∫ −32805+ex(−164025x+164025x2)+e2x(−328050x2+656100x3−328050x4)+e3x(−328050x3+984150x4−984150x5+328050x6)+e4x(−164025x4+656100x5−984150x6+656100x7−164025x8−13x12−4x13)+e5x(−32805x5+164025x6−328050x7+328050x8−164025x9+32805x10−9x13+5x14)__________________________________________________________________________________________________________________________________________________________________________________________________________ −6561+ex(−32805x+32805x2)+e2x(−65610x2+131220x3−65610x4)+e3x(−65610x3+196830x4−196830x5+65610x6)+e4x(−32805x4+131220x5−196830x6+131220x7−32805x8)+e5x(−6561x5+32805x6−65610x7+65610x8−32805x9+6561x10) dx

3.31.90 \(\int \frac {-32805+e^x (-164025 x+164025 x^2)+e^{2 x} (-328050 x^2+656100 x^3-328050 x^4)+e^{3 x} (-328050 x^3+984150 x^4-984150 x^5+328050 x^6)+e^{4 x} (-164025 x^4+656100 x^5-984150 x^6+656100 x^7-164025 x^8-13 x^{12}-4 x^{13})+e^{5 x} (-32805 x^5+164025 x^6-328050 x^7+328050 x^8-164025 x^9+32805 x^{10}-9 x^{13}+5 x^{14})}{-6561+e^x (-32805 x+32805 x^2)+e^{2 x} (-65610 x^2+131220 x^3-65610 x^4)+e^{3 x} (-65610 x^3+196830 x^4-196830 x^5+65610 x^6)+e^{4 x} (-32805 x^4+131220 x^5-196830 x^6+131220 x^7-32805 x^8)+e^{5 x} (-6561 x^5+32805 x^6-65610 x^7+65610 x^8-32805 x^9+6561 x^{10})} \, dx\)

Optimal. Leaf size=27 \[ x \left (5+\frac {x^{12}}{6561 \left (-e^{-x}-x+x^2\right )^4}\right ) \]

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Rubi [F] time = 9.32, 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 {-32805+e^x \left (-164025 x+164025 x^2\right )+e^{2 x} \left (-328050 x^2+656100 x^3-328050 x^4\right )+e^{3 x} \left (-328050 x^3+984150 x^4-984150 x^5+328050 x^6\right )+e^{4 x} \left (-164025 x^4+656100 x^5-984150 x^6+656100 x^7-164025 x^8-13 x^{12}-4 x^{13}\right )+e^{5 x} \left (-32805 x^5+164025 x^6-328050 x^7+328050 x^8-164025 x^9+32805 x^{10}-9 x^{13}+5 x^{14}\right )}{-6561+e^x \left (-32805 x+32805 x^2\right )+e^{2 x} \left (-65610 x^2+131220 x^3-65610 x^4\right )+e^{3 x} \left (-65610 x^3+196830 x^4-196830 x^5+65610 x^6\right )+e^{4 x} \left (-32805 x^4+131220 x^5-196830 x^6+131220 x^7-32805 x^8\right )+e^{5 x} \left (-6561 x^5+32805 x^6-65610 x^7+65610 x^8-32805 x^9+6561 x^{10}\right )} \, dx \end {gather*}

Veriﬁcation is not applicable to the result.

[In]

Int[(-32805 + E^x*(-164025*x + 164025*x^2) + E^(2*x)*(-328050*x^2 + 656100*x^3 - 328050*x^4) + E^(3*x)*(-32805

0*x^3 + 984150*x^4 - 984150*x^5 + 328050*x^6) + E^(4*x)*(-164025*x^4 + 656100*x^5 - 984150*x^6 + 656100*x^7 -

164025*x^8 - 13*x^12 - 4*x^13) + E^(5*x)*(-32805*x^5 + 164025*x^6 - 328050*x^7 + 328050*x^8 - 164025*x^9 + 328

05*x^10 - 9*x^13 + 5*x^14))/(-6561 + E^x*(-32805*x + 32805*x^2) + E^(2*x)*(-65610*x^2 + 131220*x^3 - 65610*x^4

) + E^(3*x)*(-65610*x^3 + 196830*x^4 - 196830*x^5 + 65610*x^6) + E^(4*x)*(-32805*x^4 + 131220*x^5 - 196830*x^6

+ 131220*x^7 - 32805*x^8) + E^(5*x)*(-6561*x^5 + 32805*x^6 - 65610*x^7 + 65610*x^8 - 32805*x^9 + 6561*x^10)),

[Out]

1/(6561*(1 - x)^4) - 1/(729*(1 - x)^3) + 4/(729*(1 - x)^2) - 28/(2187*(1 - x)) + (32840*x)/6561 + (20*x^2)/656

1 + (10*x^3)/6561 + (4*x^4)/6561 + x^5/6561 - (644*Defer[Int][(-1 + E^x*(-1 + x)*x)^(-5), x])/6561 - (40*Defer

