3.90.71 \(\int \frac {25 e^{2 e^3}+125 x^4-100 x^5+e^{e^3} (150 x^2-100 x^3)+e^{2 e^{x+x^2}} (5 x^4-4 x^5+e^{x+x^2} (2 x^5+2 x^6-4 x^7)+e^{2 e^3} (1+e^{x+x^2} (2 x+2 x^2-4 x^3))+e^{e^3} (6 x^2-4 x^3+e^{x+x^2} (4 x^3+4 x^4-8 x^5)))+e^{e^{x+x^2}} (-50 x^4+40 x^5+e^{x+x^2} (-10 x^5-10 x^6+20 x^7)+e^{2 e^3} (-10+e^{x+x^2} (-10 x-10 x^2+20 x^3))+e^{e^3} (-60 x^2+40 x^3+e^{x+x^2} (-20 x^3-20 x^4+40 x^5)))}{1-2 x+x^2} \, dx\) [8971]

Optimal. Leaf size=37 \[ \frac {\left (-5+e^{e^{x+x^2}}\right )^2 x^2 \left (e^{e^3}+x^2\right )^2}{x-x^2} \]

[Out]

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

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Rubi [F]
time = 20.06, 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 {25 e^{2 e^3}+125 x^4-100 x^5+e^{e^3} \left (150 x^2-100 x^3\right )+e^{2 e^{x+x^2}} \left (5 x^4-4 x^5+e^{x+x^2} \left (2 x^5+2 x^6-4 x^7\right )+e^{2 e^3} \left (1+e^{x+x^2} \left (2 x+2 x^2-4 x^3\right )\right )+e^{e^3} \left (6 x^2-4 x^3+e^{x+x^2} \left (4 x^3+4 x^4-8 x^5\right )\right )\right )+e^{e^{x+x^2}} \left (-50 x^4+40 x^5+e^{x+x^2} \left (-10 x^5-10 x^6+20 x^7\right )+e^{2 e^3} \left (-10+e^{x+x^2} \left (-10 x-10 x^2+20 x^3\right )\right )+e^{e^3} \left (-60 x^2+40 x^3+e^{x+x^2} \left (-20 x^3-20 x^4+40 x^5\right )\right )\right )}{1-2 x+x^2} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(25*E^(2*E^3) + 125*x^4 - 100*x^5 + E^E^3*(150*x^2 - 100*x^3) + E^(2*E^(x + x^2))*(5*x^4 - 4*x^5 + E^(x +
x^2)*(2*x^5 + 2*x^6 - 4*x^7) + E^(2*E^3)*(1 + E^(x + x^2)*(2*x + 2*x^2 - 4*x^3)) + E^E^3*(6*x^2 - 4*x^3 + E^(x
+ x^2)*(4*x^3 + 4*x^4 - 8*x^5))) + E^E^(x + x^2)*(-50*x^4 + 40*x^5 + E^(x + x^2)*(-10*x^5 - 10*x^6 + 20*x^7)
+ E^(2*E^3)*(-10 + E^(x + x^2)*(-10*x - 10*x^2 + 20*x^3)) + E^E^3*(-60*x^2 + 40*x^3 + E^(x + x^2)*(-20*x^3 - 2
0*x^4 + 40*x^5))))/(1 - 2*x + x^2),x]

[Out]

