3.70.47 \(\int \frac {-108-80 x+108 x^2+48 x^3-15 x^4-6 x^5+e^x (-108-108 x+108 x^2+36 x^3-15 x^4-3 x^5)}{11664 x^2+8640 x^3-6176 x^4-5472 x^5+984 x^6+1320 x^7+8 x^8-144 x^9-15 x^{10}+6 x^{11}+x^{12}+e^{2 x} (11664 x^2-7776 x^4+1944 x^6-216 x^8+9 x^{10})+e^x (23328 x^2+8640 x^3-15552 x^4-5472 x^5+3888 x^6+1320 x^7-432 x^8-144 x^9+18 x^{10}+6 x^{11})} \, dx\)

Optimal. Leaf size=28 \[ \frac {1}{x \left (4 x+\left (3+3 e^x+x\right ) \left (6-x^2\right )^2\right )} \]

________________________________________________________________________________________

Rubi [F]  time = 6.90, 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 {-108-80 x+108 x^2+48 x^3-15 x^4-6 x^5+e^x \left (-108-108 x+108 x^2+36 x^3-15 x^4-3 x^5\right )}{11664 x^2+8640 x^3-6176 x^4-5472 x^5+984 x^6+1320 x^7+8 x^8-144 x^9-15 x^{10}+6 x^{11}+x^{12}+e^{2 x} \left (11664 x^2-7776 x^4+1944 x^6-216 x^8+9 x^{10}\right )+e^x \left (23328 x^2+8640 x^3-15552 x^4-5472 x^5+3888 x^6+1320 x^7-432 x^8-144 x^9+18 x^{10}+6 x^{11}\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-108 - 80*x + 108*x^2 + 48*x^3 - 15*x^4 - 6*x^5 + E^x*(-108 - 108*x + 108*x^2 + 36*x^3 - 15*x^4 - 3*x^5))
/(11664*x^2 + 8640*x^3 - 6176*x^4 - 5472*x^5 + 984*x^6 + 1320*x^7 + 8*x^8 - 144*x^9 - 15*x^10 + 6*x^11 + x^12
+ E^(2*x)*(11664*x^2 - 7776*x^4 + 1944*x^6 - 216*x^8 + 9*x^10) + E^x*(23328*x^2 + 8640*x^3 - 15552*x^4 - 5472*
x^5 + 3888*x^6 + 1320*x^7 - 432*x^8 - 144*x^9 + 18*x^10 + 6*x^11)),x]

[Out]

