∫ ex(18−18x+27x2−3x3+e5(−75x+15x2))___________________________________________________________ −7776x2−6480x4−2160x6+3125e25x7−360x8−30x10−x12+e20(−18750x6−3125x8)+e15(45000x5+15000x7+1250x9)+e10(−54000x4−27000x6−4500x8−250x10)+e5(32400x3+21600x5+5400x7+600x9+25x11) dx [10124]

3.102.24 $\int \frac {e^x (18-18 x+27 x^2-3 x^3+e^5 (-75 x+15 x^2))}{-7776 x^2-6480 x^4-2160 x^6+3125 e^{25} x^7-360 x^8-30 x^{10}-x^{12}+e^{20} (-18750 x^6-3125 x^8)+e^{15} (45000 x^5+15000 x^7+1250 x^9)+e^{10} (-54000 x^4-27000 x^6-4500 x^8-250 x^{10})+e^5 (32400 x^3+21600 x^5+5400 x^7+600 x^9+25 x^{11})} \, dx$ [10124]

Optimal. Leaf size=21 \[ \frac {3 e^x}{x \left (6-5 e^5 x+x^2\right )^4} \]

[Out]

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

________________________________________________________________________________________

Rubi [C] Result contains higher order function than in optimal. Order 4 vs. order 3 in optimal.
time = 14.24, antiderivative size = 8979, normalized size of antiderivative = 427.57, number of steps used = 171, number of rules used = 6, integrand size = 163, $\frac {\text {number of rules}}{\text {integrand size}}$ = 0.037, Rules used = {6820, 12, 6874, 2208, 2209, 2302} \begin {gather*} \text {Too large to display} \end {gather*}

Antiderivative was successfully veriﬁed.

[In]

Int[(E^x*(18 - 18*x + 27*x^2 - 3*x^3 + E^5*(-75*x + 15*x^2)))/(-7776*x^2 - 6480*x^4 - 2160*x^6 + 3125*E^25*x^7

- 360*x^8 - 30*x^10 - x^12 + E^20*(-18750*x^6 - 3125*x^8) + E^15*(45000*x^5 + 15000*x^7 + 1250*x^9) + E^10*(-

54000*x^4 - 27000*x^6 - 4500*x^8 - 250*x^10) + E^5*(32400*x^3 + 21600*x^5 + 5400*x^7 + 600*x^9 + 25*x^11)),x]

[Out]

(-8*E^x*(12 - 25*E^10))/((-24 + 25*E^10)^(5/2)*(5*E^5 - Sqrt[-24 + 25*E^10] - 2*x)^4) - (20*E^(5 + x)*(5*E^5 -

Sqrt[-24 + 25*E^10]))/((-24 + 25*E^10)^(5/2)*(5*E^5 - Sqrt[-24 + 25*E^10] - 2*x)^4) - (80*E^x*(12 - 25*E^10))

/(3*(24 - 25*E^10)^3*(5*E^5 - Sqrt[-24 + 25*E^10] - 2*x)^3) + (4*E^x*(12 - 25*E^10))/(3*(-24 + 25*E^10)^(5/2)*

(5*E^5 - Sqrt[-24 + 25*E^10] - 2*x)^3) + (2*E^x*(2 + 10*E^5 + 25*E^10))/(3*(24 - 25*E^10)^2*(5*E^5 - Sqrt[-24

+ 25*E^10] - 2*x)^3) - (40*E^(5 + x)*(25*E^5 - 3*Sqrt[-24 + 25*E^10]))/(3*(24 - 25*E^10)^3*(5*E^5 - Sqrt[-24 +

25*E^10] - 2*x)^3) - (E^x*(2 + 5*E^5)*(5*E^5 - Sqrt[-24 + 25*E^10]))/(3*(24 - 25*E^10)^2*(5*E^5 - Sqrt[-24 +

25*E^10] - 2*x)^3) + (10*E^(5 + x)*(5*E^5 - Sqrt[-24 + 25*E^10]))/(3*(-24 + 25*E^10)^(5/2)*(5*E^5 - Sqrt[-24 +