(25*(1 + E^E^3))/(1 - x) + (25*E^E^3*(1 + E^E^3))/(1 - x) + 25*E^E^3*x - 25*(1 + 3*E^E^3)*x - 25*(1 + 2*E^E^3)
*x^2 - 25*x^3 - 25*x^4 - 5*E^E^3*Defer[Int][E^E^(x*(1 + x)), x] + 10*(1 + 3*E^E^3)*Defer[Int][E^E^(x*(1 + x)),
x] - (1 + 3*E^E^3)*Defer[Int][E^(2*E^(x + x^2)), x] + Defer[Int][E^(E^3 + 2*E^(x*(1 + x))), x] - 5*Defer[Int]
[E^(E^3 + E^(x + x^2)), x] - 6*(1 + E^E^3)^2*Defer[Int][E^(2*E^(x*(1 + x)) + x + x^2), x] + 30*(1 + E^E^3)^2*D
efer[Int][E^(E^(x + x^2) + x + x^2), x] - 10*(1 + E^E^3)*Defer[Int][E^E^(x*(1 + x))/(-1 + x)^2, x] - 5*E^E^3*(
1 + E^E^3)*Defer[Int][E^E^(x*(1 + x))/(-1 + x)^2, x] + (1 + E^E^3)*Defer[Int][E^(2*E^(x + x^2))/(-1 + x)^2, x]
+ (1 + E^E^3)*Defer[Int][E^(E^3 + 2*E^(x*(1 + x)))/(-1 + x)^2, x] - 5*(1 + E^E^3)*Defer[Int][E^(E^3 + E^(x +
x^2))/(-1 + x)^2, x] - 10*E^E^3*Defer[Int][E^E^(x*(1 + x))/(-1 + x), x] + 20*Defer[Int][E^(E^3 + E^(x*(1 + x))
)/(-1 + x), x] + 2*Defer[Int][E^(E^3 + 2*E^(x*(1 + x)))/(-1 + x), x] - 10*Defer[Int][E^(E^3 + E^(x + x^2))/(-1
+ x), x] - 2*Defer[Int][E^(E^3 + 2*E^(x + x^2))/(-1 + x), x] - 6*(1 + E^E^3)^2*Defer[Int][E^(2*E^(x*(1 + x))
+ x + x^2)/(-1 + x), x] + 30*(1 + E^E^3)^2*Defer[Int][E^(E^(x + x^2) + x + x^2)/(-1 + x), x] + 20*(1 + 2*E^E^3
)*Defer[Int][E^E^(x*(1 + x))*x, x] - 2*(1 + 2*E^E^3)*Defer[Int][E^(2*E^(x + x^2))*x, x] - 2*(3 + 6*E^E^3 + 2*E
^(2*E^3))*Defer[Int][E^(2*E^(x*(1 + x)) + x + x^2)*x, x] + 10*(3 + 6*E^E^3 + 2*E^(2*E^3))*Defer[Int][E^(E^(x +
x^2) + x + x^2)*x, x] + 30*Defer[Int][E^E^(x*(1 + x))*x^2, x] - 3*Defer[Int][E^(2*E^(x + x^2))*x^2, x] - 6*(1
+ 2*E^E^3)*Defer[Int][E^(2*E^(x*(1 + x)) + x + x^2)*x^2, x] + 30*(1 + 2*E^E^3)*Defer[Int][E^(E^(x + x^2) + x
+ x^2)*x^2, x] + 40*Defer[Int][E^E^(x*(1 + x))*x^3, x] - 4*Defer[Int][E^(2*E^(x + x^2))*x^3, x] - 2*(3 + 4*E^E
^3)*Defer[Int][E^(2*E^(x*(1 + x)) + x + x^2)*x^3, x] + 10*(3 + 4*E^E^3)*Defer[Int][E^(E^(x + x^2) + x + x^2)*x
^3, x] - 6*Defer[Int][E^(2*E^(x*(1 + x)) + x + x^2)*x^4, x] + 30*Defer[Int][E^(E^(x + x^2) + x + x^2)*x^4, x]
- 4*Defer[Int][E^(2*E^(x*(1 + x)) + x + x^2)*x^5, x] + 20*Defer[Int][E^(E^(x + x^2) + x + x^2)*x^5, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {25 e^{2 e^3}+125 x^4-100 x^5+e^{e^3} \left (150 x^2-100 x^3\right )+e^{2 e^{x+x^2}} \left (5 x^4-4 x^5+e^{x+x^2} \left (2 x^5+2 x^6-4 x^7\right )+e^{2 e^3} \left (1+e^{x+x^2} \left (2 x+2 x^2-4 x^3\right )\right )+e^{e^3} \left (6 x^2-4 x^3+e^{x+x^2} \left (4 x^3+4 x^4-8 x^5\right )\right )\right )+e^{e^{x+x^2}} \left (-50 x^4+40 x^5+e^{x+x^2} \left (-10 x^5-10 x^6+20 x^7\right )+e^{2 e^3} \left (-10+e^{x+x^2} \left (-10 x-10 x^2+20 x^3\right )\right )+e^{e^3} \left (-60 x^2+40 x^3+e^{x+x^2} \left (-20 x^3-20 x^4+40 x^5\right )\right )\right )}{(-1+x)^2} \, dx\\ &=\int \frac {\left (5-e^{e^{x+x^2}}\right ) \left (e^{e^3}+x^2\right ) \left (5 e^{e^3}-e^{e^3+e^{x+x^2}}+5 (5-4 x) x^2+e^{e^{x+x^2}} x^2 (-5+4 x)+2 e^{e^3+e^{x+x^2}+x+x^2} x \left (-1-x+2 x^2\right )+2 e^{e^{x+x^2}+x+x^2} x^3 \left (-1-x+2 x^2\right )\right )}{(1-x)^2} \, dx\\ &=\int \left (\frac {e^{e^{x (1+x)}} \left (5-e^{e^{x+x^2}}\right ) (5-4 x) x^2 \left (-e^{e^3}-x^2\right )}{(1-x)^2}-\frac {5 e^{e^3} \left (-5+e^{e^{x+x^2}}\right ) \left (e^{e^3}+x^2\right )}{(-1+x)^2}+\frac {e^{e^3+e^{x+x^2}} \left (-5+e^{e^{x+x^2}}\right ) \left (e^{e^3}+x^2\right )}{(-1+x)^2}+\frac {5 \left (-5+e^{e^{x+x^2}}\right ) x^2 (-5+4 x) \left (e^{e^3}+x^2\right )}{(-1+x)^2}-\frac {2 e^{e^{x+x^2}+x+x^2} \left (-5+e^{e^{x+x^2}}\right ) x (1+2 x) \left (e^{e^3}+x^2\right )^2}{-1+x}\right ) \, dx\\ &=-\left (2 \int \frac {e^{e^{x+x^2}+x+x^2} \left (-5+e^{e^{x+x^2}}\right ) x (1+2 x) \left (e^{e^3}+x^2\right )^2}{-1+x} \, dx\right )+5 \int \frac {\left (-5+e^{e^{x+x^2}}\right ) x^2 (-5+4 x) \left (e^{e^3}+x^2\right )}{(-1+x)^2} \, dx-\left (5 e^{e^3}\right ) \int \frac {\left (-5+e^{e^{x+x^2}}\right ) \left (e^{e^3}+x^2\right )}{(-1+x)^2} \, dx+\int \frac {e^{e^{x (1+x)}} \left (5-e^{e^{x+x^2}}\right ) (5-4 x) x^2 \left (-e^{e^3}-x^2\right )}{(1-x)^2} \, dx+\int \frac {e^{e^3+e^{x+x^2}} \left (-5+e^{e^{x+x^2}}\right ) \left (e^{e^3}+x^2\right )}{(-1+x)^2} \, dx\\ &=-\left (2 \int \left (\frac {e^{e^{x (1+x)}+e^{x+x^2}+x+x^2} (-1-2 x) x \left (e^{e^3}+x^2\right )^2}{1-x}-\frac {5 e^{e^{x+x^2}+x+x^2} x (1+2 x) \left (e^{e^3}+x^2\right )^2}{-1+x}\right ) \, dx\right )+5 \int \left (\frac {e^{e^{x (1+x)}} (5-4 x) x^2 \left (-e^{e^3}-x^2\right )}{(1-x)^2}-\frac {5 x^2 (-5+4 x) \left (e^{e^3}+x^2\right )}{(-1+x)^2}\right ) \, dx-\left (5 e^{e^3}\right ) \int \left (\frac {e^{e^{x (1+x)}} \left (e^{e^3}+x^2\right )}{(1-x)^2}-\frac {5 \left (e^{e^3}+x^2\right )}{(-1+x)^2}\right ) \, dx+\int \left (\frac {e^{e^3+e^{x (1+x)}+e^{x+x^2}} \left (e^{e^3}+x^2\right )}{(1-x)^2}-\frac {5 e^{e^3+e^{x+x^2}} \left (e^{e^3}+x^2\right )}{(-1+x)^2}\right ) \, dx+\int \left (\frac {e^{2 e^{x (1+x)}} (5-4 x) x^2 \left (e^{e^3}+x^2\right )}{(1-x)^2}+\frac {5 e^{e^{x (1+x)}} x^2 (-5+4 x) \left (e^{e^3}+x^2\right )}{(-1+x)^2}\right ) \, dx\\ &=-\left (2 \int \frac {e^{e^{x (1+x)}+e^{x+x^2}+x+x^2} (-1-2 x) x \left (e^{e^3}+x^2\right )^2}{1-x} \, dx\right )+5 \int \frac {e^{e^{x (1+x)}} (5-4 x) x^2 \left (-e^{e^3}-x^2\right )}{(1-x)^2} \, dx-5 \int \frac {e^{e^3+e^{x+x^2}} \left (e^{e^3}+x^2\right )}{(-1+x)^2} \, dx+5 \int \frac {e^{e^{x (1+x)}} x^2 (-5+4 x) \left (e^{e^3}+x^2\right )}{(-1+x)^2} \, dx+10 \int \frac {e^{e^{x+x^2}+x+x^2} x (1+2 x) \left (e^{e^3}+x^2\right )^2}{-1+x} \, dx-25 \int \frac {x^2 (-5+4 x) \left (e^{e^3}+x^2\right )}{(-1+x)^2} \, dx-\left (5 e^{e^3}\right ) \int \frac {e^{e^{x (1+x)}} \left (e^{e^3}+x^2\right )}{(1-x)^2} \, dx+\left (25 e^{e^3}\right ) \int \frac {e^{e^3}+x^2}{(-1+x)^2} \, dx+\int \frac {e^{e^3+e^{x (1+x)}+e^{x+x^2}} \left (e^{e^3}+x^2\right )}{(1-x)^2} \, dx+\int \frac {e^{2 e^{x (1+x)}} (5-4 x) x^2 \left (e^{e^3}+x^2\right )}{(1-x)^2} \, dx\\ &=-\left (2 \int \frac {e^{2 e^{x (1+x)}+x+x^2} (-1-2 x) x \left (e^{e^3}+x^2\right )^2}{1-x} \, dx\right )-5 \int \left (e^{e^3+e^{x+x^2}}+\frac {e^{e^3+e^{x+x^2}} \left (1+e^{e^3}\right )}{(-1+x)^2}+\frac {2 e^{e^3+e^{x+x^2}}}{-1+x}\right ) \, dx+2 \left (5 \int \left (e^{e^{x (1+x)}} \left (1+3 e^{e^3}\right )-\frac {e^{e^{x (1+x)}} \left (1+e^{e^3}\right )}{(-1+x)^2}+\frac {2 e^{e^3+e^{x (1+x)}}}{-1+x}+2 e^{e^{x (1+x)}} \left (1+2 e^{e^3}\right ) x+3 e^{e^{x (1+x)}} x^2+4 e^{e^{x (1+x)}} x^3\right ) \, dx\right )+10 \int \left (3 e^{e^{x+x^2}+x+x^2} \left (1+e^{e^3}\right )^2+\frac {3 e^{e^{x+x^2}+x+x^2} \left (1+e^{e^3}\right )^2}{-1+x}+e^{e^{x+x^2}+x+x^2} \left (3+6 e^{e^3}+2 e^{2 e^3}\right ) x+3 e^{e^{x+x^2}+x+x^2} \left (1+2 e^{e^3}\right ) x^2+e^{e^{x+x^2}+x+x^2} \left (3+4 e^{e^3}\right ) x^3+3 e^{e^{x+x^2}+x+x^2} x^4+2 e^{e^{x+x^2}+x+x^2} x^5\right ) \, dx-25 \int \left (1+3 e^{e^3}-\frac {1+e^{e^3}}{(-1+x)^2}+\frac {2 e^{e^3}}{-1+x}+2 \left (1+2 e^{e^3}\right ) x+3 x^2+4 x^3\right ) \, dx-\left (5 e^{e^3}\right ) \int \left (e^{e^{x (1+x)}}+\frac {e^{e^{x (1+x)}} \left (1+e^{e^3}\right )}{(-1+x)^2}+\frac {2 e^{e^{x (1+x)}}}{-1+x}\right ) \, dx+\left (25 e^{e^3}\right ) \int \left (1+\frac {1+e^{e^3}}{(-1+x)^2}+\frac {2}{-1+x}\right ) \, dx+\int \frac {e^{e^3+2 e^{x (1+x)}} \left (e^{e^3}+x^2\right )}{(1-x)^2} \, dx+\int \frac {e^{2 e^{x+x^2}} (5-4 x) x^2 \left (e^{e^3}+x^2\right )}{(1-x)^2} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(144\) vs. \(2(37)=74\).
time = 0.23, size = 144, normalized size = 3.89 \begin {gather*} -\frac {25 e^{2 e^3}+e^{2 \left (e^3+e^{x+x^2}\right )} x-10 e^{2 e^3+e^{x+x^2}} x-20 e^{e^3+e^{x+x^2}} x^3+2 e^{e^3+2 e^{x+x^2}} x^3-10 e^{e^{x+x^2}} x^5+e^{2 e^{x+x^2}} x^5+50 e^{e^3} \left (1-x+x^3\right )+25 \left (1-x+x^5\right )}{-1+x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(25*E^(2*E^3) + 125*x^4 - 100*x^5 + E^E^3*(150*x^2 - 100*x^3) + E^(2*E^(x + x^2))*(5*x^4 - 4*x^5 + E
^(x + x^2)*(2*x^5 + 2*x^6 - 4*x^7) + E^(2*E^3)*(1 + E^(x + x^2)*(2*x + 2*x^2 - 4*x^3)) + E^E^3*(6*x^2 - 4*x^3
+ E^(x + x^2)*(4*x^3 + 4*x^4 - 8*x^5))) + E^E^(x + x^2)*(-50*x^4 + 40*x^5 + E^(x + x^2)*(-10*x^5 - 10*x^6 + 20
*x^7) + E^(2*E^3)*(-10 + E^(x + x^2)*(-10*x - 10*x^2 + 20*x^3)) + E^E^3*(-60*x^2 + 40*x^3 + E^(x + x^2)*(-20*x
^3 - 20*x^4 + 40*x^5))))/(1 - 2*x + x^2),x]

