3.66.95 \(\int \frac {-432 x+1296 x^2-1224 x^3+456 x^4-72 x^5+4 x^6+e^4 (-432 x+216 x^2-36 x^3+2 x^4)+e^2 (864 x-1512 x^2+660 x^3-108 x^4+6 x^5)+e^{9 x} (2 x^4+2 e^4 x^4-6 x^5+4 x^6+e^2 (-4 x^4+6 x^5))+e^{3 x} (216 x^2-660 x^3+528 x^4-114 x^5+6 x^6+e^4 (216 x^2-72 x^3+6 x^4)+e^2 (-432 x^2+732 x^3-184 x^4+12 x^5))+e^{6 x} (-36 x^3+110 x^4-78 x^5+6 x^6+e^4 (-36 x^3+6 x^4)+e^2 (72 x^3-116 x^4+12 x^5))}{-216+108 x-18 x^2+x^3+e^{9 x} x^3+e^{3 x} (108 x-36 x^2+3 x^3)+e^{6 x} (-18 x^2+3 x^3)} \, dx\)

Optimal. Leaf size=26 \[ \left (x-x \left (e^2+x+\frac {x}{-6+x+e^{3 x} x}\right )\right )^2 \]

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Rubi [F]  time = 6.77, 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 {-432 x+1296 x^2-1224 x^3+456 x^4-72 x^5+4 x^6+e^4 \left (-432 x+216 x^2-36 x^3+2 x^4\right )+e^2 \left (864 x-1512 x^2+660 x^3-108 x^4+6 x^5\right )+e^{9 x} \left (2 x^4+2 e^4 x^4-6 x^5+4 x^6+e^2 \left (-4 x^4+6 x^5\right )\right )+e^{3 x} \left (216 x^2-660 x^3+528 x^4-114 x^5+6 x^6+e^4 \left (216 x^2-72 x^3+6 x^4\right )+e^2 \left (-432 x^2+732 x^3-184 x^4+12 x^5\right )\right )+e^{6 x} \left (-36 x^3+110 x^4-78 x^5+6 x^6+e^4 \left (-36 x^3+6 x^4\right )+e^2 \left (72 x^3-116 x^4+12 x^5\right )\right )}{-216+108 x-18 x^2+x^3+e^{9 x} x^3+e^{3 x} \left (108 x-36 x^2+3 x^3\right )+e^{6 x} \left (-18 x^2+3 x^3\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-432*x + 1296*x^2 - 1224*x^3 + 456*x^4 - 72*x^5 + 4*x^6 + E^4*(-432*x + 216*x^2 - 36*x^3 + 2*x^4) + E^2*(
864*x - 1512*x^2 + 660*x^3 - 108*x^4 + 6*x^5) + E^(9*x)*(2*x^4 + 2*E^4*x^4 - 6*x^5 + 4*x^6 + E^2*(-4*x^4 + 6*x
^5)) + E^(3*x)*(216*x^2 - 660*x^3 + 528*x^4 - 114*x^5 + 6*x^6 + E^4*(216*x^2 - 72*x^3 + 6*x^4) + E^2*(-432*x^2
+ 732*x^3 - 184*x^4 + 12*x^5)) + E^(6*x)*(-36*x^3 + 110*x^4 - 78*x^5 + 6*x^6 + E^4*(-36*x^3 + 6*x^4) + E^2*(7
2*x^3 - 116*x^4 + 12*x^5)))/(-216 + 108*x - 18*x^2 + x^3 + E^(9*x)*x^3 + E^(3*x)*(108*x - 36*x^2 + 3*x^3) + E^
(6*x)*(-18*x^2 + 3*x^3)),x]

[Out]

