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3.26.7 \(\int \frac {-40000+36000 x-30800 x^2+25080 x^3-10800 x^4+2160 x^5-226 x^6+e^{2 x} (-1200 x^2+1560 x^3-1920 x^4+828 x^5-108 x^6)+e^{4 x} (4 x^5-2 x^6)+e^{3 x} (-40 x^3+120 x^4-116 x^5+24 x^6)+e^x (-12000 x+11200 x^2-12680 x^3+8280 x^4-2268 x^5+216 x^6)}{10000 x-12000 x^2+5400 x^3-1080 x^4+113 x^5+e^{4 x} x^5+e^x (4000 x^2-3600 x^3+1080 x^4-108 x^5)+e^{3 x} (40 x^4-12 x^5)+e^{2 x} (600 x^3-360 x^4+54 x^5)} \, dx\)

Optimal. Leaf size=37 \[ -x^2+\log \left (2+\left (\frac {4}{x}-\frac {-1+x+\frac {1}{2} \left (1-e^x\right ) x}{x}\right )^4\right ) \]

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Rubi [F]  time = 33.51, 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*} \int \frac {-40000+36000 x-30800 x^2+25080 x^3-10800 x^4+2160 x^5-226 x^6+e^{2 x} \left (-1200 x^2+1560 x^3-1920 x^4+828 x^5-108 x^6\right )+e^{4 x} \left (4 x^5-2 x^6\right )+e^{3 x} \left (-40 x^3+120 x^4-116 x^5+24 x^6\right )+e^x \left (-12000 x+11200 x^2-12680 x^3+8280 x^4-2268 x^5+216 x^6\right )}{10000 x-12000 x^2+5400 x^3-1080 x^4+113 x^5+e^{4 x} x^5+e^x \left (4000 x^2-3600 x^3+1080 x^4-108 x^5\right )+e^{3 x} \left (40 x^4-12 x^5\right )+e^{2 x} \left (600 x^3-360 x^4+54 x^5\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-40000 + 36000*x - 30800*x^2 + 25080*x^3 - 10800*x^4 + 2160*x^5 - 226*x^6 + E^(2*x)*(-1200*x^2 + 1560*x^3
 - 1920*x^4 + 828*x^5 - 108*x^6) + E^(4*x)*(4*x^5 - 2*x^6) + E^(3*x)*(-40*x^3 + 120*x^4 - 116*x^5 + 24*x^6) +
E^x*(-12000*x + 11200*x^2 - 12680*x^3 + 8280*x^4 - 2268*x^5 + 216*x^6))/(10000*x - 12000*x^2 + 5400*x^3 - 1080
*x^4 + 113*x^5 + E^(4*x)*x^5 + E^x*(4000*x^2 - 3600*x^3 + 1080*x^4 - 108*x^5) + E^(3*x)*(40*x^4 - 12*x^5) + E^
(2*x)*(600*x^3 - 360*x^4 + 54*x^5)),x]

[Out]