[Out]

-((25*E^(2*E^3) + E^(2*(E^3 + E^(x + x^2)))*x - 10*E^(2*E^3 + E^(x + x^2))*x - 20*E^(E^3 + E^(x + x^2))*x^3 +
2*E^(E^3 + 2*E^(x + x^2))*x^3 - 10*E^E^(x + x^2)*x^5 + E^(2*E^(x + x^2))*x^5 + 50*E^E^3*(1 - x + x^3) + 25*(1
- x + x^5))/(-1 + x))

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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(128\) vs. \(2(33)=66\).
time = 3.61, size = 129, normalized size = 3.49

method	result	size
risch	\(-25 x^{4}-50 x^{2} {\mathrm e}^{{\mathrm e}^{3}}-25 x^{3}-50 x \,{\mathrm e}^{{\mathrm e}^{3}}-25 x^{2}-25 x -\frac {25 \,{\mathrm e}^{2 \,{\mathrm e}^{3}}}{x -1}-\frac {50 \,{\mathrm e}^{{\mathrm e}^{3}}}{x -1}-\frac {25}{x -1}-\frac {x \left (x^{4}+2 x^{2} {\mathrm e}^{{\mathrm e}^{3}}+{\mathrm e}^{2 \,{\mathrm e}^{3}}\right ) {\mathrm e}^{2 \,{\mathrm e}^{\left (x +1\right ) x}}}{x -1}+\frac {10 x \left (x^{4}+2 x^{2} {\mathrm e}^{{\mathrm e}^{3}}+{\mathrm e}^{2 \,{\mathrm e}^{3}}\right ) {\mathrm e}^{{\mathrm e}^{\left (x +1\right ) x}}}{x -1}\)	\(129\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((((-4*x^3+2*x^2+2*x)*exp(x^2+x)+1)*exp(exp(3))^2+((-8*x^5+4*x^4+4*x^3)*exp(x^2+x)-4*x^3+6*x^2)*exp(exp(3)
)+(-4*x^7+2*x^6+2*x^5)*exp(x^2+x)-4*x^5+5*x^4)*exp(exp(x^2+x))^2+(((20*x^3-10*x^2-10*x)*exp(x^2+x)-10)*exp(exp
(3))^2+((40*x^5-20*x^4-20*x^3)*exp(x^2+x)+40*x^3-60*x^2)*exp(exp(3))+(20*x^7-10*x^6-10*x^5)*exp(x^2+x)+40*x^5-
50*x^4)*exp(exp(x^2+x))+25*exp(exp(3))^2+(-100*x^3+150*x^2)*exp(exp(3))-100*x^5+125*x^4)/(x^2-2*x+1),x,method=
_RETURNVERBOSE)

[Out]