[Int][x/(-1 + E^x*(-1 + x)*x)^5, x])/729 - (20*Defer[Int][x^2/(-1 + E^x*(-1 + x)*x)^5, x])/729 - (76*Defer[Int

][x^3/(-1 + E^x*(-1 + x)*x)^5, x])/6561 - (8*Defer[Int][x^4/(-1 + E^x*(-1 + x)*x)^5, x])/2187 - (4*Defer[Int][

x^5/(-1 + E^x*(-1 + x)*x)^5, x])/6561 - (3724*Defer[Int][(-1 + E^x*(-1 + x)*x)^(-3), x])/6561 - (2000*Defer[In

t][x/(-1 + E^x*(-1 + x)*x)^3, x])/6561 - (320*Defer[Int][x^2/(-1 + E^x*(-1 + x)*x)^3, x])/2187 - (392*Defer[In

t][x^3/(-1 + E^x*(-1 + x)*x)^3, x])/6561 - (124*Defer[Int][x^4/(-1 + E^x*(-1 + x)*x)^3, x])/6561 - (8*Defer[In

t][x^5/(-1 + E^x*(-1 + x)*x)^3, x])/2187 - (56*Defer[Int][(-1 + E^x*(-1 + x)*x)^(-1), x])/729 - (200*Defer[Int

][x/(-1 + E^x*(-1 + x)*x), x])/6561 - (20*Defer[Int][x^2/(-1 + E^x*(-1 + x)*x), x])/2187 - (4*Defer[Int][x^3/(

-1 + E^x*(-1 + x)*x), x])/2187 - (4*Defer[Int][x^4/(-1 + E^x*(-1 + x)*x), x])/6561 - (4*Defer[Int][x^5/(-1 + E

^x*(-1 + x)*x), x])/6561 - (4*Defer[Int][1/((-1 + x)^5*(-1 - E^x*x + E^x*x^2)^5), x])/6561 - (44*Defer[Int][1/

((-1 + x)^4*(-1 - E^x*x + E^x*x^2)^5), x])/6561 - (212*Defer[Int][1/((-1 + x)^3*(-1 - E^x*x + E^x*x^2)^5), x])

/6561 - (592*Defer[Int][1/((-1 + x)^2*(-1 - E^x*x + E^x*x^2)^5), x])/6561 - (1064*Defer[Int][1/((-1 + x)*(-1 -

E^x*x + E^x*x^2)^5), x])/6561 - (847*Defer[Int][(-1 - E^x*x + E^x*x^2)^(-4), x])/2187 - (20*Defer[Int][1/((-1

+ x)^5*(-1 - E^x*x + E^x*x^2)^4), x])/6561 - (203*Defer[Int][1/((-1 + x)^4*(-1 - E^x*x + E^x*x^2)^4), x])/656

1 - (920*Defer[Int][1/((-1 + x)^3*(-1 - E^x*x + E^x*x^2)^4), x])/6561 - (2452*Defer[Int][1/((-1 + x)^2*(-1 - E

^x*x + E^x*x^2)^4), x])/6561 - (4256*Defer[Int][1/((-1 + x)*(-1 - E^x*x + E^x*x^2)^4), x])/6561 - (1400*Defer[

Int][x/(-1 - E^x*x + E^x*x^2)^4, x])/6561 - (230*Defer[Int][x^2/(-1 - E^x*x + E^x*x^2)^4, x])/2187 - (32*Defer

[Int][x^3/(-1 - E^x*x + E^x*x^2)^4, x])/729 - (91*Defer[Int][x^4/(-1 - E^x*x + E^x*x^2)^4, x])/6561 - (16*Defe

r[Int][x^5/(-1 - E^x*x + E^x*x^2)^4, x])/6561 - (40*Defer[Int][1/((-1 + x)^5*(-1 - E^x*x + E^x*x^2)^3), x])/65

61 - (124*Defer[Int][1/((-1 + x)^4*(-1 - E^x*x + E^x*x^2)^3), x])/2187 - (520*Defer[Int][1/((-1 + x)^3*(-1 - E

^x*x + E^x*x^2)^3), x])/2187 - (16*Defer[Int][1/((-1 + x)^2*(-1 - E^x*x + E^x*x^2)^3), x])/27 - (2128*Defer[In

t][1/((-1 + x)*(-1 - E^x*x + E^x*x^2)^3), x])/2187 - (2366*Defer[Int][(-1 - E^x*x + E^x*x^2)^(-2), x])/6561 -

(40*Defer[Int][1/((-1 + x)^5*(-1 - E^x*x + E^x*x^2)^2), x])/6561 - (338*Defer[Int][1/((-1 + x)^4*(-1 - E^x*x +

E^x*x^2)^2), x])/6561 - (1280*Defer[Int][1/((-1 + x)^3*(-1 - E^x*x + E^x*x^2)^2), x])/6561 - (2872*Defer[Int]