(1 - E^2)^2*x^2 - 2*(1 - E)*(1 + E)*x^3 + x^4 - 12*Defer[Int][x^3/(-6 + x + E^(3*x)*x)^3, x] - 36*Defer[Int][x
^4/(-6 + x + E^(3*x)*x)^3, x] + 6*Defer[Int][x^5/(-6 + x + E^(3*x)*x)^3, x] + 12*(1 - E)*(1 + E)*Defer[Int][x^
2/(-6 + x + E^(3*x)*x)^2, x] + 2*(13 - 18*E^2)*Defer[Int][x^3/(-6 + x + E^(3*x)*x)^2, x] - 6*(8 - E^2)*Defer[I
nt][x^4/(-6 + x + E^(3*x)*x)^2, x] + 6*Defer[Int][x^5/(-6 + x + E^(3*x)*x)^2, x] - 4*(1 - E)*(1 + E)*Defer[Int
][x^2/(-6 + x + E^(3*x)*x), x] + 6*(2 - E^2)*Defer[Int][x^3/(-6 + x + E^(3*x)*x), x] - 6*Defer[Int][x^4/(-6 +
x + E^(3*x)*x), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {432 x-1296 x^2+1224 x^3-456 x^4+72 x^5-4 x^6-e^4 \left (-432 x+216 x^2-36 x^3+2 x^4\right )-e^2 \left (864 x-1512 x^2+660 x^3-108 x^4+6 x^5\right )-e^{9 x} \left (2 x^4+2 e^4 x^4-6 x^5+4 x^6+e^2 \left (-4 x^4+6 x^5\right )\right )-e^{3 x} \left (216 x^2-660 x^3+528 x^4-114 x^5+6 x^6+e^4 \left (216 x^2-72 x^3+6 x^4\right )+e^2 \left (-432 x^2+732 x^3-184 x^4+12 x^5\right )\right )-e^{6 x} \left (-36 x^3+110 x^4-78 x^5+6 x^6+e^4 \left (-36 x^3+6 x^4\right )+e^2 \left (72 x^3-116 x^4+12 x^5\right )\right )}{\left (6-x-e^{3 x} x\right )^3} \, dx\\ &=\int \left (\frac {6 x^3 \left (-2-6 x+x^2\right )}{\left (-6+x+e^{3 x} x\right )^3}+2 x \left (\left (-1+e^2\right )^2-3 \left (1-e^2\right ) x+2 x^2\right )+\frac {2 x^2 \left (2 \left (1-e^2\right )-3 \left (2-e^2\right ) x+3 x^2\right )}{6-x-e^{3 x} x}+\frac {2 x^2 \left (6 \left (1-e^2\right )+\left (13-18 e^2\right ) x-3 \left (8-e^2\right ) x^2+3 x^3\right )}{\left (6-x-e^{3 x} x\right )^2}\right ) \, dx\\ &=2 \int x \left (\left (-1+e^2\right )^2-3 \left (1-e^2\right ) x+2 x^2\right ) \, dx+2 \int \frac {x^2 \left (2 \left (1-e^2\right )-3 \left (2-e^2\right ) x+3 x^2\right )}{6-x-e^{3 x} x} \, dx+2 \int \frac {x^2 \left (6 \left (1-e^2\right )+\left (13-18 e^2\right ) x-3 \left (8-e^2\right ) x^2+3 x^3\right )}{\left (6-x-e^{3 x} x\right )^2} \, dx+6 \int \frac {x^3 \left (-2-6 x+x^2\right )}{\left (-6+x+e^{3 x} x\right )^3} \, dx\\ &=2 \int \left (\left (-1+e^2\right )^2 x+3 (-1+e) (1+e) x^2+2 x^3\right ) \, dx+2 \int \left (-\frac {6 (-1+e) (1+e) x^2}{\left (-6+x+e^{3 x} x\right )^2}-\frac {\left (-13+18 e^2\right ) x^3}{\left (-6+x+e^{3 x} x\right )^2}+\frac {3 \left (-8+e^2\right ) x^4}{\left (-6+x+e^{3 x} x\right )^2}+\frac {3 x^5}{\left (-6+x+e^{3 x} x\right )^2}\right ) \, dx+2 \int \left (\frac {2 (-1+e) (1+e) x^2}{-6+x+e^{3 x} x}-\frac {3 \left (-2+e^2\right ) x^3}{-6+x+e^{3 x} x}-\frac {3 x^4}{-6+x+e^{3 x} x}\right ) \, dx+6 \int \left (-\frac {2 x^3}{\left (-6+x+e^{3 x} x\right )^3}-\frac {6 x^4}{\left (-6+x+e^{3 x} x\right )^3}+\frac {x^5}{\left (-6+x+e^{3 x} x\right )^3}\right ) \, dx\\ &=\left (1-e^2\right )^2 x^2-2 (1-e) (1+e) x^3+x^4+6 \int \frac {x^5}{\left (-6+x+e^{3 x} x\right )^3} \, dx+6 \int \frac {x^5}{\left (-6+x+e^{3 x} x\right )^2} \, dx-6 \int \frac {x^4}{-6+x+e^{3 x} x} \, dx-12 \int \frac {x^3}{\left (-6+x+e^{3 x} x\right )^3} \, dx-36 \int \frac {x^4}{\left (-6+x+e^{3 x} x\right )^3} \, dx+(12 (1-e) (1+e)) \int \frac {x^2}{\left (-6+x+e^{3 x} x\right )^2} \, dx+(4 (-1+e) (1+e)) \int \frac {x^2}{-6+x+e^{3 x} x} \, dx+\left (2 \left (13-18 e^2\right )\right ) \int \frac {x^3}{\left (-6+x+e^{3 x} x\right )^2} \, dx+\left (6 \left (2-e^2\right )\right ) \int \frac {x^3}{-6+x+e^{3 x} x} \, dx-\left (6 \left (8-e^2\right )\right ) \int \frac {x^4}{\left (-6+x+e^{3 x} x\right )^2} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.18, size = 60, normalized size = 2.31 \begin {gather*} x^2 \left (\left (-1+e^2\right )^2+2 \left (-1+e^2\right ) x+x^2+\frac {x^2}{\left (-6+x+e^{3 x} x\right )^2}+\frac {2 x \left (-1+e^2+x\right )}{-6+x+e^{3 x} x}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-432*x + 1296*x^2 - 1224*x^3 + 456*x^4 - 72*x^5 + 4*x^6 + E^4*(-432*x + 216*x^2 - 36*x^3 + 2*x^4) +
E^2*(864*x - 1512*x^2 + 660*x^3 - 108*x^4 + 6*x^5) + E^(9*x)*(2*x^4 + 2*E^4*x^4 - 6*x^5 + 4*x^6 + E^2*(-4*x^4
+ 6*x^5)) + E^(3*x)*(216*x^2 - 660*x^3 + 528*x^4 - 114*x^5 + 6*x^6 + E^4*(216*x^2 - 72*x^3 + 6*x^4) + E^2*(-4
32*x^2 + 732*x^3 - 184*x^4 + 12*x^5)) + E^(6*x)*(-36*x^3 + 110*x^4 - 78*x^5 + 6*x^6 + E^4*(-36*x^3 + 6*x^4) +
E^2*(72*x^3 - 116*x^4 + 12*x^5)))/(-216 + 108*x - 18*x^2 + x^3 + E^(9*x)*x^3 + E^(3*x)*(108*x - 36*x^2 + 3*x^3
) + E^(6*x)*(-18*x^2 + 3*x^3)),x]