-25*x^4-50*x^2*exp(exp(3))-25*x^3-50*x*exp(exp(3))-25*x^2-25*x-25*exp(2*exp(3))/(x-1)-50/(x-1)*exp(exp(3))-25/
(x-1)-x*(x^4+2*x^2*exp(exp(3))+exp(2*exp(3)))/(x-1)*exp(2*exp((x+1)*x))+10*x*(x^4+2*x^2*exp(exp(3))+exp(2*exp(
3)))/(x-1)*exp(exp((x+1)*x))

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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 148 vs. \(2 (34) = 68\).
time = 0.34, size = 148, normalized size = 4.00 \begin {gather*} -25 \, x^{4} - 25 \, x^{3} - 25 \, x^{2} - 50 \, {\left (x^{2} + 4 \, x - \frac {2}{x - 1} + 6 \, \log \left (x - 1\right )\right )} e^{\left (e^{3}\right )} + 150 \, {\left (x - \frac {1}{x - 1} + 2 \, \log \left (x - 1\right )\right )} e^{\left (e^{3}\right )} - 25 \, x - \frac {{\left (x^{5} + 2 \, x^{3} e^{\left (e^{3}\right )} + x e^{\left (2 \, e^{3}\right )}\right )} e^{\left (2 \, e^{\left (x^{2} + x\right )}\right )} - 10 \, {\left (x^{5} + 2 \, x^{3} e^{\left (e^{3}\right )} + x e^{\left (2 \, e^{3}\right )}\right )} e^{\left (e^{\left (x^{2} + x\right )}\right )}}{x - 1} - \frac {25 \, e^{\left (2 \, e^{3}\right )}}{x - 1} - \frac {25}{x - 1} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((-4*x^3+2*x^2+2*x)*exp(x^2+x)+1)*exp(exp(3))^2+((-8*x^5+4*x^4+4*x^3)*exp(x^2+x)-4*x^3+6*x^2)*exp(
exp(3))+(-4*x^7+2*x^6+2*x^5)*exp(x^2+x)-4*x^5+5*x^4)*exp(exp(x^2+x))^2+(((20*x^3-10*x^2-10*x)*exp(x^2+x)-10)*e
xp(exp(3))^2+((40*x^5-20*x^4-20*x^3)*exp(x^2+x)+40*x^3-60*x^2)*exp(exp(3))+(20*x^7-10*x^6-10*x^5)*exp(x^2+x)+4
0*x^5-50*x^4)*exp(exp(x^2+x))+25*exp(exp(3))^2+(-100*x^3+150*x^2)*exp(exp(3))-100*x^5+125*x^4)/(x^2-2*x+1),x,
algorithm="maxima")

[Out]

-25*x^4 - 25*x^3 - 25*x^2 - 50*(x^2 + 4*x - 2/(x - 1) + 6*log(x - 1))*e^(e^3) + 150*(x - 1/(x - 1) + 2*log(x -
1))*e^(e^3) - 25*x - ((x^5 + 2*x^3*e^(e^3) + x*e^(2*e^3))*e^(2*e^(x^2 + x)) - 10*(x^5 + 2*x^3*e^(e^3) + x*e^(
2*e^3))*e^(e^(x^2 + x)))/(x - 1) - 25*e^(2*e^3)/(x - 1) - 25/(x - 1)

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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 94 vs. \(2 (34) = 68\).
time = 0.39, size = 94, normalized size = 2.54 \begin {gather*} -\frac {25 \, x^{5} + {\left (x^{5} + 2 \, x^{3} e^{\left (e^{3}\right )} + x e^{\left (2 \, e^{3}\right )}\right )} e^{\left (2 \, e^{\left (x^{2} + x\right )}\right )} + 50 \, {\left (x^{3} - x + 1\right )} e^{\left (e^{3}\right )} - 10 \, {\left (x^{5} + 2 \, x^{3} e^{\left (e^{3}\right )} + x e^{\left (2 \, e^{3}\right )}\right )} e^{\left (e^{\left (x^{2} + x\right )}\right )} - 25 \, x + 25 \, e^{\left (2 \, e^{3}\right )} + 25}{x - 1} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((-4*x^3+2*x^2+2*x)*exp(x^2+x)+1)*exp(exp(3))^2+((-8*x^5+4*x^4+4*x^3)*exp(x^2+x)-4*x^3+6*x^2)*exp(
exp(3))+(-4*x^7+2*x^6+2*x^5)*exp(x^2+x)-4*x^5+5*x^4)*exp(exp(x^2+x))^2+(((20*x^3-10*x^2-10*x)*exp(x^2+x)-10)*e
xp(exp(3))^2+((40*x^5-20*x^4-20*x^3)*exp(x^2+x)+40*x^3-60*x^2)*exp(exp(3))+(20*x^7-10*x^6-10*x^5)*exp(x^2+x)+4
0*x^5-50*x^4)*exp(exp(x^2+x))+25*exp(exp(3))^2+(-100*x^3+150*x^2)*exp(exp(3))-100*x^5+125*x^4)/(x^2-2*x+1),x,
algorithm="fricas")