-(2 - x)^2 - 4000*Defer[Int][(10000 + 4000*(-3 + E^x)*x + 600*(-3 + E^x)^2*x^2 + 40*(-3 + E^x)^3*x^3 + (113 -
108*E^x + 54*E^(2*x) - 12*E^(3*x) + E^(4*x))*x^4)^(-1), x] - 12000*Defer[Int][E^x/(10000 + 4000*(-3 + E^x)*x +
 600*(-3 + E^x)^2*x^2 + 40*(-3 + E^x)^3*x^3 + (113 - 108*E^x + 54*E^(2*x) - 12*E^(3*x) + E^(4*x))*x^4), x] - 4
0000*Defer[Int][1/(x*(10000 + 4000*(-3 + E^x)*x + 600*(-3 + E^x)^2*x^2 + 40*(-3 + E^x)^3*x^3 + (113 - 108*E^x
+ 54*E^(2*x) - 12*E^(3*x) + E^(4*x))*x^4)), x] + 37200*Defer[Int][x/(10000 + 4000*(-3 + E^x)*x + 600*(-3 + E^x
)^2*x^2 + 40*(-3 + E^x)^3*x^3 + (113 - 108*E^x + 54*E^(2*x) - 12*E^(3*x) + E^(4*x))*x^4), x] - 4800*Defer[Int]
[(E^x*x)/(10000 + 4000*(-3 + E^x)*x + 600*(-3 + E^x)^2*x^2 + 40*(-3 + E^x)^3*x^3 + (113 - 108*E^x + 54*E^(2*x)
 - 12*E^(3*x) + E^(4*x))*x^4), x] - 1200*Defer[Int][(E^(2*x)*x)/(10000 + 4000*(-3 + E^x)*x + 600*(-3 + E^x)^2*
x^2 + 40*(-3 + E^x)^3*x^3 + (113 - 108*E^x + 54*E^(2*x) - 12*E^(3*x) + E^(4*x))*x^4), x] - 20520*Defer[Int][x^
2/(10000 + 4000*(-3 + E^x)*x + 600*(-3 + E^x)^2*x^2 + 40*(-3 + E^x)^3*x^3 + (113 - 108*E^x + 54*E^(2*x) - 12*E
^(3*x) + E^(4*x))*x^4), x] + 9720*Defer[Int][(E^x*x^2)/(10000 + 4000*(-3 + E^x)*x + 600*(-3 + E^x)^2*x^2 + 40*
(-3 + E^x)^3*x^3 + (113 - 108*E^x + 54*E^(2*x) - 12*E^(3*x) + E^(4*x))*x^4), x] - 840*Defer[Int][(E^(2*x)*x^2)
/(10000 + 4000*(-3 + E^x)*x + 600*(-3 + E^x)^2*x^2 + 40*(-3 + E^x)^3*x^3 + (113 - 108*E^x + 54*E^(2*x) - 12*E^
(3*x) + E^(4*x))*x^4), x] - 40*Defer[Int][(E^(3*x)*x^2)/(10000 + 4000*(-3 + E^x)*x + 600*(-3 + E^x)^2*x^2 + 40
*(-3 + E^x)^3*x^3 + (113 - 108*E^x + 54*E^(2*x) - 12*E^(3*x) + E^(4*x))*x^4), x] + 4320*Defer[Int][x^3/(10000
+ 4000*(-3 + E^x)*x + 600*(-3 + E^x)^2*x^2 + 40*(-3 + E^x)^3*x^3 + (113 - 108*E^x + 54*E^(2*x) - 12*E^(3*x) +
E^(4*x))*x^4), x] - 3240*Defer[Int][(E^x*x^3)/(10000 + 4000*(-3 + E^x)*x + 600*(-3 + E^x)^2*x^2 + 40*(-3 + E^x
)^3*x^3 + (113 - 108*E^x + 54*E^(2*x) - 12*E^(3*x) + E^(4*x))*x^4), x] + 720*Defer[Int][(E^(2*x)*x^3)/(10000 +
 4000*(-3 + E^x)*x + 600*(-3 + E^x)^2*x^2 + 40*(-3 + E^x)^3*x^3 + (113 - 108*E^x + 54*E^(2*x) - 12*E^(3*x) + E
^(4*x))*x^4), x] - 40*Defer[Int][(E^(3*x)*x^3)/(10000 + 4000*(-3 + E^x)*x + 600*(-3 + E^x)^2*x^2 + 40*(-3 + E^
x)^3*x^3 + (113 - 108*E^x + 54*E^(2*x) - 12*E^(3*x) + E^(4*x))*x^4), x] - 452*Defer[Int][x^4/(10000 + 4000*(-3
 + E^x)*x + 600*(-3 + E^x)^2*x^2 + 40*(-3 + E^x)^3*x^3 + (113 - 108*E^x + 54*E^(2*x) - 12*E^(3*x) + E^(4*x))*x
^4), x] + 324*Defer[Int][(E^x*x^4)/(10000 + 4000*(-3 + E^x)*x + 600*(-3 + E^x)^2*x^2 + 40*(-3 + E^x)^3*x^3 + (
113 - 108*E^x + 54*E^(2*x) - 12*E^(3*x) + E^(4*x))*x^4), x] - 108*Defer[Int][(E^(2*x)*x^4)/(10000 + 4000*(-3 +
 E^x)*x + 600*(-3 + E^x)^2*x^2 + 40*(-3 + E^x)^3*x^3 + (113 - 108*E^x + 54*E^(2*x) - 12*E^(3*x) + E^(4*x))*x^4