25*E^10] - 2*x)^3) + (20*E^x*(12 - 25*E^10))/(3*(24 - 25*E^10)^3*(5*E^5 - Sqrt[-24 + 25*E^10] - 2*x)^2) - (60

*E^x*(12 - 25*E^10))/((-24 + 25*E^10)^(7/2)*(5*E^5 - Sqrt[-24 + 25*E^10] - 2*x)^2) - (E^x*(12 - 25*E^10))/(3*(

-24 + 25*E^10)^(5/2)*(5*E^5 - Sqrt[-24 + 25*E^10] - 2*x)^2) - (E^x*(2 + 10*E^5 + 25*E^10))/(6*(24 - 25*E^10)^2

*(5*E^5 - Sqrt[-24 + 25*E^10] - 2*x)^2) - (2*E^x*(2 + 10*E^5 + 25*E^10))/((-24 + 25*E^10)^(5/2)*(5*E^5 - Sqrt[

-24 + 25*E^10] - 2*x)^2) + (E^x*(3 + 15*E^5 + 25*E^10))/(18*(-24 + 25*E^10)^(3/2)*(5*E^5 - Sqrt[-24 + 25*E^10]

- 2*x)^2) + (10*E^(5 + x)*(25*E^5 - 3*Sqrt[-24 + 25*E^10]))/(3*(24 - 25*E^10)^3*(5*E^5 - Sqrt[-24 + 25*E^10]

- 2*x)^2) + (E^x*(2 + 5*E^5)*(5*E^5 - Sqrt[-24 + 25*E^10]))/(12*(24 - 25*E^10)^2*(5*E^5 - Sqrt[-24 + 25*E^10]

- 2*x)^2) - (5*E^(5 + x)*(5*E^5 - Sqrt[-24 + 25*E^10]))/(6*(-24 + 25*E^10)^(5/2)*(5*E^5 - Sqrt[-24 + 25*E^10]

- 2*x)^2) - (E^x*(3 + 5*E^5)*(5*E^5 - Sqrt[-24 + 25*E^10]))/(36*(-24 + 25*E^10)^(3/2)*(5*E^5 - Sqrt[-24 + 25*E

^10] - 2*x)^2) + (E^x*(2 + 5*E^5)*(10*E^5 - Sqrt[-24 + 25*E^10]))/(2*(-24 + 25*E^10)^(5/2)*(5*E^5 - Sqrt[-24 +

25*E^10] - 2*x)^2) - (50*E^(5 + x)*(15*E^5 - Sqrt[-24 + 25*E^10]))/((-24 + 25*E^10)^(7/2)*(5*E^5 - Sqrt[-24 +

25*E^10] - 2*x)^2) + (140*E^x*(12 - 25*E^10))/((24 - 25*E^10)^4*(5*E^5 - Sqrt[-24 + 25*E^10] - 2*x)) - (10*E^

x*(12 - 25*E^10))/(3*(24 - 25*E^10)^3*(5*E^5 - Sqrt[-24 + 25*E^10] - 2*x)) + (30*E^x*(12 - 25*E^10))/((-24 + 2

5*E^10)^(7/2)*(5*E^5 - Sqrt[-24 + 25*E^10] - 2*x)) + (E^x*(12 - 25*E^10))/(6*(-24 + 25*E^10)^(5/2)*(5*E^5 - Sq

rt[-24 + 25*E^10] - 2*x)) - (5*E^x*(2 + 10*E^5 + 25*E^10))/((24 - 25*E^10)^3*(5*E^5 - Sqrt[-24 + 25*E^10] - 2*

x)) + (E^x*(2 + 10*E^5 + 25*E^10))/(12*(24 - 25*E^10)^2*(5*E^5 - Sqrt[-24 + 25*E^10] - 2*x)) + (E^x*(2 + 10*E^

5 + 25*E^10))/((-24 + 25*E^10)^(5/2)*(5*E^5 - Sqrt[-24 + 25*E^10] - 2*x)) - (E^x*(3 + 15*E^5 + 25*E^10))/(6*(2

4 - 25*E^10)^2*(5*E^5 - Sqrt[-24 + 25*E^10] - 2*x)) - (E^x*(3 + 15*E^5 + 25*E^10))/(36*(-24 + 25*E^10)^(3/2)*(

