3.17.24 $\int \frac{3e^{6e^{x}x}+20x-90e^{5e^{x}x}{x}^2+3x^3+2000x^4+225x^6+5625x^9+46875x^{12}+e^{4e^{x}x}(9x+1125x^4)+e^{3e^{x}x}(-180x^3-7500x^6)+e^{2e^{x}x}(9x^2+1350x^5+28125x^8+e^x(40x+40x^2))+e^{e^{x}x}(-400x^2-90x^4-4500x^7-56250x^{10}+e^x(-200x^3-200x^4))}{3e^{6e^{x}x}x-90e^{5e^{x}x}{x}^3+3x^4+225x^7+5625x^{10}+46875x^{13}+e^{4e^{x}x}(9x^2+1125x^5)+e^{3e^{x}x}(-180x^4-7500x^7)+e^{2e^{x}x}(9x^3+1350x^6+28125x^9)+e^{e^{x}x}(-90x^5-4500x^8-56250x^{11})}dx$

Optimal. Leaf size=26 $$-\frac{10}{3{(x+{(e^{e^{x}x}-5x^2)}^2)}^2}+\log (x)$$

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Rubi [F]  time = 9.75, 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 = {} $$\begin{array}{c}\int \frac{3e^{6e^{x}x}+20x-90e^{5e^{x}x}{x}^2+3x^3+2000x^4+225x^6+5625x^9+46875x^{12}+e^{4e^{x}x}(9x+1125x^4)+e^{3e^{x}x}(-180x^3-7500x^6)+e^{2e^{x}x}(9x^2+1350x^5+28125x^8+e^x(40x+40x^2))+e^{e^{x}x}(-400x^2-90x^4-4500x^7-56250x^{10}+e^x(-200x^3-200x^4))}{3e^{6e^{x}x}x-90e^{5e^{x}x}{x}^3+3x^4+225x^7+5625x^{10}+46875x^{13}+e^{4e^{x}x}(9x^2+1125x^5)+e^{3e^{x}x}(-180x^4-7500x^7)+e^{2e^{x}x}(9x^3+1350x^6+28125x^9)+e^{e^{x}x}(-90x^5-4500x^8-56250x^{11})}dx\end{array}$$

Verification is not applicable to the result.

[In]

Int[(3*E^(6*E^x*x) + 20*x - 90*E^(5*E^x*x)*x^2 + 3*x^3 + 2000*x^4 + 225*x^6 + 5625*x^9 + 46875*x^12 + E^(4*E^x
*x)*(9*x + 1125*x^4) + E^(3*E^x*x)*(-180*x^3 - 7500*x^6) + E^(2*E^x*x)*(9*x^2 + 1350*x^5 + 28125*x^8 + E^x*(40
*x + 40*x^2)) + E^(E^x*x)*(-400*x^2 - 90*x^4 - 4500*x^7 - 56250*x^10 + E^x*(-200*x^3 - 200*x^4)))/(3*E^(6*E^x*
x)*x - 90*E^(5*E^x*x)*x^3 + 3*x^4 + 225*x^7 + 5625*x^10 + 46875*x^13 + E^(4*E^x*x)*(9*x^2 + 1125*x^5) + E^(3*E
^x*x)*(-180*x^4 - 7500*x^7) + E^(2*E^x*x)*(9*x^3 + 1350*x^6 + 28125*x^9) + E^(E^x*x)*(-90*x^5 - 4500*x^8 - 562
50*x^11)),x]

[Out]