40*Defer[Int][(108 + 108*E^x + 40*x - 36*x^2 - 36*E^x*x^2 - 12*x^3 + 3*x^4 + 3*E^x*x^4 + x^5)^(-2), x] - 8*Def
er[Int][1/((Sqrt[6] - x)*(108 + 108*E^x + 40*x - 36*x^2 - 36*E^x*x^2 - 12*x^3 + 3*x^4 + 3*E^x*x^4 + x^5)^2), x
] + 68*Defer[Int][1/(x*(108 + 108*E^x + 40*x - 36*x^2 - 36*E^x*x^2 - 12*x^3 + 3*x^4 + 3*E^x*x^4 + x^5)^2), x]
- 24*Defer[Int][x/(108 + 108*E^x + 40*x - 36*x^2 - 36*E^x*x^2 - 12*x^3 + 3*x^4 + 3*E^x*x^4 + x^5)^2, x] - 12*D
efer[Int][x^2/(108 + 108*E^x + 40*x - 36*x^2 - 36*E^x*x^2 - 12*x^3 + 3*x^4 + 3*E^x*x^4 + x^5)^2, x] + 2*Defer[
Int][x^3/(108 + 108*E^x + 40*x - 36*x^2 - 36*E^x*x^2 - 12*x^3 + 3*x^4 + 3*E^x*x^4 + x^5)^2, x] + Defer[Int][x^
4/(108 + 108*E^x + 40*x - 36*x^2 - 36*E^x*x^2 - 12*x^3 + 3*x^4 + 3*E^x*x^4 + x^5)^2, x] + 8*Defer[Int][1/((Sqr
t[6] + x)*(108 + 108*E^x + 40*x - 36*x^2 - 36*E^x*x^2 - 12*x^3 + 3*x^4 + 3*E^x*x^4 + x^5)^2), x] + Sqrt[2/3]*D
efer[Int][1/((Sqrt[6] - x)*(108 + 108*E^x + 40*x - 36*x^2 - 36*E^x*x^2 - 12*x^3 + 3*x^4 + 3*E^x*x^4 + x^5)), x
] - Defer[Int][1/(x^2*(108 + 108*E^x + 40*x - 36*x^2 - 36*E^x*x^2 - 12*x^3 + 3*x^4 + 3*E^x*x^4 + x^5)), x] - D
efer[Int][1/(x*(108 + 108*E^x + 40*x - 36*x^2 - 36*E^x*x^2 - 12*x^3 + 3*x^4 + 3*E^x*x^4 + x^5)), x] + Sqrt[2/3
]*Defer[Int][1/((Sqrt[6] + x)*(108 + 108*E^x + 40*x - 36*x^2 - 36*E^x*x^2 - 12*x^3 + 3*x^4 + 3*E^x*x^4 + x^5))
, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-108-80 x+108 x^2+48 x^3-15 x^4-6 x^5-3 e^x \left (36+36 x-36 x^2-12 x^3+5 x^4+x^5\right )}{x^2 \left (108+40 x-36 x^2-12 x^3+3 x^4+x^5+3 e^x \left (-6+x^2\right )^2\right )^2} \, dx\\ &=\int \left (-\frac {-6-6 x+5 x^2+x^3}{x^2 \left (-6+x^2\right ) \left (108+108 e^x+40 x-36 x^2-36 e^x x^2-12 x^3+3 x^4+3 e^x x^4+x^5\right )}+\frac {-408-240 x+228 x^2+112 x^3-36 x^4-18 x^5+2 x^6+x^7}{x \left (-6+x^2\right ) \left (108+108 e^x+40 x-36 x^2-36 e^x x^2-12 x^3+3 x^4+3 e^x x^4+x^5\right )^2}\right ) \, dx\\ &=-\int \frac {-6-6 x+5 x^2+x^3}{x^2 \left (-6+x^2\right ) \left (108+108 e^x+40 x-36 x^2-36 e^x x^2-12 x^3+3 x^4+3 e^x x^4+x^5\right )} \, dx+\int \frac {-408-240 x+228 x^2+112 x^3-36 x^4-18 x^5+2 x^6+x^7}{x \left (-6+x^2\right ) \left (108+108 e^x+40 x-36 x^2-36 e^x x^2-12 x^3+3 x^4+3 e^x x^4+x^5\right )^2} \, dx\\ &=\int \left (\frac {40}{\left (108+108 e^x+40 x-36 x^2-36 e^x x^2-12 x^3+3 x^4+3 e^x x^4+x^5\right )^2}+\frac {68}{x \left (108+108 e^x+40 x-36 x^2-36 e^x x^2-12 x^3+3 x^4+3 e^x x^4+x^5\right )^2}-\frac {24 x}{\left (108+108 e^x+40 x-36 x^2-36 e^x x^2-12 x^3+3 x^4+3 e^x x^4+x^5\right )^2}-\frac {12 x^2}{\left (108+108 e^x+40 x-36 x^2-36 e^x x^2-12 x^3+3 x^4+3 e^x