5*E^5 - Sqrt[-24 + 25*E^10] - 2*x)) - (E^x*(6 + 30*E^5 + 25*E^10))/(216*(24 - 25*E^10)*(5*E^5 - Sqrt[-24 + 25*

E^10] - 2*x)) - (5*E^(5 + x)*(25*E^5 - 3*Sqrt[-24 + 25*E^10]))/(3*(24 - 25*E^10)^3*(5*E^5 - Sqrt[-24 + 25*E^10

] - 2*x)) - (E^x*(2 + 5*E^5)*(5*E^5 - Sqrt[-24 + 25*E^10]))/(24*(24 - 25*E^10)^2*(5*E^5 - Sqrt[-24 + 25*E^10]

- 2*x)) + (E^x*(6 + 5*E^5)*(5*E^5 - Sqrt[-24 + 25*E^10]))/(432*(24 - 25*E^10)*(5*E^5 - Sqrt[-24 + 25*E^10] - 2

*x)) + (5*E^(5 + x)*(5*E^5 - Sqrt[-24 + 25*E^10]))/(12*(-24 + 25*E^10)^(5/2)*(5*E^5 - Sqrt[-24 + 25*E^10] - 2*

x)) + (E^x*(3 + 5*E^5)*(5*E^5 - Sqrt[-24 + 25*E^10]))/(72*(-24 + 25*E^10)^(3/2)*(5*E^5 - Sqrt[-24 + 25*E^10] -

2*x)) - (E^x*(2 + 5*E^5)*(10*E^5 - Sqrt[-24 + 25*E^10]))/(4*(-24 + 25*E^10)^(5/2)*(5*E^5 - Sqrt[-24 + 25*E^10

] - 2*x)) + (E^x*(3 + 5*E^5)*(15*E^5 - Sqrt[-24 + 25*E^10]))/(36*(24 - 25*E^10)^2*(5*E^5 - Sqrt[-24 + 25*E^10]

- 2*x)) + (25*E^(5 + x)*(15*E^5 - Sqrt[-24 + 25*E^10]))/((-24 + 25*E^10)^(7/2)*(5*E^5 - Sqrt[-24 + 25*E^10] -

2*x)) + (E^x*(2 + 5*E^5)*(25*E^5 - Sqrt[-24 + 25*E^10]))/(2*(24 - 25*E^10)^3*(5*E^5 - Sqrt[-24 + 25*E^10] - 2

*x)) + (50*E^(5 + x)*(35*E^5 - Sqrt[-24 + 25*E^10]))/((24 - 25*E^10)^4*(5*E^5 - Sqrt[-24 + 25*E^10] - 2*x)) +

(8*E^x*(12 - 25*E^10))/((-24 + 25*E^10)^(5/2)*(5*E^5 + Sqrt[-24 + 25*E^10] - 2*x)^4) + (20*E^(5 + x)*(5*E^5 +

Sqrt[-24 + 25*E^10]))/((-24 + 25*E^10)^(5/2)*(5*E^5 + Sqrt[-24 + 25*E^10] - 2*x)^4) - (80*E^x*(12 - 25*E^10))/

(3*(24 - 25*E^10)^3*(5*E^5 + Sqrt[-24 + 25*E^10] - 2*x)^3) - (4*E^x*(12 - 25*E^10))/(3*(-24 + 25*E^10)^(5/2)*(

5*E^5 + Sqrt[-24 + 25*E^10] - 2*x)^3) + (2*E^x*(2 + 10*E^5 + 25*E^10))/(3*(24 - 25*E^10)^2*(5*E^5 + Sqrt[-24 +

25*E^10] - 2*x)^3) - (E^x*(2 + 5*E^5)*(5*E^5 + Sqrt[-24 + 25*E^10]))/(3*(24 - 25*E^10)^2*(5*E^5 + Sqrt[-24 +

25*E^10] - 2*x)^3) - (10*E^(5 + x)*(5*E^5 + Sqrt[-24 + 25*E^10]))/(3*(-24 + 25*E^10)^(5/2)*(5*E^5 + Sqrt[-24 +