Log[x] + (20*Defer[Int][(E^(2*E^x*x) + x - 10*E^(E^x*x)*x^2 + 25*x^4)^(-3), x])/3 - (40*Defer[Int][(E^x*x)/(E^
(2*E^x*x) + x - 10*E^(E^x*x)*x^2 + 25*x^4)^3, x])/3 - (400*Defer[Int][(E^(E^x*x)*x)/(E^(2*E^x*x) + x - 10*E^(E
^x*x)*x^2 + 25*x^4)^3, x])/3 - (40*Defer[Int][(E^x*x^2)/(E^(2*E^x*x) + x - 10*E^(E^x*x)*x^2 + 25*x^4)^3, x])/3
+ (200*Defer[Int][(E^(x + E^x*x)*x^2)/(E^(2*E^x*x) + x - 10*E^(E^x*x)*x^2 + 25*x^4)^3, x])/3 + (2000*Defer[In
t][x^3/(E^(2*E^x*x) + x - 10*E^(E^x*x)*x^2 + 25*x^4)^3, x])/3 + (200*Defer[Int][(E^(x + E^x*x)*x^3)/(E^(2*E^x*
x) + x - 10*E^(E^x*x)*x^2 + 25*x^4)^3, x])/3 - (1000*Defer[Int][(E^x*x^4)/(E^(2*E^x*x) + x - 10*E^(E^x*x)*x^2
+ 25*x^4)^3, x])/3 - (1000*Defer[Int][(E^x*x^5)/(E^(2*E^x*x) + x - 10*E^(E^x*x)*x^2 + 25*x^4)^3, x])/3 + (40*D
efer[Int][E^x/(E^(2*E^x*x) + x - 10*E^(E^x*x)*x^2 + 25*x^4)^2, x])/3 + (40*Defer[Int][(E^x*x)/(E^(2*E^x*x) + x
- 10*E^(E^x*x)*x^2 + 25*x^4)^2, x])/3