), x] + 12*Defer[Int][(E^(3*x)*x^4)/(10000 + 4000*(-3 + E^x)*x + 600*(-3 + E^x)^2*x^2 + 40*(-3 + E^x)^3*x^3 +
(113 - 108*E^x + 54*E^(2*x) - 12*E^(3*x) + E^(4*x))*x^4), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-2 (-2+x)+\frac {4 \left (-10000-1000 x-3000 e^x x+9300 x^2-1200 e^x x^2-300 e^{2 x} x^2-5130 x^3+2430 e^x x^3-210 e^{2 x} x^3-10 e^{3 x} x^3+1080 x^4-810 e^x x^4+180 e^{2 x} x^4-10 e^{3 x} x^4-113 x^5+81 e^x x^5-27 e^{2 x} x^5+3 e^{3 x} x^5\right )}{x \left (10000-12000 x+4000 e^x x+5400 x^2-3600 e^x x^2+600 e^{2 x} x^2-1080 x^3+1080 e^x x^3-360 e^{2 x} x^3+40 e^{3 x} x^3+113 x^4-108 e^x x^4+54 e^{2 x} x^4-12 e^{3 x} x^4+e^{4 x} x^4\right )}\right ) \, dx\\ &=-(2-x)^2+4 \int \frac {-10000-1000 x-3000 e^x x+9300 x^2-1200 e^x x^2-300 e^{2 x} x^2-5130 x^3+2430 e^x x^3-210 e^{2 x} x^3-10 e^{3 x} x^3+1080 x^4-810 e^x x^4+180 e^{2 x} x^4-10 e^{3 x} x^4-113 x^5+81 e^x x^5-27 e^{2 x} x^5+3 e^{3 x} x^5}{x \left (10000-12000 x+4000 e^x x+5400 x^2-3600 e^x x^2+600 e^{2 x} x^2-1080 x^3+1080 e^x x^3-360 e^{2 x} x^3+40 e^{3 x} x^3+113 x^4-108 e^x x^4+54 e^{2 x} x^4-12 e^{3 x} x^4+e^{4 x} x^4\right )} \, dx\\ &=-(2-x)^2+4 \int \frac {-10000-1000 \left (1+3 e^x\right ) x-300 \left (-31+4 e^x+e^{2 x}\right ) x^2-10 \left (513-243 e^x+21 e^{2 x}+e^{3 x}\right ) x^3-10 \left (-12+e^x\right ) \left (-3+e^x\right )^2 x^4-\left (113-81 e^x+27 e^{2 x}-3 e^{3 x}\right ) x^5}{x \left (10000+4000 \left (-3+e^x\right ) x+600 \left (-3+e^x\right )^2 x^2+40 \left (-3+e^x\right )^3 x^3+\left (113-108 e^x+54 e^{2 x}-12 e^{3 x}+e^{4 x}\right ) x^4\right )} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [F]  time = 4.35, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {-40000+36000 x-30800 x^2+25080 x^3-10800 x^4+2160 x^5-226 x^6+e^{2 x} \left (-1200 x^2+1560 x^3-1920 x^4+828 x^5-108 x^6\right )+e^{4 x} \left (4 x^5-2 x^6\right )+e^{3 x} \left (-40 x^3+120 x^4-116 x^5+24 x^6\right )+e^x \left (-12000 x+11200 x^2-12680 x^3+8280 x^4-2268 x^5+216 x^6\right )}{10000 x-12000 x^2+5400 x^3-1080 x^4+113 x^5+e^{4 x} x^5+e^x \left (4000 x^2-3600 x^3+1080 x^4-108 x^5\right )+e^{3 x} \left (40 x^4-12 x^5\right )+e^{2 x} \left (600 x^3-360 x^4+54 x^5\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[(-40000 + 36000*x - 30800*x^2 + 25080*x^3 - 10800*x^4 + 2160*x^5 - 226*x^6 + E^(2*x)*(-1200*x^2 + 15
60*x^3 - 1920*x^4 + 828*x^5 - 108*x^6) + E^(4*x)*(4*x^5 - 2*x^6) + E^(3*x)*(-40*x^3 + 120*x^4 - 116*x^5 + 24*x
^6) + E^x*(-12000*x + 11200*x^2 - 12680*x^3 + 8280*x^4 - 2268*x^5 + 216*x^6))/(10000*x - 12000*x^2 + 5400*x^3
- 1080*x^4 + 113*x^5 + E^(4*x)*x^5 + E^x*(4000*x^2 - 3600*x^3 + 1080*x^4 - 108*x^5) + E^(3*x)*(40*x^4 - 12*x^5
) + E^(2*x)*(600*x^3 - 360*x^4 + 54*x^5)),x]