x^4+x^5\right )^2}+\frac {2 x^3}{\left (108+108 e^x+40 x-36 x^2-36 e^x x^2-12 x^3+3 x^4+3 e^x x^4+x^5\right )^2}+\frac {x^4}{\left (108+108 e^x+40 x-36 x^2-36 e^x x^2-12 x^3+3 x^4+3 e^x x^4+x^5\right )^2}+\frac {16 x}{\left (-6+x^2\right ) \left (108+108 e^x+40 x-36 x^2-36 e^x x^2-12 x^3+3 x^4+3 e^x x^4+x^5\right )^2}\right ) \, dx-\int \left (\frac {1}{x^2 \left (108+108 e^x+40 x-36 x^2-36 e^x x^2-12 x^3+3 x^4+3 e^x x^4+x^5\right )}+\frac {1}{x \left (108+108 e^x+40 x-36 x^2-36 e^x x^2-12 x^3+3 x^4+3 e^x x^4+x^5\right )}+\frac {4}{\left (-6+x^2\right ) \left (108+108 e^x+40 x-36 x^2-36 e^x x^2-12 x^3+3 x^4+3 e^x x^4+x^5\right )}\right ) \, dx\\ &=2 \int \frac {x^3}{\left (108+108 e^x+40 x-36 x^2-36 e^x x^2-12 x^3+3 x^4+3 e^x x^4+x^5\right )^2} \, dx-4 \int \frac {1}{\left (-6+x^2\right ) \left (108+108 e^x+40 x-36 x^2-36 e^x x^2-12 x^3+3 x^4+3 e^x x^4+x^5\right )} \, dx-12 \int \frac {x^2}{\left (108+108 e^x+40 x-36 x^2-36 e^x x^2-12 x^3+3 x^4+3 e^x x^4+x^5\right )^2} \, dx+16 \int \frac {x}{\left (-6+x^2\right ) \left (108+108 e^x+40 x-36 x^2-36 e^x x^2-12 x^3+3 x^4+3 e^x x^4+x^5\right )^2} \, dx-24 \int \frac {x}{\left (108+108 e^x+40 x-36 x^2-36 e^x x^2-12 x^3+3 x^4+3 e^x x^4+x^5\right )^2} \, dx+40 \int \frac {1}{\left (108+108 e^x+40 x-36 x^2-36 e^x x^2-12 x^3+3 x^4+3 e^x x^4+x^5\right )^2} \, dx+68 \int \frac {1}{x \left (108+108 e^x+40 x-36 x^2-36 e^x x^2-12 x^3+3 x^4+3 e^x x^4+x^5\right )^2} \, dx+\int \frac {x^4}{\left (108+108 e^x+40 x-36 x^2-36 e^x x^2-12 x^3+3 x^4+3 e^x x^4+x^5\right )^2} \, dx-\int \frac {1}{x^2 \left (108+108 e^x+40 x-36 x^2-36 e^x x^2-12 x^3+3 x^4+3 e^x x^4+x^5\right )} \, dx-\int \frac {1}{x \left (108+108 e^x+40 x-36 x^2-36 e^x x^2-12 x^3+3 x^4+3 e^x x^4+x^5\right )} \, dx\\ &=2 \int \frac {x^3}{\left (108+108 e^x+40 x-36 x^2-36 e^x x^2-12 x^3+3 x^4+3 e^x x^4+x^5\right )^2} \, dx-4 \int \left (-\frac {1}{2 \sqrt {6} \left (\sqrt {6}-x\right ) \left (108+108 e^x+40 x-36 x^2-36 e^x x^2-12 x^3+3 x^4+3 e^x x^4+x^5\right )}-\frac {1}{2 \sqrt {6} \left (\sqrt {6}+x\right ) \left (108+108 e^x+40 x-36 x^2-36 e^x x^2-12 x^3+3 x^4+3 e^x x^4+x^5\right )}\right ) \, dx-12 \int \frac {x^2}{\left (108+108 e^x+40 x-36 x^2-36 e^x x^2-12 x^3+3 x^4+3 e^x x^4+x^5\right )^2} \, dx+16 \int \left (-\frac {1}{2 \left (\sqrt {6}-x\right ) \left (108+108 e^x+40 x-36 x^2-36 e^x x^2-12 x^3+3 x^4+3 e^x x^4+x^5\right )^2}+\frac {1}{2 \left (\sqrt {6}+x\right ) \left (108+108 e^x+40 x-36 x^2-36 e^x x^2-12 x^3+3 x^4+3 e^x x^4+x^5\right )^2}\right ) \, dx-24 \int \frac {x}{\left (108+108 e^x+40 x-36 x^2-36 e^x x^2-12 x^3+3 x^4+3 e^x