e^(4*x))) - 4*x*e^(160*e^(4*x)/(16*x^2 + 8*x*e^(2*x)
+ e^(4*x)) + 8192*e^(2*x)/(64*x^3 + 48*x^2*e^(2*x) + 12*x*e^(4*x) + e^(6*x)) + 160))*e^(-160*e^(4*x)/(16*x^2 +
8*x*e^(2*x) + e^(4*x)) - 8192*e^(2*x)/(64*x^3 + 48*x^2*e^(2*x) + 12*x*e^(4*x) + e^(6*x)) - 160)

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mupad [B]  time = 3.94, size = 419, normalized size = 11.32 \begin {gather*} x^2\,{\mathrm {e}}^{\frac {25\,x^2\,{\mathrm {e}}^{8\,x}}{{\mathrm {e}}^{8\,x}+16\,x\,{\mathrm {e}}^{6\,x}+256\,x^3\,{\mathrm {e}}^{2\,x}+96\,x^2\,{\mathrm {e}}^{4\,x}+256\,x^4}}\,{\mathrm {e}}^{\frac {400\,x^3\,{\mathrm {e}}^{6\,x}}{{\mathrm {e}}^{8\,x}+16\,x\,{\mathrm {e}}^{6\,x}+256\,x^3\,{\mathrm {e}}^{2\,x}+96\,x^2\,{\mathrm {e}}^{4\,x}+256\,x^4}}\,{\mathrm {e}}^{\frac {2400\,x^4\,{\mathrm {e}}^{4\,x}}{{\mathrm {e}}^{8\,x}+16\,x\,{\mathrm {e}}^{6\,x}+256\,x^3\,{\mathrm {e}}^{2\,x}+96\,x^2\,{\mathrm {e}}^{4\,x}+256\,x^4}}\,{\mathrm {e}}^{-\frac {2560\,x^2\,{\mathrm {e}}^{4\,x}}{{\mathrm {e}}^{8\,x}+16\,x\,{\mathrm {e}}^{6\,x}+256\,x^3\,{\mathrm {e}}^{2\,x}+96\,x^2\,{\mathrm {e}}^{4\,x}+256\,x^4}}\,{\mathrm {e}}^{\frac {6400\,x^5\,{\mathrm {e}}^{2\,x}}{{\mathrm {e}}^{8\,x}+16\,x\,{\mathrm {e}}^{6\,x}+256\,x^3\,{\mathrm {e}}^{2\,x}+96\,x^2\,{\mathrm {e}}^{4\,x}+256\,x^4}}\,{\mathrm {e}}^{-\frac {20480\,x^3\,{\mathrm {e}}^{2\,x}}{{\mathrm {e}}^{8\,x}+16\,x\,{\mathrm {e}}^{6\,x}+256\,x^3\,{\mathrm {e}}^{2\,x}+96\,x^2\,{\mathrm {e}}^{4\,x}+256\,x^4}}\,{\mathrm {e}}^{\frac {6400\,x^6}{{\mathrm {e}}^{8\,x}+16\,x\,{\mathrm {e}}^{6\,x}+256\,x^3\,{\mathrm {e}}^{2\,x}+96\,x^2\,{\mathrm {e}}^{4\,x}+256\,x^4}}\,{\mathrm {e}}^{-\frac {40960\,x^4}{{\mathrm {e}}^{8\,x}+16\,x\,{\mathrm {e}}^{6\,x}+256\,x^3\,{\mathrm {e}}^{2\,x}+96\,x^2\,{\mathrm {e}}^{4\,x}+256\,x^4}}\,{\mathrm {e}}^{\frac {65536\,x^2}{{\mathrm {e}}^{8\,x}+16\,x\,{\mathrm {e}}^{6\,x}+256\,x^3\,{\mathrm {e}}^{2\,x}+96\,x^2\,{\mathrm {e}}^{4\,x}+256\,x^4}}-\frac {4\,x}{3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(4*exp(10*x) + 80*x*exp(8*x) + 5120*x^4*exp(2*x) + 2560*x^3*exp(4*x) + 640*x^2*exp(6*x) + 4096*x^5 - exp(
(400*x^3*exp(6*x) - exp(2*x)*(20480*x^3 - 6400*x^5) - exp(4*x)*(2560*x^2 - 2400*x^4) + 25*x^2*exp(8*x) + 65536
*x^2 - 40960*x^4 + 6400*x^6)/(exp(8*x) + 16*x*exp(6*x) + 256*x^3*exp(2*x) + 96*x^2*exp(4*x) + 256*x^4))*(exp(1
0*x)*(6*x + 150*x^3) + exp(2*x)*(393216*x^3 - 1572864*x^4 - 238080*x^5 + 491520*x^6 + 192000*x^7) + exp(8*x)*(
120*x^2 + 3000*x^4) + exp(6*x)*(30720*x^4 - 14400*x^3 + 24000*x^5) + exp(4*x)*(245760*x^5 - 119040*x^4 + 96000
*x^6) - 1572864*x^4 + 6144*x^6 + 153600*x^8))/(3*exp(10*x) + 60*x*exp(8*x) + 3840*x^4*exp(2*x) + 1920*x^3*exp(
4*x) + 480*x^2*exp(6*x) + 3072*x^5),x)