[Out]

Integrate[(-40000 + 36000*x - 30800*x^2 + 25080*x^3 - 10800*x^4 + 2160*x^5 - 226*x^6 + E^(2*x)*(-1200*x^2 + 15
60*x^3 - 1920*x^4 + 828*x^5 - 108*x^6) + E^(4*x)*(4*x^5 - 2*x^6) + E^(3*x)*(-40*x^3 + 120*x^4 - 116*x^5 + 24*x
^6) + E^x*(-12000*x + 11200*x^2 - 12680*x^3 + 8280*x^4 - 2268*x^5 + 216*x^6))/(10000*x - 12000*x^2 + 5400*x^3
- 1080*x^4 + 113*x^5 + E^(4*x)*x^5 + E^x*(4000*x^2 - 3600*x^3 + 1080*x^4 - 108*x^5) + E^(3*x)*(40*x^4 - 12*x^5
) + E^(2*x)*(600*x^3 - 360*x^4 + 54*x^5)), x]

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fricas [B]  time = 0.70, size = 101, normalized size = 2.73 \begin {gather*} -x^{2} + \log \left (\frac {x^{4} e^{\left (4 \, x\right )} + 113 \, x^{4} - 1080 \, x^{3} + 5400 \, x^{2} - 4 \, {\left (3 \, x^{4} - 10 \, x^{3}\right )} e^{\left (3 \, x\right )} + 6 \, {\left (9 \, x^{4} - 60 \, x^{3} + 100 \, x^{2}\right )} e^{\left (2 \, x\right )} - 4 \, {\left (27 \, x^{4} - 270 \, x^{3} + 900 \, x^{2} - 1000 \, x\right )} e^{x} - 12000 \, x + 10000}{x^{4}}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-2*x^6+4*x^5)*exp(x)^4+(24*x^6-116*x^5+120*x^4-40*x^3)*exp(x)^3+(-108*x^6+828*x^5-1920*x^4+1560*x^
3-1200*x^2)*exp(x)^2+(216*x^6-2268*x^5+8280*x^4-12680*x^3+11200*x^2-12000*x)*exp(x)-226*x^6+2160*x^5-10800*x^4
+25080*x^3-30800*x^2+36000*x-40000)/(x^5*exp(x)^4+(-12*x^5+40*x^4)*exp(x)^3+(54*x^5-360*x^4+600*x^3)*exp(x)^2+
(-108*x^5+1080*x^4-3600*x^3+4000*x^2)*exp(x)+113*x^5-1080*x^4+5400*x^3-12000*x^2+10000*x),x, algorithm="fricas
")