x^4+x^5\right )^2} \, dx+40 \int \frac {1}{\left (108+108 e^x+40 x-36 x^2-36 e^x x^2-12 x^3+3 x^4+3 e^x x^4+x^5\right )^2} \, dx+68 \int \frac {1}{x \left (108+108 e^x+40 x-36 x^2-36 e^x x^2-12 x^3+3 x^4+3 e^x x^4+x^5\right )^2} \, dx+\int \frac {x^4}{\left (108+108 e^x+40 x-36 x^2-36 e^x x^2-12 x^3+3 x^4+3 e^x x^4+x^5\right )^2} \, dx-\int \frac {1}{x^2 \left (108+108 e^x+40 x-36 x^2-36 e^x x^2-12 x^3+3 x^4+3 e^x x^4+x^5\right )} \, dx-\int \frac {1}{x \left (108+108 e^x+40 x-36 x^2-36 e^x x^2-12 x^3+3 x^4+3 e^x x^4+x^5\right )} \, dx\\ &=2 \int \frac {x^3}{\left (108+108 e^x+40 x-36 x^2-36 e^x x^2-12 x^3+3 x^4+3 e^x x^4+x^5\right )^2} \, dx-8 \int \frac {1}{\left (\sqrt {6}-x\right ) \left (108+108 e^x+40 x-36 x^2-36 e^x x^2-12 x^3+3 x^4+3 e^x x^4+x^5\right )^2} \, dx+8 \int \frac {1}{\left (\sqrt {6}+x\right ) \left (108+108 e^x+40 x-36 x^2-36 e^x x^2-12 x^3+3 x^4+3 e^x x^4+x^5\right )^2} \, dx-12 \int \frac {x^2}{\left (108+108 e^x+40 x-36 x^2-36 e^x x^2-12 x^3+3 x^4+3 e^x x^4+x^5\right )^2} \, dx-24 \int \frac {x}{\left (108+108 e^x+40 x-36 x^2-36 e^x x^2-12 x^3+3 x^4+3 e^x x^4+x^5\right )^2} \, dx+40 \int \frac {1}{\left (108+108 e^x+40 x-36 x^2-36 e^x x^2-12 x^3+3 x^4+3 e^x x^4+x^5\right )^2} \, dx+68 \int \frac {1}{x \left (108+108 e^x+40 x-36 x^2-36 e^x x^2-12 x^3+3 x^4+3 e^x x^4+x^5\right )^2} \, dx+\sqrt {\frac {2}{3}} \int \frac {1}{\left (\sqrt {6}-x\right ) \left (108+108 e^x+40 x-36 x^2-36 e^x x^2-12 x^3+3 x^4+3 e^x x^4+x^5\right )} \, dx+\sqrt {\frac {2}{3}} \int \frac {1}{\left (\sqrt {6}+x\right ) \left (108+108 e^x+40 x-36 x^2-36 e^x x^2-12 x^3+3 x^4+3 e^x x^4+x^5\right )} \, dx+\int \frac {x^4}{\left (108+108 e^x+40 x-36 x^2-36 e^x x^2-12 x^3+3 x^4+3 e^x x^4+x^5\right )^2} \, dx-\int \frac {1}{x^2 \left (108+108 e^x+40 x-36 x^2-36 e^x x^2-12 x^3+3 x^4+3 e^x x^4+x^5\right )} \, dx-\int \frac {1}{x \left (108+108 e^x+40 x-36 x^2-36 e^x x^2-12 x^3+3 x^4+3 e^x x^4+x^5\right )} \, dx\\ \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [A]  time = 0.07, size = 41, normalized size = 1.46 \begin {gather*} \frac {1}{x \left (108+40 x-36 x^2-12 x^3+3 x^4+x^5+3 e^x \left (-6+x^2\right )^2\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-108 - 80*x + 108*x^2 + 48*x^3 - 15*x^4 - 6*x^5 + E^x*(-108 - 108*x + 108*x^2 + 36*x^3 - 15*x^4 - 3
*x^5))/(11664*x^2 + 8640*x^3 - 6176*x^4 - 5472*x^5 + 984*x^6 + 1320*x^7 + 8*x^8 - 144*x^9 - 15*x^10 + 6*x^11 +
x^12 + E^(2*x)*(11664*x^2 - 7776*x^4 + 1944*x^6 - 216*x^8 + 9*x^10) + E^x*(23328*x^2 + 8640*x^3 - 15552*x^4 -
5472*x^5 + 3888*x^6 + 1320*x^7 - 432*x^8 - 144*x^9 + 18*x^10 + 6*x^11)),x]