[Out]

x^2*((-1 + E^2)^2 + 2*(-1 + E^2)*x + x^2 + x^2/(-6 + x + E^(3*x)*x)^2 + (2*x*(-1 + E^2 + x))/(-6 + x + E^(3*x)
*x))

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fricas [B]  time = 0.63, size = 188, normalized size = 7.23 \begin {gather*} \frac {x^{6} - 12 \, x^{5} + 48 \, x^{4} - 72 \, x^{3} + 36 \, x^{2} + {\left (x^{4} - 12 \, x^{3} + 36 \, x^{2}\right )} e^{4} + 2 \, {\left (x^{5} - 12 \, x^{4} + 42 \, x^{3} - 36 \, x^{2}\right )} e^{2} + {\left (x^{6} - 2 \, x^{5} + x^{4} e^{4} + x^{4} + 2 \, {\left (x^{5} - x^{4}\right )} e^{2}\right )} e^{\left (6 \, x\right )} + 2 \, {\left (x^{6} - 7 \, x^{5} + 12 \, x^{4} - 6 \, x^{3} + {\left (x^{4} - 6 \, x^{3}\right )} e^{4} + {\left (2 \, x^{5} - 13 \, x^{4} + 12 \, x^{3}\right )} e^{2}\right )} e^{\left (3 \, x\right )}}{x^{2} e^{\left (6 \, x\right )} + x^{2} + 2 \, {\left (x^{2} - 6 \, x\right )} e^{\left (3 \, x\right )} - 12 \, x + 36} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*x^4*exp(2)^2+(6*x^5-4*x^4)*exp(2)+4*x^6-6*x^5+2*x^4)*exp(3*x)^3+((6*x^4-36*x^3)*exp(2)^2+(12*x^5
-116*x^4+72*x^3)*exp(2)+6*x^6-78*x^5+110*x^4-36*x^3)*exp(3*x)^2+((6*x^4-72*x^3+216*x^2)*exp(2)^2+(12*x^5-184*x
^4+732*x^3-432*x^2)*exp(2)+6*x^6-114*x^5+528*x^4-660*x^3+216*x^2)*exp(3*x)+(2*x^4-36*x^3+216*x^2-432*x)*exp(2)
^2+(6*x^5-108*x^4+660*x^3-1512*x^2+864*x)*exp(2)+4*x^6-72*x^5+456*x^4-1224*x^3+1296*x^2-432*x)/(x^3*exp(3*x)^3
+(3*x^3-18*x^2)*exp(3*x)^2+(3*x^3-36*x^2+108*x)*exp(3*x)+x^3-18*x^2+108*x-216),x, algorithm="fricas")