Rubi steps

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =\int \frac{3e^{6e^{x}x}-90e^{5e^{x}x}{x}^2+40e^{x+2e^{x}x}x(1+x)-200e^{x+e^{x}x}{x}^3(1+x)+9e^{4e^{x}x}x(1+125x^3)-60e^{3e^{x}x}{x}^3(3+125x^3)+9e^{2e^{x}x}{x}^2(1+150x^3+3125x^6)-10e^{e^{x}x}{x}^2(40+9x^2+450x^5+5625x^8)+x(20+3x^2+2000x^3+225x^5+5625x^8+46875x^{11})}{3x{(e^{2e^{x}x}+x-10e^{e^{x}x}{x}^2+25x^4)}^3}dx\\ & =\frac{1}{3}\int \frac{3e^{6e^{x}x}-90e^{5e^{x}x}{x}^2+40e^{x+2e^{x}x}x(1+x)-200e^{x+e^{x}x}{x}^3(1+x)+9e^{4e^{x}x}x(1+125x^3)-60e^{3e^{x}x}{x}^3(3+125x^3)+9e^{2e^{x}x}{x}^2(1+150x^3+3125x^6)-10e^{e^{x}x}{x}^2(40+9x^2+450x^5+5625x^8)+x(20+3x^2+2000x^3+225x^5+5625x^8+46875x^{11})}{x{(e^{2e^{x}x}+x-10e^{e^{x}x}{x}^2+25x^4)}^3}dx\\ & =\frac{1}{3}\int (\frac{3}{x}+\frac{40e^x(1+x)}{{(e^{2e^{x}x}+x-10e^{e^{x}x}{x}^2+25x^4)}^2}+\frac{20(1-2e^{x}x-20e^{e^{x}x}x-2e^x{x}^2+10e^{x+e^{x}x}{x}^2+100x^3+10e^{x+e^{x}x}{x}^3-50e^x{x}^4-50e^x{x}^5)}{{(e^{2e^{x}x}+x-10e^{e^{x}x}{x}^2+25x^4)}^3})dx\\ & =\log (x)+\frac{20}{3}\int \frac{1-2e^{x}x-20e^{e^{x}x}x-2e^x{x}^2+10e^{x+e^{x}x}{x}^2+100x^3+10e^{x+e^{x}x}{x}^3-50e^x{x}^4-50e^x{x}^5}{{(e^{2e^{x}x}+x-10e^{e^{x}x}{x}^2+25x^4)}^3}dx+\frac{40}{3}\int \frac{e^x(1+x)}{{(e^{2e^{x}x}+x-10e^{e^{x}x}{x}^2+25x^4)}^2}dx\\ & =\log (x)+\frac{20}{3}\int \frac{1-20e^{e^{x}x}x+100x^3+10e^{x+e^{x}x}{x}^2(1+x)-2e^{x}x(1+x+25x^3+25x^4)}{{(e^{2e^{x}x}+x-10e^{e^{x}x}{x}^2+25x^4)}^3}dx+\frac{40}{3}\int (\frac{e^x}{{(e^{2e^{x}x}+x-10e^{e^{x}x}{x}^2+25x^4)}^2}+\frac{e^{x}x}{{(e^{2e^{x}x}+x-10e^{e^{x}x}{x}^2+25x^4)}^2})dx\\ & =\log (x)+\frac{20}{3}\int (\frac{1}{{(e^{2e^{x}x}+x-10e^{e^{x}x}{x}^2+25x^4)}^3}-\frac{2e^{x}x}{{(e^{2e^{x}x}+x-10e^{e^{x}x}{x}^2+25x^4)}^3}-\frac{20e^{e^{x}x}x}{{(e^{2e^{x}x}+x-10e^{e^{x}x}{x}^2+25x^4)}^3}-\frac{2e^x{x}^2}{{(e^{2e^{x}x}+x-10e^{e^{x}x}{x}^2+25x^4)}^3}+\frac{10e^{x+e^{x}x}{x}^2}{{(e^{2e^{x}x}+x-10e^{e^{x}x}{x}^2+25x^4)}^3}+\frac{100x^3}{{(e^{2e^{x}x}+x-10e^{e^{x}x}{x}^2+25x^4)}^3}+\frac{10e^{x+e^{x}x}{x}^3}{{(e^{2e^{x}x}+x-10e^{e^{x}x}{x}^2+25x^4)}^3}-\frac{50e^x{x}^4}{{(e^{2e^{x}x}+x-10e^{e^{x}x}{x}^2+25x^4)}^3}-\frac{50e^x{x}^5}{{(e^{2e^{x}x}+x-10e^{e^{x}x}{x}^2+25x^4)}^3})dx+\frac{40}{3}\int \frac{e^x}{{(e^{2e^{x}x}+x-10e^{e^{x}x}{x}^2+25x^4)}^2}dx+\frac{40}{3}\int \frac{e^{x}x}{{(e^{2e^{x}x}+x-10e^{e^{x}x}{x}^2+25x^4)}^2}dx\\ & =\log (x)+\frac{20}{3}\int \frac{1}{{(e^{2e^{x}x}+x-10e^{e^{x}x}{x}^2+25x^4)}^3}dx-\frac{40}{3}\int \frac{e^{x}x}{{(e^{2e^{x}x}+x-10e^{e^{x}x}{x}^2+25x^4)}^3}dx-\frac{40}{3}\int \frac{e^x{x}^2}{{(e^{2e^{x}x}+x-10e^{e^{x}x}{x}^2+25x^4)}^3}dx+\frac{40}{3}\int \frac{e^x}{{(e^{2e^{x}x}+x-10e^{e^{x}x}{x}^2+25x^4)}^2}dx+\frac{40}{3}\int \frac{e^{x}x}{{(e^{2e^{x}x}+x-10e^{e^{x}x}{x}^2+25x^4)}^2}dx+\frac{200}{3}\int \frac{e^{x+e^{x}x}{x}^2}{{(e^{2e^{x}x}+x-10e^{e^{x}x}{x}^2+25x^4)}^3}dx+\frac{200}{3}\int \frac{e^{x+e^{x}x}{x}^3}{{(e^{2e^{x}x}+x-10e^{e^{x}x}{x}^2+25x^4)}^3}dx-\frac{400}{3}\int \frac{e^{e^{x}x}x}{{(e^{2e^{x}x}+x-10e^{e^{x}x}{x}^2+25x^4)}^3}dx-\frac{1000}{3}\int \frac{e^x{x}^4}{{(e^{2e^{x}x}+x-10e^{e^{x}x}{x}^2+25x^4)}^3}dx-\frac{1000}{3}\int \frac{e^x{x}^5}{{(e^{2e^{x}x}+x-10e^{e^{x}x}{x}^2+25x^4)}^3}dx+\frac{2000}{3}\int \frac{x^3}{{(e^{2e^{x}x}+x-10e^{e^{x}x}{x}^2+25x^4)}^3}dx\end{array}\end{array}$$

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Mathematica [A]  time = 0.16, size = 40, normalized size = 1.54 $$\begin{array}{c}\frac{1}{3}(-\frac{10}{{(e^{2e^{x}x}+x-10e^{e^{x}x}{x}^2+25x^4)}^2}+3\log (x))\end{array}$$

Antiderivative was successfully verified.