[Out]

-x^2 + log((x^4*e^(4*x) + 113*x^4 - 1080*x^3 + 5400*x^2 - 4*(3*x^4 - 10*x^3)*e^(3*x) + 6*(9*x^4 - 60*x^3 + 100
*x^2)*e^(2*x) - 4*(27*x^4 - 270*x^3 + 900*x^2 - 1000*x)*e^x - 12000*x + 10000)/x^4)

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giac [B]  time = 0.78, size = 110, normalized size = 2.97 \begin {gather*} -x^{2} + \log \left (x^{4} e^{\left (4 \, x\right )} - 12 \, x^{4} e^{\left (3 \, x\right )} + 54 \, x^{4} e^{\left (2 \, x\right )} - 108 \, x^{4} e^{x} + 113 \, x^{4} + 40 \, x^{3} e^{\left (3 \, x\right )} - 360 \, x^{3} e^{\left (2 \, x\right )} + 1080 \, x^{3} e^{x} - 1080 \, x^{3} + 600 \, x^{2} e^{\left (2 \, x\right )} - 3600 \, x^{2} e^{x} + 5400 \, x^{2} + 4000 \, x e^{x} - 12000 \, x + 10000\right ) - 4 \, \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-2*x^6+4*x^5)*exp(x)^4+(24*x^6-116*x^5+120*x^4-40*x^3)*exp(x)^3+(-108*x^6+828*x^5-1920*x^4+1560*x^
3-1200*x^2)*exp(x)^2+(216*x^6-2268*x^5+8280*x^4-12680*x^3+11200*x^2-12000*x)*exp(x)-226*x^6+2160*x^5-10800*x^4
+25080*x^3-30800*x^2+36000*x-40000)/(x^5*exp(x)^4+(-12*x^5+40*x^4)*exp(x)^3+(54*x^5-360*x^4+600*x^3)*exp(x)^2+
(-108*x^5+1080*x^4-3600*x^3+4000*x^2)*exp(x)+113*x^5-1080*x^4+5400*x^3-12000*x^2+10000*x),x, algorithm="giac")

[Out]

-x^2 + log(x^4*e^(4*x) - 12*x^4*e^(3*x) + 54*x^4*e^(2*x) - 108*x^4*e^x + 113*x^4 + 40*x^3*e^(3*x) - 360*x^3*e^
(2*x) + 1080*x^3*e^x - 1080*x^3 + 600*x^2*e^(2*x) - 3600*x^2*e^x + 5400*x^2 + 4000*x*e^x - 12000*x + 10000) -
4*log(x)

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maple [B]  time = 0.08, size = 92, normalized size = 2.49

method result size
risch \(-x^{2}+\ln \left ({\mathrm e}^{4 x}-\frac {4 \left (3 x -10\right ) {\mathrm e}^{3 x}}{x}+\frac {6 \left (9 x^{2}-60 x +100\right ) {\mathrm e}^{2 x}}{x^{2}}-\frac {4 \left (27 x^{3}-270 x^{2}+900 x -1000\right ) {\mathrm e}^{x}}{x^{3}}+\frac {113 x^{4}-1080 x^{3}+5400 x^{2}-12000 x +10000}{x^{4}}\right )\) \(92\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-2*x^6+4*x^5)*exp(x)^4+(24*x^6-116*x^5+120*x^4-40*x^3)*exp(x)^3+(-108*x^6+828*x^5-1920*x^4+1560*x^3-1200
*x^2)*exp(x)^2+(216*x^6-2268*x^5+8280*x^4-12680*x^3+11200*x^2-12000*x)*exp(x)-226*x^6+2160*x^5-10800*x^4+25080
*x^3-30800*x^2+36000*x-40000)/(x^5*exp(x)^4+(-12*x^5+40*x^4)*exp(x)^3+(54*x^5-360*x^4+600*x^3)*exp(x)^2+(-108*
x^5+1080*x^4-3600*x^3+4000*x^2)*exp(x)+113*x^5-1080*x^4+5400*x^3-12000*x^2+10000*x),x,method=_RETURNVERBOSE)