[1/((-1 + x)^2*(-1 - E^x*x + E^x*x^2)^2), x])/6561 - (4256*Defer[Int][1/((-1 + x)*(-1 - E^x*x + E^x*x^2)^2), x

])/6561 - (400*Defer[Int][x/(-1 - E^x*x + E^x*x^2)^2, x])/2187 - (20*Defer[Int][x^2/(-1 - E^x*x + E^x*x^2)^2,

x])/243 - (208*Defer[Int][x^3/(-1 - E^x*x + E^x*x^2)^2, x])/6561 - (22*Defer[Int][x^4/(-1 - E^x*x + E^x*x^2)^2

, x])/2187 - (16*Defer[Int][x^5/(-1 - E^x*x + E^x*x^2)^2, x])/6561 - (20*Defer[Int][1/((-1 + x)^5*(-1 - E^x*x

+ E^x*x^2)), x])/6561 - (152*Defer[Int][1/((-1 + x)^4*(-1 - E^x*x + E^x*x^2)), x])/6561 - (500*Defer[Int][1/((

-1 + x)^3*(-1 - E^x*x + E^x*x^2)), x])/6561 - (928*Defer[Int][1/((-1 + x)^2*(-1 - E^x*x + E^x*x^2)), x])/6561

- (1064*Defer[Int][1/((-1 + x)*(-1 - E^x*x + E^x*x^2)), x])/6561

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {32805-164025 e^x (-1+x) x+328050 e^{2 x} (-1+x)^2 x^2-328050 e^{3 x} (-1+x)^3 x^3+e^{4 x} x^4 \left (164025-656100 x+984150 x^2-656100 x^3+164025 x^4+13 x^8+4 x^9\right )-e^{5 x} x^5 \left (-32805+164025 x-328050 x^2+328050 x^3-164025 x^4+32805 x^5-9 x^8+5 x^9\right )}{6561 \left (1-e^x (-1+x) x\right )^5} \, dx\\ &=\frac {\int \frac {32805-164025 e^x (-1+x) x+328050 e^{2 x} (-1+x)^2 x^2-328050 e^{3 x} (-1+x)^3 x^3+e^{4 x} x^4 \left (164025-656100 x+984150 x^2-656100 x^3+164025 x^4+13 x^8+4 x^9\right )-e^{5 x} x^5 \left (-32805+164025 x-328050 x^2+328050 x^3-164025 x^4+32805 x^5-9 x^8+5 x^9\right )}{\left (1-e^x (-1+x) x\right )^5} \, dx}{6561}\\ &=\frac {\int \left (-\frac {4 x^8 \left (-1+x+x^2\right )}{(-1+x)^5 \left (-1-e^x x+e^x x^2\right )^5}-\frac {x^8 \left (-7+11 x+16 x^2\right )}{(-1+x)^5 \left (-1-e^x x+e^x x^2\right )^4}-\frac {4 x^8 \left (3+x+6 x^2\right )}{(-1+x)^5 \left (-1-e^x x+e^x x^2\right )^3}-\frac {2 x^8 \left (19-7 x+8 x^2\right )}{(-1+x)^5 \left (-1-e^x x+e^x x^2\right )^2}-\frac {4 x^8 \left (8-4 x+x^2\right )}{(-1+x)^5 \left (-1-e^x x+e^x x^2\right )}+\frac {-32805+164025 x-328050 x^2+328050 x^3-164025 x^4+32805 x^5-9 x^8+5 x^9}{(-1+x)^5}\right ) \, dx}{6561}\\ &=-\frac {\int \frac {x^8 \left (-7+11 x+16 x^2\right )}{(-1+x)^5 \left (-1-e^x x+e^x x^2\right )^4} \, dx}{6561}+\frac {\int \frac {-32805+164025 x-328050 x^2+328050 x^3-164025 x^4+32805 x^5-9 x^8+5 x^9}{(-1+x)^5} \, dx}{6561}-\frac {2 \int \frac {x^8 \left (19-7 x+8 x^2\right )}{(-1+x)^5 \left (-1-e^x x+e^x x^2\right )^2} \, dx}{6561}-\frac {4 \int \frac {x^8 \left (-1+x+x^2\right )}{(-1+x)^5 \left (-1-e^x x+e^x x^2\right )^5} \, dx}{6561}-\frac {4 \int \frac {x^8 \left (3+x+6 x^2\right )}{(-1+x)^5 \left (-1-e^x x+e^x x^2\right )^3} \, dx}{6561}-\frac {4 \int \frac {x^8 \left (8-4 x+x^2\right )}{(-1+x)^5 \left (-1-e^x x+e^x x^2\right )} \, dx}{6561}\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [B] time = 0.23, size = 109, normalized size = 4.04 \begin {gather*} \frac {32840 x+20 x^2+10 x^3+4 x^4+x^5+\frac {-56+189 x-216 x^2+84 x^3}{(-1+x)^4}+\frac {x^9 \left (-1+4 e^x (-1+x) x-6 e^{2 x} (-1+x)^2 x^2+4 e^{3 x} (-1+x)^3 x^3\right )}{(-1+x)^4 \left (-1+e^x (-1+x) x\right )^4}}{6561} \end {gather*}

Antiderivative was successfully veriﬁed.