25*E^10] - 2*x)^3) - (40*E^(5 + x)*(25*E^5 + 3*Sqrt[-24 + 25*E^10]))/(3*(24 - 25*E^10)^3*(5*E^5 + Sqrt[-24 +

25*E^10] - 2*x)^3) + (20*E^x*(12 - 25*E^10))/(3*(24 - 25*E^10)^3*(5*E^5 + Sqrt[-24 + 25*E^10] - 2*x)^2) + (60*

E^x*(12 - 25*E^10))/((-24 + 25*E^10)^(7/2)*(5*E^5 + Sqrt[-24 + 25*E^10] - 2*x)^2) + (E^x*(12 - 25*E^10))/(3*(-

24 + 25*E^10)^(5/2)*(5*E^5 + Sqrt[-24 + 25*E^10...

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] && !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

Rule 2208

Int[((b_.)*(F_)^((g_.)*((e_.) + (f_.)*(x_))))^(n_.)*((c_.) + (d_.)*(x_))^(m_), x_Symbol] :> Simp[(c + d*x)^(m

+ 1)*((b*F^(g*(e + f*x)))^n/(d*(m + 1))), x] - Dist[f*g*n*(Log[F]/(d*(m + 1))), Int[(c + d*x)^(m + 1)*(b*F^(g*

(e + f*x)))^n, x], x] /; FreeQ[{F, b, c, d, e, f, g, n}, x] && LtQ[m, -1] && IntegerQ[2*m] && !TrueQ[$UseGamm

Rule 2209

Int[(F_)^((g_.)*((e_.) + (f_.)*(x_)))/((c_.) + (d_.)*(x_)), x_Symbol] :> Simp[(F^(g*(e - c*(f/d)))/d)*ExpInteg

ralEi[f*g*(c + d*x)*(Log[F]/d)], x] /; FreeQ[{F, c, d, e, f, g}, x] && !TrueQ[$UseGamma]

Rule 2302

Int[((F_)^((g_.)*((d_.) + (e_.)*(x_))^(n_.))*(u_)^(m_.))/((a_.) + (b_.)*(x_) + (c_)*(x_)^2), x_Symbol] :> Int[

ExpandIntegrand[F^(g*(d + e*x)^n), u^m/(a + b*x + c*x^2), x], x] /; FreeQ[{F, a, b, c, d, e, g, n}, x] && Poly

nomialQ[u, x] && IntegerQ[m]

Rule 6820

Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; SimplerIntegrandQ[v, u, x]]