[Out]

-x^2+ln(exp(4*x)-4/x*(3*x-10)*exp(3*x)+6/x^2*(9*x^2-60*x+100)*exp(2*x)-4/x^3*(27*x^3-270*x^2+900*x-1000)*exp(x
)+(113*x^4-1080*x^3+5400*x^2-12000*x+10000)/x^4)

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maxima [B]  time = 0.48, size = 101, normalized size = 2.73 \begin {gather*} -x^{2} + \log \left (\frac {x^{4} e^{\left (4 \, x\right )} + 113 \, x^{4} - 1080 \, x^{3} + 5400 \, x^{2} - 4 \, {\left (3 \, x^{4} - 10 \, x^{3}\right )} e^{\left (3 \, x\right )} + 6 \, {\left (9 \, x^{4} - 60 \, x^{3} + 100 \, x^{2}\right )} e^{\left (2 \, x\right )} - 4 \, {\left (27 \, x^{4} - 270 \, x^{3} + 900 \, x^{2} - 1000 \, x\right )} e^{x} - 12000 \, x + 10000}{x^{4}}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-2*x^6+4*x^5)*exp(x)^4+(24*x^6-116*x^5+120*x^4-40*x^3)*exp(x)^3+(-108*x^6+828*x^5-1920*x^4+1560*x^
3-1200*x^2)*exp(x)^2+(216*x^6-2268*x^5+8280*x^4-12680*x^3+11200*x^2-12000*x)*exp(x)-226*x^6+2160*x^5-10800*x^4
+25080*x^3-30800*x^2+36000*x-40000)/(x^5*exp(x)^4+(-12*x^5+40*x^4)*exp(x)^3+(54*x^5-360*x^4+600*x^3)*exp(x)^2+
(-108*x^5+1080*x^4-3600*x^3+4000*x^2)*exp(x)+113*x^5-1080*x^4+5400*x^3-12000*x^2+10000*x),x, algorithm="maxima
")

[Out]

-x^2 + log((x^4*e^(4*x) + 113*x^4 - 1080*x^3 + 5400*x^2 - 4*(3*x^4 - 10*x^3)*e^(3*x) + 6*(9*x^4 - 60*x^3 + 100
*x^2)*e^(2*x) - 4*(27*x^4 - 270*x^3 + 900*x^2 - 1000*x)*e^x - 12000*x + 10000)/x^4)