[Out]

(x^6 - 12*x^5 + 48*x^4 - 72*x^3 + 36*x^2 + (x^4 - 12*x^3 + 36*x^2)*e^4 + 2*(x^5 - 12*x^4 + 42*x^3 - 36*x^2)*e^
2 + (x^6 - 2*x^5 + x^4*e^4 + x^4 + 2*(x^5 - x^4)*e^2)*e^(6*x) + 2*(x^6 - 7*x^5 + 12*x^4 - 6*x^3 + (x^4 - 6*x^3
)*e^4 + (2*x^5 - 13*x^4 + 12*x^3)*e^2)*e^(3*x))/(x^2*e^(6*x) + x^2 + 2*(x^2 - 6*x)*e^(3*x) - 12*x + 36)

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giac [B]  time = 0.83, size = 255, normalized size = 9.81 \begin {gather*} \frac {x^{6} e^{\left (6 \, x\right )} + 2 \, x^{6} e^{\left (3 \, x\right )} + x^{6} + 2 \, x^{5} e^{2} - 2 \, x^{5} e^{\left (6 \, x\right )} - 14 \, x^{5} e^{\left (3 \, x\right )} + 2 \, x^{5} e^{\left (6 \, x + 2\right )} + 4 \, x^{5} e^{\left (3 \, x + 2\right )} - 12 \, x^{5} + x^{4} e^{4} - 24 \, x^{4} e^{2} + x^{4} e^{\left (6 \, x\right )} + 24 \, x^{4} e^{\left (3 \, x\right )} + x^{4} e^{\left (6 \, x + 4\right )} - 2 \, x^{4} e^{\left (6 \, x + 2\right )} + 2 \, x^{4} e^{\left (3 \, x + 4\right )} - 26 \, x^{4} e^{\left (3 \, x + 2\right )} + 48 \, x^{4} - 12 \, x^{3} e^{4} + 84 \, x^{3} e^{2} - 12 \, x^{3} e^{\left (3 \, x\right )} - 12 \, x^{3} e^{\left (3 \, x + 4\right )} + 24 \, x^{3} e^{\left (3 \, x + 2\right )} - 72 \, x^{3} + 36 \, x^{2} e^{4} - 72 \, x^{2} e^{2} + 36 \, x^{2}}{x^{2} e^{\left (6 \, x\right )} + 2 \, x^{2} e^{\left (3 \, x\right )} + x^{2} - 12 \, x e^{\left (3 \, x\right )} - 12 \, x + 36} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*x^4*exp(2)^2+(6*x^5-4*x^4)*exp(2)+4*x^6-6*x^5+2*x^4)*exp(3*x)^3+((6*x^4-36*x^3)*exp(2)^2+(12*x^5
-116*x^4+72*x^3)*exp(2)+6*x^6-78*x^5+110*x^4-36*x^3)*exp(3*x)^2+((6*x^4-72*x^3+216*x^2)*exp(2)^2+(12*x^5-184*x
^4+732*x^3-432*x^2)*exp(2)+6*x^6-114*x^5+528*x^4-660*x^3+216*x^2)*exp(3*x)+(2*x^4-36*x^3+216*x^2-432*x)*exp(2)
^2+(6*x^5-108*x^4+660*x^3-1512*x^2+864*x)*exp(2)+4*x^6-72*x^5+456*x^4-1224*x^3+1296*x^2-432*x)/(x^3*exp(3*x)^3
+(3*x^3-18*x^2)*exp(3*x)^2+(3*x^3-36*x^2+108*x)*exp(3*x)+x^3-18*x^2+108*x-216),x, algorithm="giac")

