3.100.26 \(\int \frac {e^{2 e^{-\frac {e^4}{45+5 e+30 x+5 x^2}}-\frac {e^4}{45+5 e+30 x+5 x^2}} (e^9 (12+4 x)+e^4 (-12 x-4 x^2)+e^{\frac {e^4}{45+5 e+30 x+5 x^2}} (405+5 e^2+540 x+270 x^2+60 x^3+5 x^4+e (90+60 x+10 x^2)))}{405 x^2+5 e^2 x^2+540 x^3+270 x^4+60 x^5+5 x^6+e (90 x^2+60 x^3+10 x^4)+e^{10} (405+5 e^2+540 x+270 x^2+60 x^3+5 x^4+e (90+60 x+10 x^2))+e^5 (-810 x-10 e^2 x-1080 x^2-540 x^3-120 x^4-10 x^5+e (-180 x-120 x^2-20 x^3))} \, dx\)

Optimal. Leaf size=32 \[ \frac {e^{2 e^{-\frac {e^4}{5 \left (e+(3+x)^2\right )}}}}{e^5-x} \]

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Rubi [F]  time = 103.11, 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 {\exp \left (2 e^{-\frac {e^4}{45+5 e+30 x+5 x^2}}-\frac {e^4}{45+5 e+30 x+5 x^2}\right ) \left (e^9 (12+4 x)+e^4 \left (-12 x-4 x^2\right )+e^{\frac {e^4}{45+5 e+30 x+5 x^2}} \left (405+5 e^2+540 x+270 x^2+60 x^3+5 x^4+e \left (90+60 x+10 x^2\right )\right )\right )}{405 x^2+5 e^2 x^2+540 x^3+270 x^4+60 x^5+5 x^6+e \left (90 x^2+60 x^3+10 x^4\right )+e^{10} \left (405+5 e^2+540 x+270 x^2+60 x^3+5 x^4+e \left (90+60 x+10 x^2\right )\right )+e^5 \left (-810 x-10 e^2 x-1080 x^2-540 x^3-120 x^4-10 x^5+e \left (-180 x-120 x^2-20 x^3\right )\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^(2/E^(E^4/(45 + 5*E + 30*x + 5*x^2)) - E^4/(45 + 5*E + 30*x + 5*x^2))*(E^9*(12 + 4*x) + E^4*(-12*x - 4*
x^2) + E^(E^4/(45 + 5*E + 30*x + 5*x^2))*(405 + 5*E^2 + 540*x + 270*x^2 + 60*x^3 + 5*x^4 + E*(90 + 60*x + 10*x
^2))))/(405*x^2 + 5*E^2*x^2 + 540*x^3 + 270*x^4 + 60*x^5 + 5*x^6 + E*(90*x^2 + 60*x^3 + 10*x^4) + E^10*(405 +
5*E^2 + 540*x + 270*x^2 + 60*x^3 + 5*x^4 + E*(90 + 60*x + 10*x^2)) + E^5*(-810*x - 10*E^2*x - 1080*x^2 - 540*x
^3 - 120*x^4 - 10*x^5 + E*(-180*x - 120*x^2 - 20*x^3))),x]

[Out]