[Out]

-(25*x^5 + (x^5 + 2*x^3*e^(e^3) + x*e^(2*e^3))*e^(2*e^(x^2 + x)) + 50*(x^3 - x + 1)*e^(e^3) - 10*(x^5 + 2*x^3*
e^(e^3) + x*e^(2*e^3))*e^(e^(x^2 + x)) - 25*x + 25*e^(2*e^3) + 25)/(x - 1)

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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 177 vs. \(2 (29) = 58\).
time = 0.32, size = 177, normalized size = 4.78 \begin {gather*} - 25 x^{4} - 25 x^{3} - x^{2} \cdot \left (25 + 50 e^{e^{3}}\right ) - x \left (25 + 50 e^{e^{3}}\right ) + \frac {\left (- x^{6} + x^{5} - 2 x^{4} e^{e^{3}} + 2 x^{3} e^{e^{3}} - x^{2} e^{2 e^{3}} + x e^{2 e^{3}}\right ) e^{2 e^{x^{2} + x}} + \left (10 x^{6} - 10 x^{5} + 20 x^{4} e^{e^{3}} - 20 x^{3} e^{e^{3}} + 10 x^{2} e^{2 e^{3}} - 10 x e^{2 e^{3}}\right ) e^{e^{x^{2} + x}}}{x^{2} - 2 x + 1} - \frac {25 + 50 e^{e^{3}} + 25 e^{2 e^{3}}}{x - 1} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((-4*x**3+2*x**2+2*x)*exp(x**2+x)+1)*exp(exp(3))**2+((-8*x**5+4*x**4+4*x**3)*exp(x**2+x)-4*x**3+6*
x**2)*exp(exp(3))+(-4*x**7+2*x**6+2*x**5)*exp(x**2+x)-4*x**5+5*x**4)*exp(exp(x**2+x))**2+(((20*x**3-10*x**2-10
*x)*exp(x**2+x)-10)*exp(exp(3))**2+((40*x**5-20*x**4-20*x**3)*exp(x**2+x)+40*x**3-60*x**2)*exp(exp(3))+(20*x**
7-10*x**6-10*x**5)*exp(x**2+x)+40*x**5-50*x**4)*exp(exp(x**2+x))+25*exp(exp(3))**2+(-100*x**3+150*x**2)*exp(ex
p(3))-100*x**5+125*x**4)/(x**2-2*x+1),x)

[Out]

-25*x**4 - 25*x**3 - x**2*(25 + 50*exp(exp(3))) - x*(25 + 50*exp(exp(3))) + ((-x**6 + x**5 - 2*x**4*exp(exp(3)
) + 2*x**3*exp(exp(3)) - x**2*exp(2*exp(3)) + x*exp(2*exp(3)))*exp(2*exp(x**2 + x)) + (10*x**6 - 10*x**5 + 20*
x**4*exp(exp(3)) - 20*x**3*exp(exp(3)) + 10*x**2*exp(2*exp(3)) - 10*x*exp(2*exp(3)))*exp(exp(x**2 + x)))/(x**2
- 2*x + 1) - (25 + 50*exp(exp(3)) + 25*exp(2*exp(3)))/(x - 1)