[Out]

1/(x*(108 + 40*x - 36*x^2 - 12*x^3 + 3*x^4 + x^5 + 3*E^x*(-6 + x^2)^2))

________________________________________________________________________________________

fricas [A]  time = 0.77, size = 45, normalized size = 1.61 \begin {gather*} \frac {1}{x^{6} + 3 \, x^{5} - 12 \, x^{4} - 36 \, x^{3} + 40 \, x^{2} + 3 \, {\left (x^{5} - 12 \, x^{3} + 36 \, x\right )} e^{x} + 108 \, x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-3*x^5-15*x^4+36*x^3+108*x^2-108*x-108)*exp(x)-6*x^5-15*x^4+48*x^3+108*x^2-80*x-108)/((9*x^10-216*
x^8+1944*x^6-7776*x^4+11664*x^2)*exp(x)^2+(6*x^11+18*x^10-144*x^9-432*x^8+1320*x^7+3888*x^6-5472*x^5-15552*x^4
+8640*x^3+23328*x^2)*exp(x)+x^12+6*x^11-15*x^10-144*x^9+8*x^8+1320*x^7+984*x^6-5472*x^5-6176*x^4+8640*x^3+1166
4*x^2),x, algorithm="fricas")

[Out]

1/(x^6 + 3*x^5 - 12*x^4 - 36*x^3 + 40*x^2 + 3*(x^5 - 12*x^3 + 36*x)*e^x + 108*x)

________________________________________________________________________________________

giac [A]  time = 0.25, size = 48, normalized size = 1.71 \begin {gather*} \frac {1}{x^{6} + 3 \, x^{5} e^{x} + 3 \, x^{5} - 12 \, x^{4} - 36 \, x^{3} e^{x} - 36 \, x^{3} + 40 \, x^{2} + 108 \, x e^{x} + 108 \, x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-3*x^5-15*x^4+36*x^3+108*x^2-108*x-108)*exp(x)-6*x^5-15*x^4+48*x^3+108*x^2-80*x-108)/((9*x^10-216*
x^8+1944*x^6-7776*x^4+11664*x^2)*exp(x)^2+(6*x^11+18*x^10-144*x^9-432*x^8+1320*x^7+3888*x^6-5472*x^5-15552*x^4
+8640*x^3+23328*x^2)*exp(x)+x^12+6*x^11-15*x^10-144*x^9+8*x^8+1320*x^7+984*x^6-5472*x^5-6176*x^4+8640*x^3+1166
4*x^2),x, algorithm="giac")

[Out]

1/(x^6 + 3*x^5*e^x + 3*x^5 - 12*x^4 - 36*x^3*e^x - 36*x^3 + 40*x^2 + 108*x*e^x + 108*x)

________________________________________________________________________________________

maple [A]  time = 0.05, size = 48, normalized size = 1.71

method	result	size
risch	\(\frac {1}{x \left (3 \,{\mathrm e}^{x} x^{4}+x^{5}+3 x^{4}-36 \,{\mathrm e}^{x} x^{2}-12 x^{3}-36 x^{2}+108 \,{\mathrm e}^{x}+40 x +108\right )}\)	\(48\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-3*x^5-15*x^4+36*x^3+108*x^2-108*x-108)*exp(x)-6*x^5-15*x^4+48*x^3+108*x^2-80*x-108)/((9*x^10-216*x^8+19
44*x^6-7776*x^4+11664*x^2)*exp(x)^2+(6*x^11+18*x^10-144*x^9-432*x^8+1320*x^7+3888*x^6-5472*x^5-15552*x^4+8640*
x^3+23328*x^2)*exp(x)+x^12+6*x^11-15*x^10-144*x^9+8*x^8+1320*x^7+984*x^6-5472*x^5-6176*x^4+8640*x^3+11664*x^2)
,x,method=_RETURNVERBOSE)

[Out]

1/x/(3*exp(x)*x^4+x^5+3*x^4-36*exp(x)*x^2-12*x^3-36*x^2+108*exp(x)+40*x+108)

________________________________________________________________________________________

maxima [A]  time = 0.53, size = 45, normalized size = 1.61 \begin {gather*} \frac {1}{x^{6} + 3 \, x^{5} - 12 \, x^{4} - 36 \, x^{3} + 40 \, x^{2} + 3 \, {\left (x^{5} - 12 \, x^{3} + 36 \, x\right )} e^{x} + 108 \, x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-3*x^5-15*x^4+36*x^3+108*x^2-108*x-108)*exp(x)-6*x^5-15*x^4+48*x^3+108*x^2-80*x-108)/((9*x^10-216*
x^8+1944*x^6-7776*x^4+11664*x^2)*exp(x)^2+(6*x^11+18*x^10-144*x^9-432*x^8+1320*x^7+3888*x^6-5472*x^5-15552*x^4
+8640*x^3+23328*x^2)*exp(x)+x^12+6*x^11-15*x^10-144*x^9+8*x^8+1320*x^7+984*x^6-5472*x^5-6176*x^4+8640*x^3+1166
4*x^2),x, algorithm="maxima")