(-4*(9 + E)*(9 - E + 6*E^5 + E^10)*Defer[Int][E^(3 + 2/E^(E^4/(5*(E + (3 + x)^2))) - E^4/(5*(E + (3 + x)^2)))/
(-6 + (2*I)*Sqrt[E] - 2*x)^2, x])/(5*(9 + E + 6*E^5 + E^10)^2) + (4*(3 - I*Sqrt[E])*(27 + 3*E + 18*E^5 + 2*E^6
+ 3*E^10)*Defer[Int][E^(3 + 2/E^(E^4/(5*(E + (3 + x)^2))) - E^4/(5*(E + (3 + x)^2)))/(-6 + (2*I)*Sqrt[E] - 2*
x)^2, x])/(5*(9 + E + 6*E^5 + E^10)^2) + (4*(3 - I*Sqrt[E])*(9 - E + 6*E^5 + E^10)*Defer[Int][E^(8 + 2/E^(E^4/
(5*(E + (3 + x)^2))) - E^4/(5*(E + (3 + x)^2)))/(-6 + (2*I)*Sqrt[E] - 2*x)^2, x])/(5*(9 + E + 6*E^5 + E^10)^2)
- (4*(27 - 9*E + 18*E^5 - 2*E^6 + 3*E^10)*Defer[Int][E^(8 + 2/E^(E^4/(5*(E + (3 + x)^2))) - E^4/(5*(E + (3 +
x)^2)))/(-6 + (2*I)*Sqrt[E] - 2*x)^2, x])/(5*(9 + E + 6*E^5 + E^10)^2) + (((2*I)/5)*(9 + E)*(9 - E + 6*E^5 + E
^10)*Defer[Int][E^(5/2 + 2/E^(E^4/(5*(E + (3 + x)^2))) - E^4/(5*(E + (3 + x)^2)))/(-6 + (2*I)*Sqrt[E] - 2*x),
x])/(9 + E + 6*E^5 + E^10)^2 - (((6*I)/5)*(27 + 3*E + 18*E^5 + 2*E^6 + 3*E^10)*Defer[Int][E^(5/2 + 2/E^(E^4/(5
*(E + (3 + x)^2))) - E^4/(5*(E + (3 + x)^2)))/(-6 + (2*I)*Sqrt[E] - 2*x), x])/(9 + E + 6*E^5 + E^10)^2 - (((6*
I)/5)*(9 - E + 6*E^5 + E^10)*Defer[Int][E^(15/2 + 2/E^(E^4/(5*(E + (3 + x)^2))) - E^4/(5*(E + (3 + x)^2)))/(-6
+ (2*I)*Sqrt[E] - 2*x), x])/(9 + E + 6*E^5 + E^10)^2 + (((2*I)/5)*(27 - 9*E + 18*E^5 - 2*E^6 + 3*E^10)*Defer[
Int][E^(15/2 + 2/E^(E^4/(5*(E + (3 + x)^2))) - E^4/(5*(E + (3 + x)^2)))/(-6 + (2*I)*Sqrt[E] - 2*x), x])/(9 + E
+ 6*E^5 + E^10)^2 + Defer[Int][E^(2/E^(E^4/(5*(9 + E + 6*x + x^2))))/(E^5 - x)^2, x] + (4*(27 + 3*E + 2*E^6 -
9*E^10 - 2*E^15)*Defer[Int][E^(4 + 2/E^(E^4/(5*(E + (3 + x)^2))) - E^4/(5*(E + (3 + x)^2)))/(E^5 - x), x])/(5
*(9 + E + 6*E^5 + E^10)^3) + (4*(27 - E + 18*E^5 + 3*E^10)*Defer[Int][E^(9 + 2/E^(E^4/(5*(E + (3 + x)^2))) - E
^4/(5*(E + (3 + x)^2)))/(E^5 - x), x])/(5*(9 + E + 6*E^5 + E^10)^3) + (4*(27 + 3*E + 2*E^6 - 9*E^10 - 2*E^15 -
(I*(81 + 9*E + 54*E^5 + 12*E^6 + 3*E^11 - 6*E^15 - E^20))/Sqrt[E])*Defer[Int][E^(4 + 2/E^(E^4/(5*(E + (3 + x)
^2))) - E^4/(5*(E + (3 + x)^2)))/(6 - (2*I)*Sqrt[E] + 2*x), x])/(5*(9 + E + 6*E^5 + E^10)^3) + (4*(27 - E + 18