[Out]

(x^6*e^(6*x) + 2*x^6*e^(3*x) + x^6 + 2*x^5*e^2 - 2*x^5*e^(6*x) - 14*x^5*e^(3*x) + 2*x^5*e^(6*x + 2) + 4*x^5*e^
(3*x + 2) - 12*x^5 + x^4*e^4 - 24*x^4*e^2 + x^4*e^(6*x) + 24*x^4*e^(3*x) + x^4*e^(6*x + 4) - 2*x^4*e^(6*x + 2)
+ 2*x^4*e^(3*x + 4) - 26*x^4*e^(3*x + 2) + 48*x^4 - 12*x^3*e^4 + 84*x^3*e^2 - 12*x^3*e^(3*x) - 12*x^3*e^(3*x
+ 4) + 24*x^3*e^(3*x + 2) - 72*x^3 + 36*x^2*e^4 - 72*x^2*e^2 + 36*x^2)/(x^2*e^(6*x) + 2*x^2*e^(3*x) + x^2 - 12
*x*e^(3*x) - 12*x + 36)

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maple [B]  time = 0.36, size = 92, normalized size = 3.54

method	result	size
risch	\(x^{4}+2 x^{3} {\mathrm e}^{2}-2 x^{3}-2 x^{2} {\mathrm e}^{2}+x^{2} {\mathrm e}^{4}+x^{2}+\frac {\left (2 x \,{\mathrm e}^{3 x +2}+2 x^{2} {\mathrm e}^{3 x}+2 \,{\mathrm e}^{2} x +2 x^{2}-2 x \,{\mathrm e}^{3 x}-12 \,{\mathrm e}^{2}-13 x +12\right ) x^{3}}{\left (x +x \,{\mathrm e}^{3 x}-6\right )^{2}}\)	\(92\)
norman	\(\frac {x^{6}+\left (-12+2 \,{\mathrm e}^{2}\right ) x^{5}+\left (-72+84 \,{\mathrm e}^{2}-12 \,{\mathrm e}^{4}\right ) x^{3}+\left (48-24 \,{\mathrm e}^{2}+{\mathrm e}^{4}\right ) x^{4}+\left (36-72 \,{\mathrm e}^{2}+36 \,{\mathrm e}^{4}\right ) x^{2}+{\mathrm e}^{6 x} x^{6}+\left (2 \,{\mathrm e}^{2}-2\right ) x^{5} {\mathrm e}^{6 x}+\left (4 \,{\mathrm e}^{2}-14\right ) x^{5} {\mathrm e}^{3 x}+\left (-12+24 \,{\mathrm e}^{2}-12 \,{\mathrm e}^{4}\right ) x^{3} {\mathrm e}^{3 x}+\left (24+2 \,{\mathrm e}^{4}-26 \,{\mathrm e}^{2}\right ) x^{4} {\mathrm e}^{3 x}+\left ({\mathrm e}^{4}-2 \,{\mathrm e}^{2}+1\right ) x^{4} {\mathrm e}^{6 x}+2 \,{\mathrm e}^{3 x} x^{6}}{\left (x +x \,{\mathrm e}^{3 x}-6\right )^{2}}\)	\(182\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((2*x^4*exp(2)^2+(6*x^5-4*x^4)*exp(2)+4*x^6-6*x^5+2*x^4)*exp(3*x)^3+((6*x^4-36*x^3)*exp(2)^2+(12*x^5-116*x
^4+72*x^3)*exp(2)+6*x^6-78*x^5+110*x^4-36*x^3)*exp(3*x)^2+((6*x^4-72*x^3+216*x^2)*exp(2)^2+(12*x^5-184*x^4+732
*x^3-432*x^2)*exp(2)+6*x^6-114*x^5+528*x^4-660*x^3+216*x^2)*exp(3*x)+(2*x^4-36*x^3+216*x^2-432*x)*exp(2)^2+(6*
x^5-108*x^4+660*x^3-1512*x^2+864*x)*exp(2)+4*x^6-72*x^5+456*x^4-1224*x^3+1296*x^2-432*x)/(x^3*exp(3*x)^3+(3*x^
3-18*x^2)*exp(3*x)^2+(3*x^3-36*x^2+108*x)*exp(3*x)+x^3-18*x^2+108*x-216),x,method=_RETURNVERBOSE)