[In]

Integrate[(3*E^(6*E^x*x) + 20*x - 90*E^(5*E^x*x)*x^2 + 3*x^3 + 2000*x^4 + 225*x^6 + 5625*x^9 + 46875*x^12 + E^
(4*E^x*x)*(9*x + 1125*x^4) + E^(3*E^x*x)*(-180*x^3 - 7500*x^6) + E^(2*E^x*x)*(9*x^2 + 1350*x^5 + 28125*x^8 + E
^x*(40*x + 40*x^2)) + E^(E^x*x)*(-400*x^2 - 90*x^4 - 4500*x^7 - 56250*x^10 + E^x*(-200*x^3 - 200*x^4)))/(3*E^(
6*E^x*x)*x - 90*E^(5*E^x*x)*x^3 + 3*x^4 + 225*x^7 + 5625*x^10 + 46875*x^13 + E^(4*E^x*x)*(9*x^2 + 1125*x^5) +
E^(3*E^x*x)*(-180*x^4 - 7500*x^7) + E^(2*E^x*x)*(9*x^3 + 1350*x^6 + 28125*x^9) + E^(E^x*x)*(-90*x^5 - 4500*x^8
- 56250*x^11)),x]

[Out]

(-10/(E^(2*E^x*x) + x - 10*E^(E^x*x)*x^2 + 25*x^4)^2 + 3*Log[x])/3

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fricas [B]  time = 0.74, size = 144, normalized size = 5.54 $$\begin{array}{c}-\frac{60x^2{e}^{\left(3x{e}^x\right)}\log (x)-6(75x^4+x)e^{\left(2x{e}^x\right)}\log (x)+60(25x^6+x^3)e^{\left(x{e}^x\right)}\log (x)-3(625x^8+50x^5+x^2)\log (x)-3e^{\left(4x{e}^x\right)}\log (x)+10}{3(625x^8+50x^5-20x^2{e}^{\left(3x{e}^x\right)}+x^2+2(75x^4+x)e^{\left(2x{e}^x\right)}-20(25x^6+x^3)e^{\left(x{e}^x\right)}+e^{\left(4x{e}^x\right)})}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((3*exp(exp(x)*x)^6-90*x^2*exp(exp(x)*x)^5+(1125*x^4+9*x)*exp(exp(x)*x)^4+(-7500*x^6-180*x^3)*exp(exp
(x)*x)^3+((40*x^2+40*x)*exp(x)+28125*x^8+1350*x^5+9*x^2)*exp(exp(x)*x)^2+((-200*x^4-200*x^3)*exp(x)-56250*x^10
-4500*x^7-90*x^4-400*x^2)*exp(exp(x)*x)+46875*x^12+5625*x^9+225*x^6+2000*x^4+3*x^3+20*x)/(3*x*exp(exp(x)*x)^6-
90*x^3*exp(exp(x)*x)^5+(1125*x^5+9*x^2)*exp(exp(x)*x)^4+(-7500*x^7-180*x^4)*exp(exp(x)*x)^3+(28125*x^9+1350*x^
6+9*x^3)*exp(exp(x)*x)^2+(-56250*x^11-4500*x^8-90*x^5)*exp(exp(x)*x)+46875*x^13+5625*x^10+225*x^7+3*x^4),x, al
gorithm="fricas")

[Out]

-1/3*(60*x^2*e^(3*x*e^x)*log(x) - 6*(75*x^4 + x)*e^(2*x*e^x)*log(x) + 60*(25*x^6 + x^3)*e^(x*e^x)*log(x) - 3*(
625*x^8 + 50*x^5 + x^2)*log(x) - 3*e^(4*x*e^x)*log(x) + 10)/(625*x^8 + 50*x^5 - 20*x^2*e^(3*x*e^x) + x^2 + 2*(
75*x^4 + x)*e^(2*x*e^x) - 20*(25*x^6 + x^3)*e^(x*e^x) + e^(4*x*e^x))