*E^5 + 3*E^10 - ((2*I)*(27 - 3*E + 27*E^5 - E^6 + 9*E^10 + E^15))/Sqrt[E])*Defer[Int][E^(9 + 2/E^(E^4/(5*(E +
(3 + x)^2))) - E^4/(5*(E + (3 + x)^2)))/(6 - (2*I)*Sqrt[E] + 2*x), x])/(5*(9 + E + 6*E^5 + E^10)^3) - (4*(9 +
E)*(9 - E + 6*E^5 + E^10)*Defer[Int][E^(3 + 2/E^(E^4/(5*(E + (3 + x)^2))) - E^4/(5*(E + (3 + x)^2)))/(6 + (2*I
)*Sqrt[E] + 2*x)^2, x])/(5*(9 + E + 6*E^5 + E^10)^2) + (4*(3 + I*Sqrt[E])*(27 + 3*E + 18*E^5 + 2*E^6 + 3*E^10)
*Defer[Int][E^(3 + 2/E^(E^4/(5*(E + (3 + x)^2))) - E^4/(5*(E + (3 + x)^2)))/(6 + (2*I)*Sqrt[E] + 2*x)^2, x])/(
5*(9 + E + 6*E^5 + E^10)^2) + (4*(3 + I*Sqrt[E])*(9 - E + 6*E^5 + E^10)*Defer[Int][E^(8 + 2/E^(E^4/(5*(E + (3
+ x)^2))) - E^4/(5*(E + (3 + x)^2)))/(6 + (2*I)*Sqrt[E] + 2*x)^2, x])/(5*(9 + E + 6*E^5 + E^10)^2) - (4*(27 -
9*E + 18*E^5 - 2*E^6 + 3*E^10)*Defer[Int][E^(8 + 2/E^(E^4/(5*(E + (3 + x)^2))) - E^4/(5*(E + (3 + x)^2)))/(6 +
(2*I)*Sqrt[E] + 2*x)^2, x])/(5*(9 + E + 6*E^5 + E^10)^2) + (((2*I)/5)*(9 + E)*(9 - E + 6*E^5 + E^10)*Defer[In
t][E^(5/2 + 2/E^(E^4/(5*(E + (3 + x)^2))) - E^4/(5*(E + (3 + x)^2)))/(6 + (2*I)*Sqrt[E] + 2*x), x])/(9 + E + 6
*E^5 + E^10)^2 - (((6*I)/5)*(27 + 3*E + 18*E^5 + 2*E^6 + 3*E^10)*Defer[Int][E^(5/2 + 2/E^(E^4/(5*(E + (3 + x)^
2))) - E^4/(5*(E + (3 + x)^2)))/(6 + (2*I)*Sqrt[E] + 2*x), x])/(9 + E + 6*E^5 + E^10)^2 + (4*(27 + 3*E + 2*E^6
- 9*E^10 - 2*E^15 + (I*(81 + 9*E + 54*E^5 + 12*E^6 + 3*E^11 - 6*E^15 - E^20))/Sqrt[E])*Defer[Int][E^(4 + 2/E^
(E^4/(5*(E + (3 + x)^2))) - E^4/(5*(E + (3 + x)^2)))/(6 + (2*I)*Sqrt[E] + 2*x), x])/(5*(9 + E + 6*E^5 + E^10)^
3) - (((6*I)/5)*(9 - E + 6*E^5 + E^10)*Defer[Int][E^(15/2 + 2/E^(E^4/(5*(E + (3 + x)^2))) - E^4/(5*(E + (3 + x
)^2)))/(6 + (2*I)*Sqrt[E] + 2*x), x])/(9 + E + 6*E^5 + E^10)^2 + (((2*I)/5)*(27 - 9*E + 18*E^5 - 2*E^6 + 3*E^1
0)*Defer[Int][E^(15/2 + 2/E^(E^4/(5*(E + (3 + x)^2))) - E^4/(5*(E + (3 + x)^2)))/(6 + (2*I)*Sqrt[E] + 2*x), x]
)/(9 + E + 6*E^5 + E^10)^2 + (4*(27 - E + 18*E^5 + 3*E^10 + ((2*I)*(27 - 3*E + 27*E^5 - E^6 + 9*E^10 + E^15))/
Sqrt[E])*Defer[Int][E^(9 + 2/E^(E^4/(5*(E + (3 + x)^2))) - E^4/(5*(E + (3 + x)^2)))/(6 + (2*I)*Sqrt[E] + 2*x),
x])/(5*(9 + E + 6*E^5 + E^10)^3)