[Out]

x^4+2*x^3*exp(2)-2*x^3-2*x^2*exp(2)+x^2*exp(4)+x^2+(2*x*exp(3*x+2)+2*x^2*exp(3*x)+2*exp(2)*x+2*x^2-2*x*exp(3*x
)-12*exp(2)-13*x+12)*x^3/(x+x*exp(3*x)-6)^2

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maxima [B]  time = 0.53, size = 158, normalized size = 6.08 \begin {gather*} \frac {x^{6} + 2 \, x^{5} {\left (e^{2} - 6\right )} + x^{4} {\left (e^{4} - 24 \, e^{2} + 48\right )} - 12 \, x^{3} {\left (e^{4} - 7 \, e^{2} + 6\right )} + 36 \, x^{2} {\left (e^{4} - 2 \, e^{2} + 1\right )} + {\left (x^{6} + 2 \, x^{5} {\left (e^{2} - 1\right )} + x^{4} {\left (e^{4} - 2 \, e^{2} + 1\right )}\right )} e^{\left (6 \, x\right )} + 2 \, {\left (x^{6} + x^{5} {\left (2 \, e^{2} - 7\right )} + x^{4} {\left (e^{4} - 13 \, e^{2} + 12\right )} - 6 \, x^{3} {\left (e^{4} - 2 \, e^{2} + 1\right )}\right )} e^{\left (3 \, x\right )}}{x^{2} e^{\left (6 \, x\right )} + x^{2} + 2 \, {\left (x^{2} - 6 \, x\right )} e^{\left (3 \, x\right )} - 12 \, x + 36} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*x^4*exp(2)^2+(6*x^5-4*x^4)*exp(2)+4*x^6-6*x^5+2*x^4)*exp(3*x)^3+((6*x^4-36*x^3)*exp(2)^2+(12*x^5
-116*x^4+72*x^3)*exp(2)+6*x^6-78*x^5+110*x^4-36*x^3)*exp(3*x)^2+((6*x^4-72*x^3+216*x^2)*exp(2)^2+(12*x^5-184*x
^4+732*x^3-432*x^2)*exp(2)+6*x^6-114*x^5+528*x^4-660*x^3+216*x^2)*exp(3*x)+(2*x^4-36*x^3+216*x^2-432*x)*exp(2)
^2+(6*x^5-108*x^4+660*x^3-1512*x^2+864*x)*exp(2)+4*x^6-72*x^5+456*x^4-1224*x^3+1296*x^2-432*x)/(x^3*exp(3*x)^3
+(3*x^3-18*x^2)*exp(3*x)^2+(3*x^3-36*x^2+108*x)*exp(3*x)+x^3-18*x^2+108*x-216),x, algorithm="maxima")

[Out]

(x^6 + 2*x^5*(e^2 - 6) + x^4*(e^4 - 24*e^2 + 48) - 12*x^3*(e^4 - 7*e^2 + 6) + 36*x^2*(e^4 - 2*e^2 + 1) + (x^6
+ 2*x^5*(e^2 - 1) + x^4*(e^4 - 2*e^2 + 1))*e^(6*x) + 2*(x^6 + x^5*(2*e^2 - 7) + x^4*(e^4 - 13*e^2 + 12) - 6*x^
3*(e^4 - 2*e^2 + 1))*e^(3*x))/(x^2*e^(6*x) + x^2 + 2*(x^2 - 6*x)*e^(3*x) - 12*x + 36)