[In]

Integrate[(-32805 + E^x*(-164025*x + 164025*x^2) + E^(2*x)*(-328050*x^2 + 656100*x^3 - 328050*x^4) + E^(3*x)*(

-328050*x^3 + 984150*x^4 - 984150*x^5 + 328050*x^6) + E^(4*x)*(-164025*x^4 + 656100*x^5 - 984150*x^6 + 656100*

x^7 - 164025*x^8 - 13*x^12 - 4*x^13) + E^(5*x)*(-32805*x^5 + 164025*x^6 - 328050*x^7 + 328050*x^8 - 164025*x^9

+ 32805*x^10 - 9*x^13 + 5*x^14))/(-6561 + E^x*(-32805*x + 32805*x^2) + E^(2*x)*(-65610*x^2 + 131220*x^3 - 656

10*x^4) + E^(3*x)*(-65610*x^3 + 196830*x^4 - 196830*x^5 + 65610*x^6) + E^(4*x)*(-32805*x^4 + 131220*x^5 - 1968

30*x^6 + 131220*x^7 - 32805*x^8) + E^(5*x)*(-6561*x^5 + 32805*x^6 - 65610*x^7 + 65610*x^8 - 32805*x^9 + 6561*x

^10)),x]

[Out]

(32840*x + 20*x^2 + 10*x^3 + 4*x^4 + x^5 + (-56 + 189*x - 216*x^2 + 84*x^3)/(-1 + x)^4 + (x^9*(-1 + 4*E^x*(-1

+ x)*x - 6*E^(2*x)*(-1 + x)^2*x^2 + 4*E^(3*x)*(-1 + x)^3*x^3))/((-1 + x)^4*(-1 + E^x*(-1 + x)*x)^4))/6561

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fricas [B] time = 0.59, size = 208, normalized size = 7.70 \begin {gather*} \frac {{\left (x^{13} + 32805 \, x^{9} - 131276 \, x^{8} + 197054 \, x^{7} - 131556 \, x^{6} + 33029 \, x^{5} - 56 \, x^{4}\right )} e^{\left (4 \, x\right )} - 4 \, {\left (32805 \, x^{7} - 98471 \, x^{6} + 98583 \, x^{5} - 32973 \, x^{4} + 56 \, x^{3}\right )} e^{\left (3 \, x\right )} + 6 \, {\left (32805 \, x^{5} - 65666 \, x^{4} + 32917 \, x^{3} - 56 \, x^{2}\right )} e^{\left (2 \, x\right )} - 4 \, {\left (32805 \, x^{3} - 32861 \, x^{2} + 56 \, x\right )} e^{x} + 32805 \, x - 56}{6561 \, {\left ({\left (x^{8} - 4 \, x^{7} + 6 \, x^{6} - 4 \, x^{5} + x^{4}\right )} e^{\left (4 \, x\right )} - 4 \, {\left (x^{6} - 3 \, x^{5} + 3 \, x^{4} - x^{3}\right )} e^{\left (3 \, x\right )} + 6 \, {\left (x^{4} - 2 \, x^{3} + x^{2}\right )} e^{\left (2 \, x\right )} - 4 \, {\left (x^{2} - x\right )} e^{x} + 1\right )}} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((5*x^14-9*x^13+32805*x^10-164025*x^9+328050*x^8-328050*x^7+164025*x^6-32805*x^5)*exp(x)^5+(-4*x^13-

13*x^12-164025*x^8+656100*x^7-984150*x^6+656100*x^5-164025*x^4)*exp(x)^4+(328050*x^6-984150*x^5+984150*x^4-328

050*x^3)*exp(x)^3+(-328050*x^4+656100*x^3-328050*x^2)*exp(x)^2+(164025*x^2-164025*x)*exp(x)-32805)/((6561*x^10

-32805*x^9+65610*x^8-65610*x^7+32805*x^6-6561*x^5)*exp(x)^5+(-32805*x^8+131220*x^7-196830*x^6+131220*x^5-32805

*x^4)*exp(x)^4+(65610*x^6-196830*x^5+196830*x^4-65610*x^3)*exp(x)^3+(-65610*x^4+131220*x^3-65610*x^2)*exp(x)^2

+(32805*x^2-32805*x)*exp(x)-6561),x, algorithm="fricas")

[Out]

1/6561*((x^13 + 32805*x^9 - 131276*x^8 + 197054*x^7 - 131556*x^6 + 33029*x^5 - 56*x^4)*e^(4*x) - 4*(32805*x^7

