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

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

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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 {gather*} \int \frac {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} \left (9 x+1125 x^4\right )+e^{3 e^x x} \left (-180 x^3-7500 x^6\right )+e^{2 e^x x} \left (9 x^2+1350 x^5+28125 x^8+e^x \left (40 x+40 x^2\right )\right )+e^{e^x x} \left (-400 x^2-90 x^4-4500 x^7-56250 x^{10}+e^x \left (-200 x^3-200 x^4\right )\right )}{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} \left (9 x^2+1125 x^5\right )+e^{3 e^x x} \left (-180 x^4-7500 x^7\right )+e^{2 e^x x} \left (9 x^3+1350 x^6+28125 x^9\right )+e^{e^x x} \left (-90 x^5-4500 x^8-56250 x^{11}\right )} \, dx \end {gather*}

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

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

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 {gather*} -\frac {60 \, x^{2} e^{\left (3 \, x e^{x}\right )} \log \relax (x) - 6 \, {\left (75 \, x^{4} + x\right )} e^{\left (2 \, x e^{x}\right )} \log \relax (x) + 60 \, {\left (25 \, x^{6} + x^{3}\right )} e^{\left (x e^{x}\right )} \log \relax (x) - 3 \, {\left (625 \, x^{8} + 50 \, x^{5} + x^{2}\right )} \log \relax (x) - 3 \, e^{\left (4 \, x e^{x}\right )} \log \relax (x) + 10}{3 \, {\left (625 \, x^{8} + 50 \, x^{5} - 20 \, x^{2} e^{\left (3 \, x e^{x}\right )} + x^{2} + 2 \, {\left (75 \, x^{4} + x\right )} e^{\left (2 \, x e^{x}\right )} - 20 \, {\left (25 \, x^{6} + x^{3}\right )} e^{\left (x e^{x}\right )} + e^{\left (4 \, x e^{x}\right )}\right )}} \end {gather*}

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 {gather*} \frac {1875 \, x^{8} \log \relax (x) - 1500 \, x^{6} e^{\left (x e^{x}\right )} \log \relax (x) + 150 \, x^{5} \log \relax (x) + 450 \, x^{4} e^{\left (2 \, x e^{x}\right )} \log \relax (x) - 60 \, x^{3} e^{\left (x e^{x}\right )} \log \relax (x) - 60 \, x^{2} e^{\left (3 \, x e^{x}\right )} \log \relax (x) + 3 \, x^{2} \log \relax (x) + 6 \, x e^{\left (2 \, x e^{x}\right )} \log \relax (x) + 3 \, e^{\left (4 \, x e^{x}\right )} \log \relax (x) - 20}{3 \, {\left (625 \, x^{8} - 500 \, x^{6} e^{\left (x e^{x}\right )} + 50 \, x^{5} + 150 \, x^{4} e^{\left (2 \, x e^{x}\right )} - 20 \, x^{3} e^{\left (x e^{x}\right )} - 20 \, x^{2} e^{\left (3 \, x e^{x}\right )} + x^{2} + 2 \, x e^{\left (2 \, x e^{x}\right )} + e^{\left (4 \, x e^{x}\right )}\right )}} \end {gather*}

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	\(\ln \relax (x )-\frac {10}{3 \left (25 x^{4}-10 \,{\mathrm e}^{{\mathrm e}^{x} x} x^{2}+{\mathrm e}^{2 \,{\mathrm e}^{x} x}+x \right )^{2}}\)	\(31\)

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 {gather*} -\frac {10}{3 \, {\left (625 \, x^{8} + 50 \, x^{5} - 20 \, x^{2} e^{\left (3 \, x e^{x}\right )} + x^{2} + 2 \, {\left (75 \, x^{4} + x\right )} e^{\left (2 \, x e^{x}\right )} - 20 \, {\left (25 \, x^{6} + x^{3}\right )} e^{\left (x e^{x}\right )} + e^{\left (4 \, x e^{x}\right )}\right )}} + \log \relax (x) \end {gather*}

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 {gather*} \int \frac {20\,x+3\,{\mathrm {e}}^{6\,x\,{\mathrm {e}}^x}+{\mathrm {e}}^{2\,x\,{\mathrm {e}}^x}\,\left ({\mathrm {e}}^x\,\left (40\,x^2+40\,x\right )+9\,x^2+1350\,x^5+28125\,x^8\right )-{\mathrm {e}}^{3\,x\,{\mathrm {e}}^x}\,\left (7500\,x^6+180\,x^3\right )-90\,x^2\,{\mathrm {e}}^{5\,x\,{\mathrm {e}}^x}-{\mathrm {e}}^{x\,{\mathrm {e}}^x}\,\left ({\mathrm {e}}^x\,\left (200\,x^4+200\,x^3\right )+400\,x^2+90\,x^4+4500\,x^7+56250\,x^{10}\right )+3\,x^3+2000\,x^4+225\,x^6+5625\,x^9+46875\,x^{12}+{\mathrm {e}}^{4\,x\,{\mathrm {e}}^x}\,\left (1125\,x^4+9\,x\right )}{{\mathrm {e}}^{4\,x\,{\mathrm {e}}^x}\,\left (1125\,x^5+9\,x^2\right )-{\mathrm {e}}^{3\,x\,{\mathrm {e}}^x}\,\left (7500\,x^7+180\,x^4\right )-90\,x^3\,{\mathrm {e}}^{5\,x\,{\mathrm {e}}^x}+{\mathrm {e}}^{2\,x\,{\mathrm {e}}^x}\,\left (28125\,x^9+1350\,x^6+9\,x^3\right )-{\mathrm {e}}^{x\,{\mathrm {e}}^x}\,\left (56250\,x^{11}+4500\,x^8+90\,x^5\right )+3\,x^4+225\,x^7+5625\,x^{10}+46875\,x^{13}+3\,x\,{\mathrm {e}}^{6\,x\,{\mathrm {e}}^x}} \,d x \end {gather*}

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 {gather*} \log {\relax (x )} - \frac {10}{1875 x^{8} + 150 x^{5} - 60 x^{2} e^{3 x e^{x}} + 3 x^{2} + \left (450 x^{4} + 6 x\right ) e^{2 x e^{x}} + \left (- 1500 x^{6} - 60 x^{3}\right ) e^{x e^{x}} + 3 e^{4 x e^{x}}} \end {gather*}

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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