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Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((-4*x^3+2*x^2+2*x)*exp(x^2+x)+1)*exp(exp(3))^2+((-8*x^5+4*x^4+4*x^3)*exp(x^2+x)-4*x^3+6*x^2)*exp(
exp(3))+(-4*x^7+2*x^6+2*x^5)*exp(x^2+x)-4*x^5+5*x^4)*exp(exp(x^2+x))^2+(((20*x^3-10*x^2-10*x)*exp(x^2+x)-10)*e
xp(exp(3))^2+((40*x^5-20*x^4-20*x^3)*exp(x^2+x)+40*x^3-60*x^2)*exp(exp(3))+(20*x^7-10*x^6-10*x^5)*exp(x^2+x)+4
0*x^5-50*x^4)*exp(exp(x^2+x))+25*exp(exp(3))^2+(-100*x^3+150*x^2)*exp(exp(3))-100*x^5+125*x^4)/(x^2-2*x+1),x,
algorithm="giac")

[Out]

integrate(-(100*x^5 - 125*x^4 + (4*x^5 - 5*x^4 + 2*(2*x^7 - x^6 - x^5)*e^(x^2 + x) + (2*(2*x^3 - x^2 - x)*e^(x
^2 + x) - 1)*e^(2*e^3) + 2*(2*x^3 - 3*x^2 + 2*(2*x^5 - x^4 - x^3)*e^(x^2 + x))*e^(e^3))*e^(2*e^(x^2 + x)) + 50
*(2*x^3 - 3*x^2)*e^(e^3) - 10*(4*x^5 - 5*x^4 + (2*x^7 - x^6 - x^5)*e^(x^2 + x) + ((2*x^3 - x^2 - x)*e^(x^2 + x
) - 1)*e^(2*e^3) + 2*(2*x^3 - 3*x^2 + (2*x^5 - x^4 - x^3)*e^(x^2 + x))*e^(e^3))*e^(e^(x^2 + x)) - 25*e^(2*e^3)
)/(x^2 - 2*x + 1), x)

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Mupad [B]
time = 0.97, size = 125, normalized size = 3.38 \begin {gather*} \frac {{\mathrm {e}}^{{\mathrm {e}}^{x^2}\,{\mathrm {e}}^x}\,\left (10\,x^5+20\,{\mathrm {e}}^{{\mathrm {e}}^3}\,x^3+10\,{\mathrm {e}}^{2\,{\mathrm {e}}^3}\,x\right )}{x-1}-\frac {25\,{\mathrm {e}}^{2\,{\mathrm {e}}^3}+50\,{\mathrm {e}}^{{\mathrm {e}}^3}+25}{x-1}-x^2\,\left (50\,{\mathrm {e}}^{{\mathrm {e}}^3}+25\right )-25\,x^3-25\,x^4-x\,\left (50\,{\mathrm {e}}^{{\mathrm {e}}^3}+25\right )-\frac {{\mathrm {e}}^{2\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^x}\,\left (x^5+2\,{\mathrm {e}}^{{\mathrm {e}}^3}\,x^3+{\mathrm {e}}^{2\,{\mathrm {e}}^3}\,x\right )}{x-1} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((25*exp(2*exp(3)) - exp(exp(x + x^2))*(exp(2*exp(3))*(exp(x + x^2)*(10*x + 10*x^2 - 20*x^3) + 10) + exp(ex
p(3))*(exp(x + x^2)*(20*x^3 + 20*x^4 - 40*x^5) + 60*x^2 - 40*x^3) + exp(x + x^2)*(10*x^5 + 10*x^6 - 20*x^7) +
50*x^4 - 40*x^5) + 125*x^4 - 100*x^5 + exp(2*exp(x + x^2))*(exp(2*exp(3))*(exp(x + x^2)*(2*x + 2*x^2 - 4*x^3)
+ 1) + exp(exp(3))*(exp(x + x^2)*(4*x^3 + 4*x^4 - 8*x^5) + 6*x^2 - 4*x^3) + exp(x + x^2)*(2*x^5 + 2*x^6 - 4*x^
7) + 5*x^4 - 4*x^5) + exp(exp(3))*(150*x^2 - 100*x^3))/(x^2 - 2*x + 1),x)

[Out]

(exp(exp(x^2)*exp(x))*(10*x*exp(2*exp(3)) + 20*x^3*exp(exp(3)) + 10*x^5))/(x - 1) - (25*exp(2*exp(3)) + 50*exp
(exp(3)) + 25)/(x - 1) - x^2*(50*exp(exp(3)) + 25) - 25*x^3 - 25*x^4 - x*(50*exp(exp(3)) + 25) - (exp(2*exp(x^
2)*exp(x))*(x*exp(2*exp(3)) + 2*x^3*exp(exp(3)) + x^5))/(x - 1)

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