- 98471*x^6 + 98583*x^5 - 32973*x^4 + 56*x^3)*e^(3*x) + 6*(32805*x^5 - 65666*x^4 + 32917*x^3 - 56*x^2)*e^(2*x)

- 4*(32805*x^3 - 32861*x^2 + 56*x)*e^x + 32805*x - 56)/((x^8 - 4*x^7 + 6*x^6 - 4*x^5 + x^4)*e^(4*x) - 4*(x^6

- 3*x^5 + 3*x^4 - x^3)*e^(3*x) + 6*(x^4 - 2*x^3 + x^2)*e^(2*x) - 4*(x^2 - x)*e^x + 1)

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giac [B] time = 5.07, size = 291, normalized size = 10.78 \begin {gather*} \frac {x^{13} e^{\left (4 \, x\right )} + 32805 \, x^{9} e^{\left (4 \, x\right )} - 131276 \, x^{8} e^{\left (4 \, x\right )} + 197054 \, x^{7} e^{\left (4 \, x\right )} - 131220 \, x^{7} e^{\left (3 \, x\right )} - 131556 \, x^{6} e^{\left (4 \, x\right )} + 393884 \, x^{6} e^{\left (3 \, x\right )} + 33029 \, x^{5} e^{\left (4 \, x\right )} - 394332 \, x^{5} e^{\left (3 \, x\right )} + 196830 \, x^{5} e^{\left (2 \, x\right )} - 56 \, x^{4} e^{\left (4 \, x\right )} + 131892 \, x^{4} e^{\left (3 \, x\right )} - 393996 \, x^{4} e^{\left (2 \, x\right )} - 224 \, x^{3} e^{\left (3 \, x\right )} + 197502 \, x^{3} e^{\left (2 \, x\right )} - 131220 \, x^{3} e^{x} - 336 \, x^{2} e^{\left (2 \, x\right )} + 131444 \, x^{2} e^{x} - 224 \, x e^{x} + 32805 \, x - 56}{6561 \, {\left (x^{8} e^{\left (4 \, x\right )} - 4 \, x^{7} e^{\left (4 \, x\right )} + 6 \, x^{6} e^{\left (4 \, x\right )} - 4 \, x^{6} e^{\left (3 \, x\right )} - 4 \, x^{5} e^{\left (4 \, x\right )} + 12 \, x^{5} e^{\left (3 \, x\right )} + x^{4} e^{\left (4 \, x\right )} - 12 \, x^{4} e^{\left (3 \, x\right )} + 6 \, x^{4} e^{\left (2 \, x\right )} + 4 \, x^{3} e^{\left (3 \, x\right )} - 12 \, x^{3} e^{\left (2 \, x\right )} + 6 \, x^{2} e^{\left (2 \, x\right )} - 4 \, x^{2} e^{x} + 4 \, x e^{x} + 1\right )}} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((5*x^14-9*x^13+32805*x^10-164025*x^9+328050*x^8-328050*x^7+164025*x^6-32805*x^5)*exp(x)^5+(-4*x^13-

13*x^12-164025*x^8+656100*x^7-984150*x^6+656100*x^5-164025*x^4)*exp(x)^4+(328050*x^6-984150*x^5+984150*x^4-328

050*x^3)*exp(x)^3+(-328050*x^4+656100*x^3-328050*x^2)*exp(x)^2+(164025*x^2-164025*x)*exp(x)-32805)/((6561*x^10

-32805*x^9+65610*x^8-65610*x^7+32805*x^6-6561*x^5)*exp(x)^5+(-32805*x^8+131220*x^7-196830*x^6+131220*x^5-32805

*x^4)*exp(x)^4+(65610*x^6-196830*x^5+196830*x^4-65610*x^3)*exp(x)^3+(-65610*x^4+131220*x^3-65610*x^2)*exp(x)^2

+(32805*x^2-32805*x)*exp(x)-6561),x, algorithm="giac")

[Out]

1/6561*(x^13*e^(4*x) + 32805*x^9*e^(4*x) - 131276*x^8*e^(4*x) + 197054*x^7*e^(4*x) - 131220*x^7*e^(3*x) - 1315

56*x^6*e^(4*x) + 393884*x^6*e^(3*x) + 33029*x^5*e^(4*x) - 394332*x^5*e^(3*x) + 196830*x^5*e^(2*x) - 56*x^4*e^(

4*x) + 131892*x^4*e^(3*x) - 393996*x^4*e^(2*x) - 224*x^3*e^(3*x) + 197502*x^3*e^(2*x) - 131220*x^3*e^x - 336*x

^2*e^(2*x) + 131444*x^2*e^x - 224*x*e^x + 32805*x - 56)/(x^8*e^(4*x) - 4*x^7*e^(4*x) + 6*x^6*e^(4*x) - 4*x^6*e

^(3*x) - 4*x^5*e^(4*x) + 12*x^5*e^(3*x) + x^4*e^(4*x) - 12*x^4*e^(3*x) + 6*x^4*e^(2*x) + 4*x^3*e^(3*x) - 12*x^