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giac [B]  time = 36.95, size = 169, normalized size = 6.50 $$\begin{array}{c}\frac{1875x^8\log (x)-1500x^6{e}^{\left(x{e}^x\right)}\log (x)+150x^5\log (x)+450x^4{e}^{\left(2x{e}^x\right)}\log (x)-60x^3{e}^{\left(x{e}^x\right)}\log (x)-60x^2{e}^{\left(3x{e}^x\right)}\log (x)+3x^2\log (x)+6x{e}^{\left(2x{e}^x\right)}\log (x)+3e^{\left(4x{e}^x\right)}\log (x)-20}{3(625x^8-500x^6{e}^{\left(x{e}^x\right)}+50x^5+150x^4{e}^{\left(2x{e}^x\right)}-20x^3{e}^{\left(x{e}^x\right)}-20x^2{e}^{\left(3x{e}^x\right)}+x^2+2x{e}^{\left(2x{e}^x\right)}+e^{\left(4x{e}^x\right)})}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((3*exp(exp(x)*x)^6-90*x^2*exp(exp(x)*x)^5+(1125*x^4+9*x)*exp(exp(x)*x)^4+(-7500*x^6-180*x^3)*exp(exp
(x)*x)^3+((40*x^2+40*x)*exp(x)+28125*x^8+1350*x^5+9*x^2)*exp(exp(x)*x)^2+((-200*x^4-200*x^3)*exp(x)-56250*x^10
-4500*x^7-90*x^4-400*x^2)*exp(exp(x)*x)+46875*x^12+5625*x^9+225*x^6+2000*x^4+3*x^3+20*x)/(3*x*exp(exp(x)*x)^6-
90*x^3*exp(exp(x)*x)^5+(1125*x^5+9*x^2)*exp(exp(x)*x)^4+(-7500*x^7-180*x^4)*exp(exp(x)*x)^3+(28125*x^9+1350*x^
6+9*x^3)*exp(exp(x)*x)^2+(-56250*x^11-4500*x^8-90*x^5)*exp(exp(x)*x)+46875*x^13+5625*x^10+225*x^7+3*x^4),x, al
gorithm="giac")

[Out]

1/3*(1875*x^8*log(x) - 1500*x^6*e^(x*e^x)*log(x) + 150*x^5*log(x) + 450*x^4*e^(2*x*e^x)*log(x) - 60*x^3*e^(x*e
^x)*log(x) - 60*x^2*e^(3*x*e^x)*log(x) + 3*x^2*log(x) + 6*x*e^(2*x*e^x)*log(x) + 3*e^(4*x*e^x)*log(x) - 20)/(6
25*x^8 - 500*x^6*e^(x*e^x) + 50*x^5 + 150*x^4*e^(2*x*e^x) - 20*x^3*e^(x*e^x) - 20*x^2*e^(3*x*e^x) + x^2 + 2*x*
e^(2*x*e^x) + e^(4*x*e^x))

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maple [A]  time = 0.09, size = 31, normalized size = 1.19

method	result	size
risch	$\ln (x)-\frac{10}{3{(25x^4-10{\mathrm{e}}^{{\mathrm{e}}^{x}x}{x}^2+{\mathrm{e}}^{2{\mathrm{e}}^{x}x}+x)}^2}$	$31$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((3*exp(exp(x)*x)^6-90*x^2*exp(exp(x)*x)^5+(1125*x^4+9*x)*exp(exp(x)*x)^4+(-7500*x^6-180*x^3)*exp(exp(x)*x)
^3+((40*x^2+40*x)*exp(x)+28125*x^8+1350*x^5+9*x^2)*exp(exp(x)*x)^2+((-200*x^4-200*x^3)*exp(x)-56250*x^10-4500*
x^7-90*x^4-400*x^2)*exp(exp(x)*x)+46875*x^12+5625*x^9+225*x^6+2000*x^4+3*x^3+20*x)/(3*x*exp(exp(x)*x)^6-90*x^3
*exp(exp(x)*x)^5+(1125*x^5+9*x^2)*exp(exp(x)*x)^4+(-7500*x^7-180*x^4)*exp(exp(x)*x)^3+(28125*x^9+1350*x^6+9*x^
3)*exp(exp(x)*x)^2+(-56250*x^11-4500*x^8-90*x^5)*exp(exp(x)*x)+46875*x^13+5625*x^10+225*x^7+3*x^4),x,method=_R
ETURNVERBOSE)