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {\exp \left (2 e^{-\frac {e^4}{45+5 e+30 x+5 x^2}}-\frac {e^4}{45+5 e+30 x+5 x^2}\right ) \left (e^9 (12+4 x)+e^4 \left (-12 x-4 x^2\right )+e^{\frac {e^4}{45+5 e+30 x+5 x^2}} \left (405+5 e^2+540 x+270 x^2+60 x^3+5 x^4+e \left (90+60 x+10 x^2\right )\right )\right )}{\left (405+5 e^2\right ) x^2+540 x^3+270 x^4+60 x^5+5 x^6+e \left (90 x^2+60 x^3+10 x^4\right )+e^{10} \left (405+5 e^2+540 x+270 x^2+60 x^3+5 x^4+e \left (90+60 x+10 x^2\right )\right )+e^5 \left (-810 x-10 e^2 x-1080 x^2-540 x^3-120 x^4-10 x^5+e \left (-180 x-120 x^2-20 x^3\right )\right )} \, dx\\ &=\int \frac {\exp \left (2 e^{-\frac {e^4}{5 \left (e+(3+x)^2\right )}}-\frac {e^4}{5 \left (e+(3+x)^2\right )}\right ) \left (5 e^{2+\frac {e^4}{5 \left (e+(3+x)^2\right )}}+4 e^9 (3+x)-4 e^4 x (3+x)+10 e^{1+\frac {e^4}{5 \left (e+(3+x)^2\right )}} (3+x)^2+5 e^{\frac {e^4}{5 \left (e+(3+x)^2\right )}} (3+x)^4\right )}{5 \left (e^5 (9+e)-\left (9+e-6 e^5\right ) x-\left (6-e^5\right ) x^2-x^3\right )^2} \, dx\\ &=\frac {1}{5} \int \frac {\exp \left (2 e^{-\frac {e^4}{5 \left (e+(3+x)^2\right )}}-\frac {e^4}{5 \left (e+(3+x)^2\right )}\right ) \left (5 e^{2+\frac {e^4}{5 \left (e+(3+x)^2\right )}}+4 e^9 (3+x)-4 e^4 x (3+x)+10 e^{1+\frac {e^4}{5 \left (e+(3+x)^2\right )}} (3+x)^2+5 e^{\frac {e^4}{5 \left (e+(3+x)^2\right )}} (3+x)^4\right )}{\left (e^5 (9+e)-\left (9+e-6 e^5\right ) x-\left (6-e^5\right ) x^2-x^3\right )^2} \, dx\\ &=\frac {1}{5} \int \left (\frac {5 \exp \left (2 e^{-\frac {e^4}{5 \left (e+(3+x)^2\right )}}+\frac {e^4}{5 \left (9+e+6 x+x^2\right )}-\frac {e^4}{5 \left (e+(3+x)^2\right )}\right )}{\left (e^5-x\right )^2}+\frac {4 \exp \left (9+2 e^{-\frac {e^4}{5 \left (e+(3+x)^2\right )}}-\frac {e^4}{5 \left (e+(3+x)^2\right )}\right ) (3+x)}{\left (e^5-x\right )^2 \left (9+e+6 x+x^2\right )^2}-\frac {4 \exp \left (4+2 e^{-\frac {e^4}{5 \left (e+(3+x)^2\right )}}-\frac {e^4}{5 \left (e+(3+x)^2\right )}\right ) x (3+x)}{\left (e^5-x\right )^2 \left (9+e+6 x+x^2\right )^2}\right ) \, dx\\ &=\frac {4}{5} \int \frac {\exp \left (9+2 e^{-\frac {e^4}{5 \left (e+(3+x)^2\right )}}-\frac {e^4}{5 \left (e+(3+x)^2\right )}\right ) (3+x)}{\left (e^5-x\right )^2 \left (9+e+6 x+x^2\right )^2} \, dx-\frac {4}{5} \int \frac {\exp \left (4+2 e^{-\frac {e^4}{5 \left (e+(3+x)^2\right )}}-\frac {e^4}{5 \left (e+(3+x)^2\right )}\right ) x (3+x)}{\left (e^5-x\right )^2 \left (9+e+6 x+x^2\right )^2} \, dx+\int \frac {\exp \left (2 e^{-\frac {e^4}{5 \left (e+(3+x)^2\right )}}+\frac {e^4}{5 \left (9+e+6 x+x^2\right )}-\frac {e^4}{5 \left (e+(3+x)^2\right )}\right )}{\left (e^5-x\right )^2} \, dx\\ &=\frac {4}{5} \int \left (\frac {\exp \left (9+2 e^{-\frac {e^4}{5 \left (e+(3+x)^2\right )}}-\frac {e^4}{5 \left (e+(3+x)^2\right )}\right ) \left (3+e^5\right )}{\left (9+e+6 e^5+e^{10}\right )^2 \left (e^5-x\right )^2}+\frac {\exp \left (9+2 e^{-\frac {e^4}{5 \left (e+(3+x)^2\right )}}-\frac {e^4}{5 \left (e+(3+x)^2\right )}\right ) \left (27-e+18 e^5+3 e^{10}\right )}{\left (9+e+6 e^5+e^{10}\right )^3 \left (e^5-x\right )}+\frac {\exp \left (9+2 e^{-\frac {e^4}{5 \left (e+(3+x)^2\right )}}-\frac {e^4}{5 \left (e+(3+x)^2\right )}\right ) \left (27-9 e+18 e^5-2 e^6+3 e^{10}+\left (9-e+6 e^5+e^{10}\right ) x\right )}{\left (9+e+6 e^5+e^{10}\right )^2 \left (9+e+6 x+x^2\right )^2}+\frac {\exp \left (9+2 e^{-\frac {e^4}{5 \left (e+(3+x)^2\right )}}-\frac {e^4}{5 \left (e+(3+x)^2\right )}\right ) \left (135-9 e+108 e^5-2 e^6+27 e^{10}+2 e^{15}+\left (27-e+18 e^5+3 e^{10}\right ) x\right )}{\left (9+e+6 e^5+e^{10}\right )^3 \left (9+e+6 x+x^2\right )}\right ) \, dx-\frac {4}{5} \int \left (\frac {\exp \left (9+2 e^{-\frac {e^4}{5 \left (e+(3+x)^2\right )}}-\frac {e^4}{5 \left (e+(3+x)^2\right )}\right ) \left (3+e^5\right )}{\left (9+e+6 e^5+e^{10}\right )^2 \left (e^5-x\right )^2}+\frac {\exp \left (4+2 e^{-\frac {e^4}{5 \left (e+(3+x)^2\right )}}-\frac {e^4}{5 \left (e+(3+x)^2\right )}\right ) \left (-27-3 e-2 e^6+9 e^{10}+2 e^{15}\right )}{\left (9+e+6 e^5+e^{10}\right )^3 \left (e^5-x\right )}+\frac {\exp \left (4+2 e^{-\frac {e^4}{5 \left (e+(3+x)^2\right )}}-\frac {e^4}{5 \left (e+(3+x)^2\right )}\right ) \left (-\left ((9+e) \left (9-e+6 e^5+e^{10}\right )\right )-\left (27+3 e+18 e^5+2 e^6+3 e^{10}\right ) x\right )}{\left (9+e+6 e^5+e^{10}\right )^2 \left (9+e+6 x+x^2\right )^2}+\frac {\exp \left (4+2 e^{-\frac {e^4}{5 \left (e+(3+x)^2\right )}}-\frac {e^4}{5 \left (e+(3+x)^2\right )}\right ) \left (-162-18 e-54 e^5-18 e^6+27 e^{10}-3 e^{11}+12 e^{15}+e^{20}-\left (27+3 e+2 e^6-9 e^{10}-2 e^{15}\right ) x\right )}{\left (9+e+6 e^5+e^{10}\right )^3 \left (9+e+6 x+x^2\right )}\right ) \, dx+\int \frac {e^{2 e^{-\frac {e^4}{5 \left (9+e+6 x+x^2\right )}}}}{\left (e^5-x\right )^2} \, dx\\ &=\frac {4 \int \frac {\exp \left (9+2 e^{-\frac {e^4}{5 \left (e+(3+x)^2\right )}}-\frac {e^4}{5 \left (e+(3+x)^2\right )}\right ) \left (135-9 e+108 e^5-2 e^6+27 e^{10}+2 e^{15}+\left (27-e+18 e^5+3 e^{10}\right ) x\right )}{9+e+6 x+x^2} \, dx}{5 \left (9+e+6 e^5+e^{10}\right )^3}-\frac {4 \int \frac {\exp \left (4+2 e^{-\frac {e^4}{5 \left (e+(3+x)^2\right )}}-\frac {e^4}{5 \left (e+(3+x)^2\right )}\right ) \left (-162-18 e-54 e^5-18 e^6+27 e^{10}-3 e^{11}+12 e^{15}+e^{20}-\left (27+3 e+2 e^6-9 e^{10}-2 e^{15}\right ) x\right )}{9+e+6 x+x^2} \, dx}{5 \left (9+e+6 e^5+e^{10}\right )^3}+\frac {4 \int \frac {\exp \left (9+2 e^{-\frac {e^4}{5 \left (e+(3+x)^2\right )}}-\frac {e^4}{5 \left (e+(3+x)^2\right )}\right ) \left (27-9 e+18 e^5-2 e^6+3 e^{10}+\left (9-e+6 e^5+e^{10}\right ) x\right )}{\left (9+e+6 x+x^2\right )^2} \, dx}{5 \left (9+e+6 e^5+e^{10}\right )^2}-\frac {4 \int \frac {\exp \left (4+2 e^{-\frac {e^4}{5 \left (e+(3+x)^2\right )}}-\frac {e^4}{5 \left (e+(3+x)^2\right )}\right ) \left (-\left ((9+e) \left (9-e+6 e^5+e^{10}\right )\right )-\left (27+3 e+18 e^5+2 e^6+3 e^{10}\right ) x\right )}{\left (9+e+6 x+x^2\right )^2} \, dx}{5 \left (9+e+6 e^5+e^{10}\right )^2}+\frac {\left (4 \left (27-e+18 e^5+3 e^{10}\right )\right ) \int \frac {\exp \left (9+2 e^{-\frac {e^4}{5 \left (e+(3+x)^2\right )}}-\frac {e^4}{5 \left (e+(3+x)^2\right )}\right )}{e^5-x} \, dx}{5 \left (9+e+6 e^5+e^{10}\right )^3}+\frac {\left (4 \left (27+3 e+2 e^6-9 e^{10}-2 e^{15}\right )\right ) \int \frac {\exp \left (4+2 e^{-\frac {e^4}{5 \left (e+(3+x)^2\right )}}-\frac {e^4}{5 \left (e+(3+x)^2\right )}\right )}{e^5-x} \, dx}{5 \left (9+e+6 e^5+e^{10}\right )^3}+\int \frac {e^{2 e^{-\frac {e^4}{5 \left (9+e+6 x+x^2\right )}}}}{\left (e^5-x\right )^2} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.25, size = 33, normalized size = 1.03 \begin {gather*} -\frac {e^{2 e^{-\frac {e^4}{5 \left (e+(3+x)^2\right )}}}}{-e^5+x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^(2/E^(E^4/(45 + 5*E + 30*x + 5*x^2)) - E^4/(45 + 5*E + 30*x + 5*x^2))*(E^9*(12 + 4*x) + E^4*(-12*
x - 4*x^2) + E^(E^4/(45 + 5*E + 30*x + 5*x^2))*(405 + 5*E^2 + 540*x + 270*x^2 + 60*x^3 + 5*x^4 + E*(90 + 60*x
+ 10*x^2))))/(405*x^2 + 5*E^2*x^2 + 540*x^3 + 270*x^4 + 60*x^5 + 5*x^6 + E*(90*x^2 + 60*x^3 + 10*x^4) + E^10*(
405 + 5*E^2 + 540*x + 270*x^2 + 60*x^3 + 5*x^4 + E*(90 + 60*x + 10*x^2)) + E^5*(-810*x - 10*E^2*x - 1080*x^2 -
540*x^3 - 120*x^4 - 10*x^5 + E*(-180*x - 120*x^2 - 20*x^3))),x]