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mupad [B]  time = 4.50, size = 146, normalized size = 5.62 \begin {gather*} x^3\,\left (2\,{\mathrm {e}}^2-2\right )+x^2\,{\left ({\mathrm {e}}^2-1\right )}^2+x^4-\frac {2\,\left (x^5\,{\mathrm {e}}^2-6\,x^4\,{\mathrm {e}}^2-2\,x^3\,{\mathrm {e}}^2+2\,x^3+4\,x^4-7\,x^5+x^6\right )}{\left (-x^2+6\,x+2\right )\,\left (x+x\,{\mathrm {e}}^{3\,x}-6\right )}+\frac {-x^7+6\,x^6+2\,x^5}{x\,\left (-x^2+6\,x+2\right )\,\left ({\left (x-6\right )}^2+x^2\,{\mathrm {e}}^{6\,x}+2\,x\,{\mathrm {e}}^{3\,x}\,\left (x-6\right )\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(9*x)*(2*x^4*exp(4) - exp(2)*(4*x^4 - 6*x^5) + 2*x^4 - 6*x^5 + 4*x^6) - exp(6*x)*(exp(4)*(36*x^3 - 6*x
^4) - exp(2)*(72*x^3 - 116*x^4 + 12*x^5) + 36*x^3 - 110*x^4 + 78*x^5 - 6*x^6) - exp(4)*(432*x - 216*x^2 + 36*x
^3 - 2*x^4) - 432*x + exp(3*x)*(exp(4)*(216*x^2 - 72*x^3 + 6*x^4) + 216*x^2 - 660*x^3 + 528*x^4 - 114*x^5 + 6*
x^6 - exp(2)*(432*x^2 - 732*x^3 + 184*x^4 - 12*x^5)) + exp(2)*(864*x - 1512*x^2 + 660*x^3 - 108*x^4 + 6*x^5) +
1296*x^2 - 1224*x^3 + 456*x^4 - 72*x^5 + 4*x^6)/(108*x + exp(3*x)*(108*x - 36*x^2 + 3*x^3) - exp(6*x)*(18*x^2
- 3*x^3) + x^3*exp(9*x) - 18*x^2 + x^3 - 216),x)

[Out]

x^3*(2*exp(2) - 2) + x^2*(exp(2) - 1)^2 + x^4 - (2*(x^5*exp(2) - 6*x^4*exp(2) - 2*x^3*exp(2) + 2*x^3 + 4*x^4 -
7*x^5 + x^6))/((6*x - x^2 + 2)*(x + x*exp(3*x) - 6)) + (2*x^5 + 6*x^6 - x^7)/(x*(6*x - x^2 + 2)*((x - 6)^2 +
x^2*exp(6*x) + 2*x*exp(3*x)*(x - 6)))

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sympy [B]  time = 0.38, size = 112, normalized size = 4.31 \begin {gather*} x^{4} + x^{3} \left (-2 + 2 e^{2}\right ) + x^{2} \left (- 2 e^{2} + 1 + e^{4}\right ) + \frac {2 x^{5} - 13 x^{4} + 2 x^{4} e^{2} - 12 x^{3} e^{2} + 12 x^{3} + \left (2 x^{5} - 2 x^{4} + 2 x^{4} e^{2}\right ) e^{3 x}}{x^{2} e^{6 x} + x^{2} - 12 x + \left (2 x^{2} - 12 x\right ) e^{3 x} + 36} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*x**4*exp(2)**2+(6*x**5-4*x**4)*exp(2)+4*x**6-6*x**5+2*x**4)*exp(3*x)**3+((6*x**4-36*x**3)*exp(2)
**2+(12*x**5-116*x**4+72*x**3)*exp(2)+6*x**6-78*x**5+110*x**4-36*x**3)*exp(3*x)**2+((6*x**4-72*x**3+216*x**2)*
exp(2)**2+(12*x**5-184*x**4+732*x**3-432*x**2)*exp(2)+6*x**6-114*x**5+528*x**4-660*x**3+216*x**2)*exp(3*x)+(2*
x**4-36*x**3+216*x**2-432*x)*exp(2)**2+(6*x**5-108*x**4+660*x**3-1512*x**2+864*x)*exp(2)+4*x**6-72*x**5+456*x*
*4-1224*x**3+1296*x**2-432*x)/(x**3*exp(3*x)**3+(3*x**3-18*x**2)*exp(3*x)**2+(3*x**3-36*x**2+108*x)*exp(3*x)+x
**3-18*x**2+108*x-216),x)

[Out]

x**4 + x**3*(-2 + 2*exp(2)) + x**2*(-2*exp(2) + 1 + exp(4)) + (2*x**5 - 13*x**4 + 2*x**4*exp(2) - 12*x**3*exp(
2) + 12*x**3 + (2*x**5 - 2*x**4 + 2*x**4*exp(2))*exp(3*x))/(x**2*exp(6*x) + x**2 - 12*x + (2*x**2 - 12*x)*exp(
3*x) + 36)

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