Rule 6874

Int[u_, x_Symbol] :> With[{v = ExpandIntegrand[u, x]}, Int[v, x] /; SumQ[v]]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {3 e^x \left (-6+\left (6+25 e^5\right ) x-\left (9+5 e^5\right ) x^2+x^3\right )}{x^2 \left (6-5 e^5 x+x^2\right )^5} \, dx\\ &=3 \int \frac {e^x \left (-6+\left (6+25 e^5\right ) x-\left (9+5 e^5\right ) x^2+x^3\right )}{x^2 \left (6-5 e^5 x+x^2\right )^5} \, dx\\ &=3 \int \left (-\frac {e^x}{1296 x^2}+\frac {e^x}{1296 x}-\frac {2 e^x \left (-12+25 e^{10}-5 e^5 x\right )}{3 \left (-6+5 e^5 x-x^2\right )^5}+\frac {e^x \left (-1-5 e^5+x\right )}{1296 \left (-6+5 e^5 x-x^2\right )}+\frac {e^x \left (2+10 e^5+25 e^{10}-\left (2+5 e^5\right ) x\right )}{12 \left (6-5 e^5 x+x^2\right )^4}+\frac {e^x \left (3+15 e^5+25 e^{10}-\left (3+5 e^5\right ) x\right )}{108 \left (6-5 e^5 x+x^2\right )^3}+\frac {e^x \left (6+30 e^5+25 e^{10}-\left (6+5 e^5\right ) x\right )}{1296 \left (6-5 e^5 x+x^2\right )^2}\right ) \, dx\\ &=-\left (\frac {1}{432} \int \frac {e^x}{x^2} \, dx\right )+\frac {1}{432} \int \frac {e^x}{x} \, dx+\frac {1}{432} \int \frac {e^x \left (-1-5 e^5+x\right )}{-6+5 e^5 x-x^2} \, dx+\frac {1}{432} \int \frac {e^x \left (6+30 e^5+25 e^{10}-\left (6+5 e^5\right ) x\right )}{\left (6-5 e^5 x+x^2\right )^2} \, dx+\frac {1}{36} \int \frac {e^x \left (3+15 e^5+25 e^{10}-\left (3+5 e^5\right ) x\right )}{\left (6-5 e^5 x+x^2\right )^3} \, dx+\frac {1}{4} \int \frac {e^x \left (2+10 e^5+25 e^{10}-\left (2+5 e^5\right ) x\right )}{\left (6-5 e^5 x+x^2\right )^4} \, dx-2 \int \frac {e^x \left (-12+25 e^{10}-5 e^5 x\right )}{\left (-6+5 e^5 x-x^2\right )^5} \, dx\\ &=\frac {e^x}{432 x}+\frac {\text {Ei}(x)}{432}+\frac {1}{432} \int \left (\frac {e^x \left (1+\frac {2+5 e^5}{\sqrt {-24+25 e^{10}}}\right )}{5 e^5-\sqrt {-24+25 e^{10}}-2 x}+\frac {e^x \left (1-\frac {2+5 e^5}{\sqrt {-24+25 e^{10}}}\right )}{5 e^5+\sqrt {-24+25 e^{10}}-2 x}\right ) \, dx-\frac {1}{432} \int \frac {e^x}{x} \, dx+\frac {1}{432} \int \left (\frac {6 e^x \left (1+\frac {5}{6} e^5 \left (6+5 e^5\right )\right )}{\left (-6+5 e^5 x-x^2\right )^2}-\frac {e^x \left (6+5 e^5\right ) x}{\left (-6+5 e^5 x-x^2\right )^2}\right ) \, dx+\frac {1}{36} \int \left (-\frac {3 e^x \left (1+\frac {5}{3} e^5 \left (3+5 e^5\right )\right )}{\left (-6+5 e^5 x-x^2\right )^3}+\frac {e^x \left (3+5 e^5\right ) x}{\left (-6+5 e^5 x-x^2\right )^3}\right ) \, dx+\frac {1}{4} \int \left (\frac {2 e^x \left (1+\frac {5}{2} e^5 \left (2+5 e^5\right )\right )}{\left (-6+5 e^5 x-x^2\right )^4}-\frac {e^x \left (2+5 e^5\right ) x}{\left (-6+5 e^5 x-x^2\right )^4}\right ) \, dx-2 \int \left (-\frac {12 e^x \left (1-\frac {25 e^{10}}{12}\right )}{\left (-6+5 e^5 x-x^2\right )^5}-\frac {5 e^{5+x} x}{\left (-6+5 e^5 x-x^2\right )^5}\right ) \, dx\\ &=\frac {e^x}{432 x}+10 \int \frac {e^{5+x} x}{\left (-6+5 e^5 x-x^2\right )^5} \, dx+\frac {1}{432} \left (-6-5 e^5\right ) \int \frac {e^x x}{\left (-6+5 e^5 x-x^2\right )^2} \, dx+\frac {1}{4} \left (-2-5 e^5\right ) \int \frac {e^x x}{\left (-6+5 e^5 x-x^2\right )^4} \, dx+\frac {1}{36} \left (3+5 e^5\right ) \int \frac {e^x x}{\left (-6+5 e^5 x-x^2\right )^3} \, dx+\left (2 \left (12-25 e^{10}\right )\right ) \int \frac {e^x}{\left (-6+5 e^5 x-x^2\right )^5} \, dx+\frac {1}{36} \left (-3-15 e^5-25 e^{10}\right ) \int \frac {e^x}{\left (-6+5 e^5 x-x^2\right )^3} \, dx+\frac {1}{4} \left (2+10 e^5+25 e^{10}\right ) \int \frac {e^x}{\left (-6+5 e^5 x-x^2\right )^4} \, dx+\frac {1}{432} \left (6+30 e^5+25 e^{10}\right ) \int \frac {e^x}{\left (-6+5 e^5 x-x^2\right )^2} \, dx+\frac {1}{432} \left (1-\frac {2+5 e^5}{\sqrt {-24+25 e^{10}}}\right ) \int \frac {e^x}{5 e^5+\sqrt {-24+25 e^{10}}-2 x} \, dx+\frac {1}{432} \left (1+\frac {2+5 e^5}{\sqrt {-24+25 e^{10}}}\right ) \int \frac {e^x}{5 e^5-\sqrt {-24+25 e^{10}}-2 x} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [A]
time = 1.87, size = 21, normalized size = 1.00 \begin {gather*} \frac {3 e^x}{x \left (6-5 e^5 x+x^2\right )^4} \end {gather*}