[Out]

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

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fricas [B]  time = 0.91, size = 94, normalized size = 2.94 \begin {gather*} -\frac {e^{\left (\frac {{\left (10 \, x^{2} + 60 \, x + 10 \, e - e^{\left (\frac {e^{4}}{5 \, {\left (x^{2} + 6 \, x + e + 9\right )}} + 4\right )} + 90\right )} e^{\left (-\frac {e^{4}}{5 \, {\left (x^{2} + 6 \, x + e + 9\right )}}\right )}}{5 \, {\left (x^{2} + 6 \, x + e + 9\right )}} + \frac {e^{4}}{5 \, {\left (x^{2} + 6 \, x + e + 9\right )}}\right )}}{x - e^{5}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((5*exp(1)^2+(10*x^2+60*x+90)*exp(1)+5*x^4+60*x^3+270*x^2+540*x+405)*exp(exp(4)/(5*exp(1)+5*x^2+30*x
+45))+(4*x+12)*exp(4)*exp(5)+(-4*x^2-12*x)*exp(4))*exp(2/exp(exp(4)/(5*exp(1)+5*x^2+30*x+45)))/((5*exp(1)^2+(1
0*x^2+60*x+90)*exp(1)+5*x^4+60*x^3+270*x^2+540*x+405)*exp(5)^2+(-10*x*exp(1)^2+(-20*x^3-120*x^2-180*x)*exp(1)-
10*x^5-120*x^4-540*x^3-1080*x^2-810*x)*exp(5)+5*x^2*exp(1)^2+(10*x^4+60*x^3+90*x^2)*exp(1)+5*x^6+60*x^5+270*x^
4+540*x^3+405*x^2)/exp(exp(4)/(5*exp(1)+5*x^2+30*x+45)),x, algorithm="fricas")

[Out]

-e^(1/5*(10*x^2 + 60*x + 10*e - e^(1/5*e^4/(x^2 + 6*x + e + 9) + 4) + 90)*e^(-1/5*e^4/(x^2 + 6*x + e + 9))/(x^
2 + 6*x + e + 9) + 1/5*e^4/(x^2 + 6*x + e + 9))/(x - e^5)

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giac [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((5*exp(1)^2+(10*x^2+60*x+90)*exp(1)+5*x^4+60*x^3+270*x^2+540*x+405)*exp(exp(4)/(5*exp(1)+5*x^2+30*x
+45))+(4*x+12)*exp(4)*exp(5)+(-4*x^2-12*x)*exp(4))*exp(2/exp(exp(4)/(5*exp(1)+5*x^2+30*x+45)))/((5*exp(1)^2+(1
0*x^2+60*x+90)*exp(1)+5*x^4+60*x^3+270*x^2+540*x+405)*exp(5)^2+(-10*x*exp(1)^2+(-20*x^3-120*x^2-180*x)*exp(1)-
10*x^5-120*x^4-540*x^3-1080*x^2-810*x)*exp(5)+5*x^2*exp(1)^2+(10*x^4+60*x^3+90*x^2)*exp(1)+5*x^6+60*x^5+270*x^
4+540*x^3+405*x^2)/exp(exp(4)/(5*exp(1)+5*x^2+30*x+45)),x, algorithm="giac")

[Out]