3*e^(2*x) + 6*x^2*e^(2*x) - 4*x^2*e^x + 4*x*e^x + 1)

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maple [B] time = 0.09, size = 178, normalized size = 6.59


method	result	size

risch	\(\frac {x^{5}}{6561}+\frac {4 x^{4}}{6561}+\frac {10 x^{3}}{6561}+\frac {20 x^{2}}{6561}+\frac {32840 x}{6561}+\frac {\frac {28}{2187} x^{3}-\frac {8}{243} x^{2}+\frac {7}{243} x -\frac {56}{6561}}{x^{4}-4 x^{3}+6 x^{2}-4 x +1}+\frac {x^{9} \left (4 x^{6} {\mathrm e}^{3 x}-12 x^{5} {\mathrm e}^{3 x}+12 x^{4} {\mathrm e}^{3 x}-6 \,{\mathrm e}^{2 x} x^{4}-4 x^{3} {\mathrm e}^{3 x}+12 \,{\mathrm e}^{2 x} x^{3}-6 \,{\mathrm e}^{2 x} x^{2}+4 \,{\mathrm e}^{x} x^{2}-4 \,{\mathrm e}^{x} x -1\right )}{6561 \left (x^{3}-3 x^{2}+3 x -1\right ) \left (x -1\right ) \left ({\mathrm e}^{x} x^{2}-{\mathrm e}^{x} x -1\right )^{4}}\)	\(178\)

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int(((5*x^14-9*x^13+32805*x^10-164025*x^9+328050*x^8-328050*x^7+164025*x^6-32805*x^5)*exp(x)^5+(-4*x^13-13*x^1

2-164025*x^8+656100*x^7-984150*x^6+656100*x^5-164025*x^4)*exp(x)^4+(328050*x^6-984150*x^5+984150*x^4-328050*x^

3)*exp(x)^3+(-328050*x^4+656100*x^3-328050*x^2)*exp(x)^2+(164025*x^2-164025*x)*exp(x)-32805)/((6561*x^10-32805

*x^9+65610*x^8-65610*x^7+32805*x^6-6561*x^5)*exp(x)^5+(-32805*x^8+131220*x^7-196830*x^6+131220*x^5-32805*x^4)*

exp(x)^4+(65610*x^6-196830*x^5+196830*x^4-65610*x^3)*exp(x)^3+(-65610*x^4+131220*x^3-65610*x^2)*exp(x)^2+(3280

5*x^2-32805*x)*exp(x)-6561),x,method=_RETURNVERBOSE)

[Out]

1/6561*x^5+4/6561*x^4+10/6561*x^3+20/6561*x^2+32840/6561*x+(28/2187*x^3-8/243*x^2+7/243*x-56/6561)/(x^4-4*x^3+

6*x^2-4*x+1)+1/6561*x^9*(4*x^6*exp(3*x)-12*x^5*exp(3*x)+12*x^4*exp(3*x)-6*exp(2*x)*x^4-4*x^3*exp(3*x)+12*exp(2

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

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maxima [B] time = 0.94, size = 208, normalized size = 7.70 \begin {gather*} \frac {{\left (x^{13} + 32805 \, x^{9} - 131276 \, x^{8} + 197054 \, x^{7} - 131556 \, x^{6} + 33029 \, x^{5} - 56 \, x^{4}\right )} e^{\left (4 \, x\right )} - 4 \, {\left (32805 \, x^{7} - 98471 \, x^{6} + 98583 \, x^{5} - 32973 \, x^{4} + 56 \, x^{3}\right )} e^{\left (3 \, x\right )} + 6 \, {\left (32805 \, x^{5} - 65666 \, x^{4} + 32917 \, x^{3} - 56 \, x^{2}\right )} e^{\left (2 \, x\right )} - 4 \, {\left (32805 \, x^{3} - 32861 \, x^{2} + 56 \, x\right )} e^{x} + 32805 \, x - 56}{6561 \, {\left ({\left (x^{8} - 4 \, x^{7} + 6 \, x^{6} - 4 \, x^{5} + x^{4}\right )} e^{\left (4 \, x\right )} - 4 \, {\left (x^{6} - 3 \, x^{5} + 3 \, x^{4} - x^{3}\right )} e^{\left (3 \, x\right )} + 6 \, {\left (x^{4} - 2 \, x^{3} + x^{2}\right )} e^{\left (2 \, x\right )} - 4 \, {\left (x^{2} - x\right )} e^{x} + 1\right )}} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((5*x^14-9*x^13+32805*x^10-164025*x^9+328050*x^8-328050*x^7+164025*x^6-32805*x^5)*exp(x)^5+(-4*x^13-

13*x^12-164025*x^8+656100*x^7-984150*x^6+656100*x^5-164025*x^4)*exp(x)^4+(328050*x^6-984150*x^5+984150*x^4-328