[Out]

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

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maxima [B]  time = 0.96, size = 69, normalized size = 2.65 $$\begin{array}{c}-\frac{10}{3(625x^8+50x^5-20x^2{e}^{\left(3x{e}^x\right)}+x^2+2(75x^4+x)e^{\left(2x{e}^x\right)}-20(25x^6+x^3)e^{\left(x{e}^x\right)}+e^{\left(4x{e}^x\right)})}+\log (x)\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((3*exp(exp(x)*x)^6-90*x^2*exp(exp(x)*x)^5+(1125*x^4+9*x)*exp(exp(x)*x)^4+(-7500*x^6-180*x^3)*exp(exp
(x)*x)^3+((40*x^2+40*x)*exp(x)+28125*x^8+1350*x^5+9*x^2)*exp(exp(x)*x)^2+((-200*x^4-200*x^3)*exp(x)-56250*x^10
-4500*x^7-90*x^4-400*x^2)*exp(exp(x)*x)+46875*x^12+5625*x^9+225*x^6+2000*x^4+3*x^3+20*x)/(3*x*exp(exp(x)*x)^6-
90*x^3*exp(exp(x)*x)^5+(1125*x^5+9*x^2)*exp(exp(x)*x)^4+(-7500*x^7-180*x^4)*exp(exp(x)*x)^3+(28125*x^9+1350*x^
6+9*x^3)*exp(exp(x)*x)^2+(-56250*x^11-4500*x^8-90*x^5)*exp(exp(x)*x)+46875*x^13+5625*x^10+225*x^7+3*x^4),x, al
gorithm="maxima")

[Out]

-10/3/(625*x^8 + 50*x^5 - 20*x^2*e^(3*x*e^x) + x^2 + 2*(75*x^4 + x)*e^(2*x*e^x) - 20*(25*x^6 + x^3)*e^(x*e^x)
+ e^(4*x*e^x)) + log(x)

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mupad [F]  time = 0.00, size = -1, normalized size = -0.04 $$\begin{array}{c}\int \frac{20x+3{\mathrm{e}}^{6x{\mathrm{e}}^x}+{\mathrm{e}}^{2x{\mathrm{e}}^x}({\mathrm{e}}^x(40x^2+40x)+9x^2+1350x^5+28125x^8)-{\mathrm{e}}^{3x{\mathrm{e}}^x}(7500x^6+180x^3)-90x^2{\mathrm{e}}^{5x{\mathrm{e}}^x}-{\mathrm{e}}^{x{\mathrm{e}}^x}({\mathrm{e}}^x(200x^4+200x^3)+400x^2+90x^4+4500x^7+56250x^{10})+3x^3+2000x^4+225x^6+5625x^9+46875x^{12}+{\mathrm{e}}^{4x{\mathrm{e}}^x}(1125x^4+9x)}{{\mathrm{e}}^{4x{\mathrm{e}}^x}(1125x^5+9x^2)-{\mathrm{e}}^{3x{\mathrm{e}}^x}(7500x^7+180x^4)-90x^3{\mathrm{e}}^{5x{\mathrm{e}}^x}+{\mathrm{e}}^{2x{\mathrm{e}}^x}(28125x^9+1350x^6+9x^3)-{\mathrm{e}}^{x{\mathrm{e}}^x}(56250x^{11}+4500x^8+90x^5)+3x^4+225x^7+5625x^{10}+46875x^{13}+3x{\mathrm{e}}^{6x{\mathrm{e}}^x}}dx\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((20*x + 3*exp(6*x*exp(x)) + exp(2*x*exp(x))*(exp(x)*(40*x + 40*x^2) + 9*x^2 + 1350*x^5 + 28125*x^8) - exp(
3*x*exp(x))*(180*x^3 + 7500*x^6) - 90*x^2*exp(5*x*exp(x)) - exp(x*exp(x))*(exp(x)*(200*x^3 + 200*x^4) + 400*x^
2 + 90*x^4 + 4500*x^7 + 56250*x^10) + 3*x^3 + 2000*x^4 + 225*x^6 + 5625*x^9 + 46875*x^12 + exp(4*x*exp(x))*(9*
x + 1125*x^4))/(exp(4*x*exp(x))*(9*x^2 + 1125*x^5) - exp(3*x*exp(x))*(180*x^4 + 7500*x^7) - 90*x^3*exp(5*x*exp
(x)) + exp(2*x*exp(x))*(9*x^3 + 1350*x^6 + 28125*x^9) - exp(x*exp(x))*(90*x^5 + 4500*x^8 + 56250*x^11) + 3*x^4
+ 225*x^7 + 5625*x^10 + 46875*x^13 + 3*x*exp(6*x*exp(x))),x)