[Out]

x^2*exp((25*x^2*exp(8*x))/(exp(8*x) + 16*x*exp(6*x) + 256*x^3*exp(2*x) + 96*x^2*exp(4*x) + 256*x^4))*exp((400*
x^3*exp(6*x))/(exp(8*x) + 16*x*exp(6*x) + 256*x^3*exp(2*x) + 96*x^2*exp(4*x) + 256*x^4))*exp((2400*x^4*exp(4*x
))/(exp(8*x) + 16*x*exp(6*x) + 256*x^3*exp(2*x) + 96*x^2*exp(4*x) + 256*x^4))*exp(-(2560*x^2*exp(4*x))/(exp(8*
x) + 16*x*exp(6*x) + 256*x^3*exp(2*x) + 96*x^2*exp(4*x) + 256*x^4))*exp((6400*x^5*exp(2*x))/(exp(8*x) + 16*x*e
xp(6*x) + 256*x^3*exp(2*x) + 96*x^2*exp(4*x) + 256*x^4))*exp(-(20480*x^3*exp(2*x))/(exp(8*x) + 16*x*exp(6*x) +
256*x^3*exp(2*x) + 96*x^2*exp(4*x) + 256*x^4))*exp((6400*x^6)/(exp(8*x) + 16*x*exp(6*x) + 256*x^3*exp(2*x) +
96*x^2*exp(4*x) + 256*x^4))*exp(-(40960*x^4)/(exp(8*x) + 16*x*exp(6*x) + 256*x^3*exp(2*x) + 96*x^2*exp(4*x) +
256*x^4))*exp((65536*x^2)/(exp(8*x) + 16*x*exp(6*x) + 256*x^3*exp(2*x) + 96*x^2*exp(4*x) + 256*x^4)) - (4*x)/3

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sympy [B]  time = 82.33, size = 114, normalized size = 3.08 \begin {gather*} x^{2} e^{\frac {6400 x^{6} - 40960 x^{4} + 400 x^{3} e^{6 x} + 25 x^{2} e^{8 x} + 65536 x^{2} + \left (2400 x^{4} - 2560 x^{2}\right ) e^{4 x} + \left (6400 x^{5} - 20480 x^{3}\right ) e^{2 x}}{256 x^{4} + 256 x^{3} e^{2 x} + 96 x^{2} e^{4 x} + 16 x e^{6 x} + e^{8 x}}} - \frac {4 x}{3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((150*x**3+6*x)*exp(x)**10+(3000*x**4+120*x**2)*exp(x)**8+(24000*x**5+30720*x**4-14400*x**3)*exp(x)
**6+(96000*x**6+245760*x**5-119040*x**4)*exp(x)**4+(192000*x**7+491520*x**6-238080*x**5-1572864*x**4+393216*x*
*3)*exp(x)**2+153600*x**8+6144*x**6-1572864*x**4)*exp((25*x**2*exp(x)**8+400*x**3*exp(x)**6+(2400*x**4-2560*x*
*2)*exp(x)**4+(6400*x**5-20480*x**3)*exp(x)**2+6400*x**6-40960*x**4+65536*x**2)/(exp(x)**8+16*x*exp(x)**6+96*x
**2*exp(x)**4+256*exp(x)**2*x**3+256*x**4))-4*exp(x)**10-80*x*exp(x)**8-640*x**2*exp(x)**6-2560*x**3*exp(x)**4
-5120*exp(x)**2*x**4-4096*x**5)/(3*exp(x)**10+60*x*exp(x)**8+480*x**2*exp(x)**6+1920*x**3*exp(x)**4+3840*exp(x
)**2*x**4+3072*x**5),x)

[Out]

x**2*exp((6400*x**6 - 40960*x**4 + 400*x**3*exp(6*x) + 25*x**2*exp(8*x) + 65536*x**2 + (2400*x**4 - 2560*x**2)
*exp(4*x) + (6400*x**5 - 20480*x**3)*exp(2*x))/(256*x**4 + 256*x**3*exp(2*x) + 96*x**2*exp(4*x) + 16*x*exp(6*x
) + exp(8*x))) - 4*x/3

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