050*x^3)*exp(x)^3+(-328050*x^4+656100*x^3-328050*x^2)*exp(x)^2+(164025*x^2-164025*x)*exp(x)-32805)/((6561*x^10

-32805*x^9+65610*x^8-65610*x^7+32805*x^6-6561*x^5)*exp(x)^5+(-32805*x^8+131220*x^7-196830*x^6+131220*x^5-32805

*x^4)*exp(x)^4+(65610*x^6-196830*x^5+196830*x^4-65610*x^3)*exp(x)^3+(-65610*x^4+131220*x^3-65610*x^2)*exp(x)^2

+(32805*x^2-32805*x)*exp(x)-6561),x, algorithm="maxima")

[Out]

1/6561*((x^13 + 32805*x^9 - 131276*x^8 + 197054*x^7 - 131556*x^6 + 33029*x^5 - 56*x^4)*e^(4*x) - 4*(32805*x^7

- 98471*x^6 + 98583*x^5 - 32973*x^4 + 56*x^3)*e^(3*x) + 6*(32805*x^5 - 65666*x^4 + 32917*x^3 - 56*x^2)*e^(2*x)

- 4*(32805*x^3 - 32861*x^2 + 56*x)*e^x + 32805*x - 56)/((x^8 - 4*x^7 + 6*x^6 - 4*x^5 + x^4)*e^(4*x) - 4*(x^6

- 3*x^5 + 3*x^4 - x^3)*e^(3*x) + 6*(x^4 - 2*x^3 + x^2)*e^(2*x) - 4*(x^2 - x)*e^x + 1)

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mupad [F] time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int \frac {{\mathrm {e}}^{4\,x}\,\left (4\,x^{13}+13\,x^{12}+164025\,x^8-656100\,x^7+984150\,x^6-656100\,x^5+164025\,x^4\right )+{\mathrm {e}}^{2\,x}\,\left (328050\,x^4-656100\,x^3+328050\,x^2\right )+{\mathrm {e}}^x\,\left (164025\,x-164025\,x^2\right )+{\mathrm {e}}^{5\,x}\,\left (-5\,x^{14}+9\,x^{13}-32805\,x^{10}+164025\,x^9-328050\,x^8+328050\,x^7-164025\,x^6+32805\,x^5\right )+{\mathrm {e}}^{3\,x}\,\left (-328050\,x^6+984150\,x^5-984150\,x^4+328050\,x^3\right )+32805}{{\mathrm {e}}^{4\,x}\,\left (32805\,x^8-131220\,x^7+196830\,x^6-131220\,x^5+32805\,x^4\right )+{\mathrm {e}}^{5\,x}\,\left (-6561\,x^{10}+32805\,x^9-65610\,x^8+65610\,x^7-32805\,x^6+6561\,x^5\right )+{\mathrm {e}}^{2\,x}\,\left (65610\,x^4-131220\,x^3+65610\,x^2\right )+{\mathrm {e}}^x\,\left (32805\,x-32805\,x^2\right )+{\mathrm {e}}^{3\,x}\,\left (-65610\,x^6+196830\,x^5-196830\,x^4+65610\,x^3\right )+6561} \,d x \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int((exp(4*x)*(164025*x^4 - 656100*x^5 + 984150*x^6 - 656100*x^7 + 164025*x^8 + 13*x^12 + 4*x^13) + exp(2*x)*(

328050*x^2 - 656100*x^3 + 328050*x^4) + exp(x)*(164025*x - 164025*x^2) + exp(5*x)*(32805*x^5 - 164025*x^6 + 32

8050*x^7 - 328050*x^8 + 164025*x^9 - 32805*x^10 + 9*x^13 - 5*x^14) + exp(3*x)*(328050*x^3 - 984150*x^4 + 98415

0*x^5 - 328050*x^6) + 32805)/(exp(4*x)*(32805*x^4 - 131220*x^5 + 196830*x^6 - 131220*x^7 + 32805*x^8) + exp(5*

x)*(6561*x^5 - 32805*x^6 + 65610*x^7 - 65610*x^8 + 32805*x^9 - 6561*x^10) + exp(2*x)*(65610*x^2 - 131220*x^3 +

65610*x^4) + exp(x)*(32805*x - 32805*x^2) + exp(3*x)*(65610*x^3 - 196830*x^4 + 196830*x^5 - 65610*x^6) + 6561

),x)

[Out]

int((exp(4*x)*(164025*x^4 - 656100*x^5 + 984150*x^6 - 656100*x^7 + 164025*x^8 + 13*x^12 + 4*x^13) + exp(2*x)*(

328050*x^2 - 656100*x^3 + 328050*x^4) + exp(x)*(164025*x - 164025*x^2) + exp(5*x)*(32805*x^5 - 164025*x^6 + 32

8050*x^7 - 328050*x^8 + 164025*x^9 - 32805*x^10 + 9*x^13 - 5*x^14) + exp(3*x)*(328050*x^3 - 984150*x^4 + 98415