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mupad [F]  time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int -\frac {{\mathrm {e}}^{2\,x}\,\left (108\,x^6-828\,x^5+1920\,x^4-1560\,x^3+1200\,x^2\right )-36000\,x-{\mathrm {e}}^{4\,x}\,\left (4\,x^5-2\,x^6\right )+{\mathrm {e}}^x\,\left (-216\,x^6+2268\,x^5-8280\,x^4+12680\,x^3-11200\,x^2+12000\,x\right )+{\mathrm {e}}^{3\,x}\,\left (-24\,x^6+116\,x^5-120\,x^4+40\,x^3\right )+30800\,x^2-25080\,x^3+10800\,x^4-2160\,x^5+226\,x^6+40000}{10000\,x+{\mathrm {e}}^{3\,x}\,\left (40\,x^4-12\,x^5\right )+x^5\,{\mathrm {e}}^{4\,x}+{\mathrm {e}}^x\,\left (-108\,x^5+1080\,x^4-3600\,x^3+4000\,x^2\right )+{\mathrm {e}}^{2\,x}\,\left (54\,x^5-360\,x^4+600\,x^3\right )-12000\,x^2+5400\,x^3-1080\,x^4+113\,x^5} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(2*x)*(1200*x^2 - 1560*x^3 + 1920*x^4 - 828*x^5 + 108*x^6) - 36000*x - exp(4*x)*(4*x^5 - 2*x^6) + exp
(x)*(12000*x - 11200*x^2 + 12680*x^3 - 8280*x^4 + 2268*x^5 - 216*x^6) + exp(3*x)*(40*x^3 - 120*x^4 + 116*x^5 -
 24*x^6) + 30800*x^2 - 25080*x^3 + 10800*x^4 - 2160*x^5 + 226*x^6 + 40000)/(10000*x + exp(3*x)*(40*x^4 - 12*x^
5) + x^5*exp(4*x) + exp(x)*(4000*x^2 - 3600*x^3 + 1080*x^4 - 108*x^5) + exp(2*x)*(600*x^3 - 360*x^4 + 54*x^5)
- 12000*x^2 + 5400*x^3 - 1080*x^4 + 113*x^5),x)

[Out]

int(-(exp(2*x)*(1200*x^2 - 1560*x^3 + 1920*x^4 - 828*x^5 + 108*x^6) - 36000*x - exp(4*x)*(4*x^5 - 2*x^6) + exp
(x)*(12000*x - 11200*x^2 + 12680*x^3 - 8280*x^4 + 2268*x^5 - 216*x^6) + exp(3*x)*(40*x^3 - 120*x^4 + 116*x^5 -
 24*x^6) + 30800*x^2 - 25080*x^3 + 10800*x^4 - 2160*x^5 + 226*x^6 + 40000)/(10000*x + exp(3*x)*(40*x^4 - 12*x^
5) + x^5*exp(4*x) + exp(x)*(4000*x^2 - 3600*x^3 + 1080*x^4 - 108*x^5) + exp(2*x)*(600*x^3 - 360*x^4 + 54*x^5)
- 12000*x^2 + 5400*x^3 - 1080*x^4 + 113*x^5), x)

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sympy [B]  time = 0.73, size = 85, normalized size = 2.30 \begin {gather*} - x^{2} + \log {\left (e^{4 x} + \frac {\left (40 - 12 x\right ) e^{3 x}}{x} + \frac {\left (54 x^{2} - 360 x + 600\right ) e^{2 x}}{x^{2}} + \frac {\left (- 108 x^{3} + 1080 x^{2} - 3600 x + 4000\right ) e^{x}}{x^{3}} + \frac {113 x^{4} - 1080 x^{3} + 5400 x^{2} - 12000 x + 10000}{x^{4}} \right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-2*x**6+4*x**5)*exp(x)**4+(24*x**6-116*x**5+120*x**4-40*x**3)*exp(x)**3+(-108*x**6+828*x**5-1920*x
**4+1560*x**3-1200*x**2)*exp(x)**2+(216*x**6-2268*x**5+8280*x**4-12680*x**3+11200*x**2-12000*x)*exp(x)-226*x**
6+2160*x**5-10800*x**4+25080*x**3-30800*x**2+36000*x-40000)/(x**5*exp(x)**4+(-12*x**5+40*x**4)*exp(x)**3+(54*x
**5-360*x**4+600*x**3)*exp(x)**2+(-108*x**5+1080*x**4-3600*x**3+4000*x**2)*exp(x)+113*x**5-1080*x**4+5400*x**3
-12000*x**2+10000*x),x)

[Out]

-x**2 + log(exp(4*x) + (40 - 12*x)*exp(3*x)/x + (54*x**2 - 360*x + 600)*exp(2*x)/x**2 + (-108*x**3 + 1080*x**2
 - 3600*x + 4000)*exp(x)/x**3 + (113*x**4 - 1080*x**3 + 5400*x**2 - 12000*x + 10000)/x**4)

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