Antiderivative was successfully veriﬁed.

[In]

Integrate[(E^x*(18 - 18*x + 27*x^2 - 3*x^3 + E^5*(-75*x + 15*x^2)))/(-7776*x^2 - 6480*x^4 - 2160*x^6 + 3125*E^

25*x^7 - 360*x^8 - 30*x^10 - x^12 + E^20*(-18750*x^6 - 3125*x^8) + E^15*(45000*x^5 + 15000*x^7 + 1250*x^9) + E

^10*(-54000*x^4 - 27000*x^6 - 4500*x^8 - 250*x^10) + E^5*(32400*x^3 + 21600*x^5 + 5400*x^7 + 600*x^9 + 25*x^11

)),x]

[Out]

(3*E^x)/(x*(6 - 5*E^5*x + x^2)^4)

________________________________________________________________________________________

Maple [C] Result contains higher order function than in optimal. Order 4 vs. order 3.
time = 0.40, size = 14908, normalized size = 709.90


method	result	size

norman	$\frac {3 \,{\mathrm e}^{x}}{x \left (5 x \,{\mathrm e}^{5}-x^{2}-6\right )^{4}}$	$22$
gosper	$\frac {3 \,{\mathrm e}^{x}}{x \left (625 x^{4} {\mathrm e}^{20}-500 x^{5} {\mathrm e}^{15}+150 x^{6} {\mathrm e}^{10}-20 x^{7} {\mathrm e}^{5}+x^{8}-3000 x^{3} {\mathrm e}^{15}+1800 x^{4} {\mathrm e}^{10}-360 x^{5} {\mathrm e}^{5}+24 x^{6}+5400 x^{2} {\mathrm e}^{10}-2160 x^{3} {\mathrm e}^{5}+216 x^{4}-4320 x \,{\mathrm e}^{5}+864 x^{2}+1296\right )}$	$110$
default	$\text {Expression too large to display}$	$14908$

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int(((15*x^2-75*x)*exp(5)-3*x^3+27*x^2-18*x+18)*exp(x)/(3125*x^7*exp(5)^5+(-3125*x^8-18750*x^6)*exp(5)^4+(1250

*x^9+15000*x^7+45000*x^5)*exp(5)^3+(-250*x^10-4500*x^8-27000*x^6-54000*x^4)*exp(5)^2+(25*x^11+600*x^9+5400*x^7

+21600*x^5+32400*x^3)*exp(5)-x^12-30*x^10-360*x^8-2160*x^6-6480*x^4-7776*x^2),x,method=_RETURNVERBOSE)

[Out]

result too large to display

________________________________________________________________________________________

Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 91 vs. $2 (19) = 38$.
time = 0.32, size = 91, normalized size = 4.33 \begin {gather*} \frac {3 \, e^{x}}{x^{9} - 20 \, x^{8} e^{5} + 6 \, x^{7} {\left (25 \, e^{10} + 4\right )} - 20 \, x^{6} {\left (25 \, e^{15} + 18 \, e^{5}\right )} + x^{5} {\left (625 \, e^{20} + 1800 \, e^{10} + 216\right )} - 120 \, x^{4} {\left (25 \, e^{15} + 18 \, e^{5}\right )} + 216 \, x^{3} {\left (25 \, e^{10} + 4\right )} - 4320 \, x^{2} e^{5} + 1296 \, x} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((15*x^2-75*x)*exp(5)-3*x^3+27*x^2-18*x+18)*exp(x)/(3125*x^7*exp(5)^5+(-3125*x^8-18750*x^6)*exp(5)^4