0*x^5 - 328050*x^6) + 32805)/(exp(4*x)*(32805*x^4 - 131220*x^5 + 196830*x^6 - 131220*x^7 + 32805*x^8) + exp(5*

x)*(6561*x^5 - 32805*x^6 + 65610*x^7 - 65610*x^8 + 32805*x^9 - 6561*x^10) + exp(2*x)*(65610*x^2 - 131220*x^3 +

65610*x^4) + exp(x)*(32805*x - 32805*x^2) + exp(3*x)*(65610*x^3 - 196830*x^4 + 196830*x^5 - 65610*x^6) + 6561

), x)

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sympy [B] time = 1.02, size = 318, normalized size = 11.78 \begin {gather*} \frac {x^{5}}{6561} + \frac {4 x^{4}}{6561} + \frac {10 x^{3}}{6561} + \frac {20 x^{2}}{6561} + \frac {32840 x}{6561} + \frac {84 x^{3} - 216 x^{2} + 189 x - 56}{6561 x^{4} - 26244 x^{3} + 39366 x^{2} - 26244 x + 6561} + \frac {- x^{9} + \left (4 x^{11} - 4 x^{10}\right ) e^{x} + \left (- 6 x^{13} + 12 x^{12} - 6 x^{11}\right ) e^{2 x} + \left (4 x^{15} - 12 x^{14} + 12 x^{13} - 4 x^{12}\right ) e^{3 x}}{6561 x^{4} - 26244 x^{3} + 39366 x^{2} - 26244 x + \left (- 26244 x^{6} + 131220 x^{5} - 262440 x^{4} + 262440 x^{3} - 131220 x^{2} + 26244 x\right ) e^{x} + \left (39366 x^{8} - 236196 x^{7} + 590490 x^{6} - 787320 x^{5} + 590490 x^{4} - 236196 x^{3} + 39366 x^{2}\right ) e^{2 x} + \left (- 26244 x^{10} + 183708 x^{9} - 551124 x^{8} + 918540 x^{7} - 918540 x^{6} + 551124 x^{5} - 183708 x^{4} + 26244 x^{3}\right ) e^{3 x} + \left (6561 x^{12} - 52488 x^{11} + 183708 x^{10} - 367416 x^{9} + 459270 x^{8} - 367416 x^{7} + 183708 x^{6} - 52488 x^{5} + 6561 x^{4}\right ) e^{4 x} + 6561} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((5*x**14-9*x**13+32805*x**10-164025*x**9+328050*x**8-328050*x**7+164025*x**6-32805*x**5)*exp(x)**5+

(-4*x**13-13*x**12-164025*x**8+656100*x**7-984150*x**6+656100*x**5-164025*x**4)*exp(x)**4+(328050*x**6-984150*

x**5+984150*x**4-328050*x**3)*exp(x)**3+(-328050*x**4+656100*x**3-328050*x**2)*exp(x)**2+(164025*x**2-164025*x

)*exp(x)-32805)/((6561*x**10-32805*x**9+65610*x**8-65610*x**7+32805*x**6-6561*x**5)*exp(x)**5+(-32805*x**8+131

220*x**7-196830*x**6+131220*x**5-32805*x**4)*exp(x)**4+(65610*x**6-196830*x**5+196830*x**4-65610*x**3)*exp(x)*

*3+(-65610*x**4+131220*x**3-65610*x**2)*exp(x)**2+(32805*x**2-32805*x)*exp(x)-6561),x)

[Out]

x**5/6561 + 4*x**4/6561 + 10*x**3/6561 + 20*x**2/6561 + 32840*x/6561 + (84*x**3 - 216*x**2 + 189*x - 56)/(6561

*x**4 - 26244*x**3 + 39366*x**2 - 26244*x + 6561) + (-x**9 + (4*x**11 - 4*x**10)*exp(x) + (-6*x**13 + 12*x**12

- 6*x**11)*exp(2*x) + (4*x**15 - 12*x**14 + 12*x**13 - 4*x**12)*exp(3*x))/(6561*x**4 - 26244*x**3 + 39366*x**

2 - 26244*x + (-26244*x**6 + 131220*x**5 - 262440*x**4 + 262440*x**3 - 131220*x**2 + 26244*x)*exp(x) + (39366*

x**8 - 236196*x**7 + 590490*x**6 - 787320*x**5 + 590490*x**4 - 236196*x**3 + 39366*x**2)*exp(2*x) + (-26244*x*

*10 + 183708*x**9 - 551124*x**8 + 918540*x**7 - 918540*x**6 + 551124*x**5 - 183708*x**4 + 26244*x**3)*exp(3*x)

+ (6561*x**12 - 52488*x**11 + 183708*x**10 - 367416*x**9 + 459270*x**8 - 367416*x**7 + 183708*x**6 - 52488*x*

*5 + 6561*x**4)*exp(4*x) + 6561)

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