[Out]

int((20*x + 3*exp(6*x*exp(x)) + exp(2*x*exp(x))*(exp(x)*(40*x + 40*x^2) + 9*x^2 + 1350*x^5 + 28125*x^8) - exp(
3*x*exp(x))*(180*x^3 + 7500*x^6) - 90*x^2*exp(5*x*exp(x)) - exp(x*exp(x))*(exp(x)*(200*x^3 + 200*x^4) + 400*x^
2 + 90*x^4 + 4500*x^7 + 56250*x^10) + 3*x^3 + 2000*x^4 + 225*x^6 + 5625*x^9 + 46875*x^12 + exp(4*x*exp(x))*(9*
x + 1125*x^4))/(exp(4*x*exp(x))*(9*x^2 + 1125*x^5) - exp(3*x*exp(x))*(180*x^4 + 7500*x^7) - 90*x^3*exp(5*x*exp
(x)) + exp(2*x*exp(x))*(9*x^3 + 1350*x^6 + 28125*x^9) - exp(x*exp(x))*(90*x^5 + 4500*x^8 + 56250*x^11) + 3*x^4
+ 225*x^7 + 5625*x^10 + 46875*x^13 + 3*x*exp(6*x*exp(x))), x)

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sympy [B]  time = 0.48, size = 78, normalized size = 3.00 $$\begin{array}{c}\log (x)-\frac{10}{1875x^8+150x^5-60x^2{e}^{3x{e}^x}+3x^2+(450x^4+6x)e^{2x{e}^x}+(-1500x^6-60x^3)e^{x{e}^x}+3e^{4x{e}^x}}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((3*exp(exp(x)*x)**6-90*x**2*exp(exp(x)*x)**5+(1125*x**4+9*x)*exp(exp(x)*x)**4+(-7500*x**6-180*x**3)*
exp(exp(x)*x)**3+((40*x**2+40*x)*exp(x)+28125*x**8+1350*x**5+9*x**2)*exp(exp(x)*x)**2+((-200*x**4-200*x**3)*ex
p(x)-56250*x**10-4500*x**7-90*x**4-400*x**2)*exp(exp(x)*x)+46875*x**12+5625*x**9+225*x**6+2000*x**4+3*x**3+20*
x)/(3*x*exp(exp(x)*x)**6-90*x**3*exp(exp(x)*x)**5+(1125*x**5+9*x**2)*exp(exp(x)*x)**4+(-7500*x**7-180*x**4)*ex
p(exp(x)*x)**3+(28125*x**9+1350*x**6+9*x**3)*exp(exp(x)*x)**2+(-56250*x**11-4500*x**8-90*x**5)*exp(exp(x)*x)+4
6875*x**13+5625*x**10+225*x**7+3*x**4),x)

[Out]

log(x) - 10/(1875*x**8 + 150*x**5 - 60*x**2*exp(3*x*exp(x)) + 3*x**2 + (450*x**4 + 6*x)*exp(2*x*exp(x)) + (-15
00*x**6 - 60*x**3)*exp(x*exp(x)) + 3*exp(4*x*exp(x)))

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