+(1250*x^9+15000*x^7+45000*x^5)*exp(5)^3+(-250*x^10-4500*x^8-27000*x^6-54000*x^4)*exp(5)^2+(25*x^11+600*x^9+54

00*x^7+21600*x^5+32400*x^3)*exp(5)-x^12-30*x^10-360*x^8-2160*x^6-6480*x^4-7776*x^2),x, algorithm="maxima")

[Out]

3*e^x/(x^9 - 20*x^8*e^5 + 6*x^7*(25*e^10 + 4) - 20*x^6*(25*e^15 + 18*e^5) + x^5*(625*e^20 + 1800*e^10 + 216) -

120*x^4*(25*e^15 + 18*e^5) + 216*x^3*(25*e^10 + 4) - 4320*x^2*e^5 + 1296*x)

________________________________________________________________________________________

Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 89 vs. $2 (19) = 38$.
time = 0.34, size = 89, normalized size = 4.24 \begin {gather*} \frac {3 \, e^{x}}{x^{9} + 24 \, x^{7} + 625 \, x^{5} e^{20} + 216 \, x^{5} + 864 \, x^{3} - 500 \, {\left (x^{6} + 6 \, x^{4}\right )} e^{15} + 150 \, {\left (x^{7} + 12 \, x^{5} + 36 \, x^{3}\right )} e^{10} - 20 \, {\left (x^{8} + 18 \, x^{6} + 108 \, x^{4} + 216 \, x^{2}\right )} e^{5} + 1296 \, x} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((15*x^2-75*x)*exp(5)-3*x^3+27*x^2-18*x+18)*exp(x)/(3125*x^7*exp(5)^5+(-3125*x^8-18750*x^6)*exp(5)^4

+(1250*x^9+15000*x^7+45000*x^5)*exp(5)^3+(-250*x^10-4500*x^8-27000*x^6-54000*x^4)*exp(5)^2+(25*x^11+600*x^9+54

00*x^7+21600*x^5+32400*x^3)*exp(5)-x^12-30*x^10-360*x^8-2160*x^6-6480*x^4-7776*x^2),x, algorithm="fricas")

[Out]

3*e^x/(x^9 + 24*x^7 + 625*x^5*e^20 + 216*x^5 + 864*x^3 - 500*(x^6 + 6*x^4)*e^15 + 150*(x^7 + 12*x^5 + 36*x^3)*

e^10 - 20*(x^8 + 18*x^6 + 108*x^4 + 216*x^2)*e^5 + 1296*x)

________________________________________________________________________________________

Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 110 vs. $2 (19) = 38$.
time = 0.18, size = 110, normalized size = 5.24 \begin {gather*} \frac {3 e^{x}}{x^{9} - 20 x^{8} e^{5} + 24 x^{7} + 150 x^{7} e^{10} - 500 x^{6} e^{15} - 360 x^{6} e^{5} + 216 x^{5} + 1800 x^{5} e^{10} + 625 x^{5} e^{20} - 3000 x^{4} e^{15} - 2160 x^{4} e^{5} + 864 x^{3} + 5400 x^{3} e^{10} - 4320 x^{2} e^{5} + 1296 x} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((15*x**2-75*x)*exp(5)-3*x**3+27*x**2-18*x+18)*exp(x)/(3125*x**7*exp(5)**5+(-3125*x**8-18750*x**6)*e

xp(5)**4+(1250*x**9+15000*x**7+45000*x**5)*exp(5)**3+(-250*x**10-4500*x**8-27000*x**6-54000*x**4)*exp(5)**2+(2

5*x**11+600*x**9+5400*x**7+21600*x**5+32400*x**3)*exp(5)-x**12-30*x**10-360*x**8-2160*x**6-6480*x**4-7776*x**2

),x)

[Out]

3*exp(x)/(x**9 - 20*x**8*exp(5) + 24*x**7 + 150*x**7*exp(10) - 500*x**6*exp(15) - 360*x**6*exp(5) + 216*x**5 +

1800*x**5*exp(10) + 625*x**5*exp(20) - 3000*x**4*exp(15) - 2160*x**4*exp(5) + 864*x**3 + 5400*x**3*exp(10) -