[Out]

1/(x^6 + 3*x^5 - 12*x^4 - 36*x^3 + 40*x^2 + 3*(x^5 - 12*x^3 + 36*x)*e^x + 108*x)

________________________________________________________________________________________

mupad [F]  time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int -\frac {80\,x+{\mathrm {e}}^x\,\left (3\,x^5+15\,x^4-36\,x^3-108\,x^2+108\,x+108\right )-108\,x^2-48\,x^3+15\,x^4+6\,x^5+108}{{\mathrm {e}}^{2\,x}\,\left (9\,x^{10}-216\,x^8+1944\,x^6-7776\,x^4+11664\,x^2\right )+{\mathrm {e}}^x\,\left (6\,x^{11}+18\,x^{10}-144\,x^9-432\,x^8+1320\,x^7+3888\,x^6-5472\,x^5-15552\,x^4+8640\,x^3+23328\,x^2\right )+11664\,x^2+8640\,x^3-6176\,x^4-5472\,x^5+984\,x^6+1320\,x^7+8\,x^8-144\,x^9-15\,x^{10}+6\,x^{11}+x^{12}} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(80*x + exp(x)*(108*x - 108*x^2 - 36*x^3 + 15*x^4 + 3*x^5 + 108) - 108*x^2 - 48*x^3 + 15*x^4 + 6*x^5 + 10
8)/(exp(2*x)*(11664*x^2 - 7776*x^4 + 1944*x^6 - 216*x^8 + 9*x^10) + exp(x)*(23328*x^2 + 8640*x^3 - 15552*x^4 -
5472*x^5 + 3888*x^6 + 1320*x^7 - 432*x^8 - 144*x^9 + 18*x^10 + 6*x^11) + 11664*x^2 + 8640*x^3 - 6176*x^4 - 54
72*x^5 + 984*x^6 + 1320*x^7 + 8*x^8 - 144*x^9 - 15*x^10 + 6*x^11 + x^12),x)

[Out]

int(-(80*x + exp(x)*(108*x - 108*x^2 - 36*x^3 + 15*x^4 + 3*x^5 + 108) - 108*x^2 - 48*x^3 + 15*x^4 + 6*x^5 + 10
8)/(exp(2*x)*(11664*x^2 - 7776*x^4 + 1944*x^6 - 216*x^8 + 9*x^10) + exp(x)*(23328*x^2 + 8640*x^3 - 15552*x^4 -
5472*x^5 + 3888*x^6 + 1320*x^7 - 432*x^8 - 144*x^9 + 18*x^10 + 6*x^11) + 11664*x^2 + 8640*x^3 - 6176*x^4 - 54
72*x^5 + 984*x^6 + 1320*x^7 + 8*x^8 - 144*x^9 - 15*x^10 + 6*x^11 + x^12), x)

________________________________________________________________________________________

sympy [B]  time = 0.48, size = 44, normalized size = 1.57 \begin {gather*} \frac {1}{x^{6} + 3 x^{5} - 12 x^{4} - 36 x^{3} + 40 x^{2} + 108 x + \left (3 x^{5} - 36 x^{3} + 108 x\right ) e^{x}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-3*x**5-15*x**4+36*x**3+108*x**2-108*x-108)*exp(x)-6*x**5-15*x**4+48*x**3+108*x**2-80*x-108)/((9*x
**10-216*x**8+1944*x**6-7776*x**4+11664*x**2)*exp(x)**2+(6*x**11+18*x**10-144*x**9-432*x**8+1320*x**7+3888*x**
6-5472*x**5-15552*x**4+8640*x**3+23328*x**2)*exp(x)+x**12+6*x**11-15*x**10-144*x**9+8*x**8+1320*x**7+984*x**6-
5472*x**5-6176*x**4+8640*x**3+11664*x**2),x)

[Out]

1/(x**6 + 3*x**5 - 12*x**4 - 36*x**3 + 40*x**2 + 108*x + (3*x**5 - 36*x**3 + 108*x)*exp(x))

________________________________________________________________________________________