4320*x**2*exp(5) + 1296*x)

________________________________________________________________________________________

Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 216 vs. $2 (19) = 38$.
time = 0.48, size = 216, normalized size = 10.29 \begin {gather*} -\frac {x^{8} e^{x} - 20 \, x^{7} e^{\left (x + 5\right )} + 150 \, x^{6} e^{\left (x + 10\right )} + 24 \, x^{6} e^{x} - 500 \, x^{5} e^{\left (x + 15\right )} - 360 \, x^{5} e^{\left (x + 5\right )} + 625 \, x^{4} e^{\left (x + 20\right )} + 1800 \, x^{4} e^{\left (x + 10\right )} + 216 \, x^{4} e^{x} - 3000 \, x^{3} e^{\left (x + 15\right )} - 2160 \, x^{3} e^{\left (x + 5\right )} + 5400 \, x^{2} e^{\left (x + 10\right )} + 864 \, x^{2} e^{x} - 4320 \, x e^{\left (x + 5\right )} - 1296 \, e^{x}}{432 \, {\left (x^{9} - 20 \, x^{8} e^{5} + 150 \, x^{7} e^{10} + 24 \, x^{7} - 500 \, x^{6} e^{15} - 360 \, x^{6} e^{5} + 625 \, x^{5} e^{20} + 1800 \, x^{5} e^{10} + 216 \, x^{5} - 3000 \, x^{4} e^{15} - 2160 \, x^{4} e^{5} + 5400 \, x^{3} e^{10} + 864 \, x^{3} - 4320 \, x^{2} e^{5} + 1296 \, x\right )}} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((15*x^2-75*x)*exp(5)-3*x^3+27*x^2-18*x+18)*exp(x)/(3125*x^7*exp(5)^5+(-3125*x^8-18750*x^6)*exp(5)^4

+(1250*x^9+15000*x^7+45000*x^5)*exp(5)^3+(-250*x^10-4500*x^8-27000*x^6-54000*x^4)*exp(5)^2+(25*x^11+600*x^9+54

00*x^7+21600*x^5+32400*x^3)*exp(5)-x^12-30*x^10-360*x^8-2160*x^6-6480*x^4-7776*x^2),x, algorithm="giac")

[Out]

-1/432*(x^8*e^x - 20*x^7*e^(x + 5) + 150*x^6*e^(x + 10) + 24*x^6*e^x - 500*x^5*e^(x + 15) - 360*x^5*e^(x + 5)

+ 625*x^4*e^(x + 20) + 1800*x^4*e^(x + 10) + 216*x^4*e^x - 3000*x^3*e^(x + 15) - 2160*x^3*e^(x + 5) + 5400*x^2

*e^(x + 10) + 864*x^2*e^x - 4320*x*e^(x + 5) - 1296*e^x)/(x^9 - 20*x^8*e^5 + 150*x^7*e^10 + 24*x^7 - 500*x^6*e

^15 - 360*x^6*e^5 + 625*x^5*e^20 + 1800*x^5*e^10 + 216*x^5 - 3000*x^4*e^15 - 2160*x^4*e^5 + 5400*x^3*e^10 + 86

4*x^3 - 4320*x^2*e^5 + 1296*x)

________________________________________________________________________________________

Mupad [F(-1)]
time = 0.00, size = -1, normalized size = -0.05 \begin {gather*} \text {Hanged} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int((exp(x)*(18*x + exp(5)*(75*x - 15*x^2) - 27*x^2 + 3*x^3 - 18))/(exp(20)*(18750*x^6 + 3125*x^8) - exp(5)*(3

2400*x^3 + 21600*x^5 + 5400*x^7 + 600*x^9 + 25*x^11) - 3125*x^7*exp(25) - exp(15)*(45000*x^5 + 15000*x^7 + 125

0*x^9) + 7776*x^2 + 6480*x^4 + 2160*x^6 + 360*x^8 + 30*x^10 + x^12 + exp(10)*(54000*x^4 + 27000*x^6 + 4500*x^8

+ 250*x^10)),x)

[Out]

\text{Hanged}

________________________________________________________________________________________

[next] [prev] [prev-tail] [front] [up]