Timed out

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maple [A]  time = 1.04, size = 30, normalized size = 0.94

method	result	size
risch	\(\frac {{\mathrm e}^{2 \,{\mathrm e}^{-\frac {{\mathrm e}^{4}}{5 \left (x^{2}+{\mathrm e}+6 x +9\right )}}}}{{\mathrm e}^{5}-x}\)	\(30\)
norman	\(\frac {\left (\left ({\mathrm e}+9\right ) {\mathrm e}^{\frac {{\mathrm e}^{4}}{5 \,{\mathrm e}+5 x^{2}+30 x +45}} {\mathrm e}^{2 \,{\mathrm e}^{-\frac {{\mathrm e}^{4}}{5 \,{\mathrm e}+5 x^{2}+30 x +45}}}+{\mathrm e}^{\frac {{\mathrm e}^{4}}{5 \,{\mathrm e}+5 x^{2}+30 x +45}} x^{2} {\mathrm e}^{2 \,{\mathrm e}^{-\frac {{\mathrm e}^{4}}{5 \,{\mathrm e}+5 x^{2}+30 x +45}}}+6 \,{\mathrm e}^{\frac {{\mathrm e}^{4}}{5 \,{\mathrm e}+5 x^{2}+30 x +45}} x \,{\mathrm e}^{2 \,{\mathrm e}^{-\frac {{\mathrm e}^{4}}{5 \,{\mathrm e}+5 x^{2}+30 x +45}}}\right ) {\mathrm e}^{-\frac {{\mathrm e}^{4}}{5 \,{\mathrm e}+5 x^{2}+30 x +45}}}{\left (x^{2}+{\mathrm e}+6 x +9\right ) \left ({\mathrm e}^{5}-x \right )}\)	\(192\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((5*exp(1)^2+(10*x^2+60*x+90)*exp(1)+5*x^4+60*x^3+270*x^2+540*x+405)*exp(exp(4)/(5*exp(1)+5*x^2+30*x+45))+
(4*x+12)*exp(4)*exp(5)+(-4*x^2-12*x)*exp(4))*exp(2/exp(exp(4)/(5*exp(1)+5*x^2+30*x+45)))/((5*exp(1)^2+(10*x^2+
60*x+90)*exp(1)+5*x^4+60*x^3+270*x^2+540*x+405)*exp(5)^2+(-10*x*exp(1)^2+(-20*x^3-120*x^2-180*x)*exp(1)-10*x^5
-120*x^4-540*x^3-1080*x^2-810*x)*exp(5)+5*x^2*exp(1)^2+(10*x^4+60*x^3+90*x^2)*exp(1)+5*x^6+60*x^5+270*x^4+540*
x^3+405*x^2)/exp(exp(4)/(5*exp(1)+5*x^2+30*x+45)),x,method=_RETURNVERBOSE)

[Out]

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

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maxima [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \frac {1}{5} \, \int \frac {{\left (4 \, {\left (x + 3\right )} e^{9} - 4 \, {\left (x^{2} + 3 \, x\right )} e^{4} + 5 \, {\left (x^{4} + 12 \, x^{3} + 54 \, x^{2} + 2 \, {\left (x^{2} + 6 \, x + 9\right )} e + 108 \, x + e^{2} + 81\right )} e^{\left (\frac {e^{4}}{5 \, {\left (x^{2} + 6 \, x + e + 9\right )}}\right )}\right )} e^{\left (-\frac {e^{4}}{5 \, {\left (x^{2} + 6 \, x + e + 9\right )}} + 2 \, e^{\left (-\frac {e^{4}}{5 \, {\left (x^{2} + 6 \, x + e + 9\right )}}\right )}\right )}}{x^{6} + 12 \, x^{5} + 54 \, x^{4} + 108 \, x^{3} + x^{2} e^{2} + 81 \, x^{2} + {\left (x^{4} + 12 \, x^{3} + 54 \, x^{2} + 2 \, {\left (x^{2} + 6 \, x + 9\right )} e + 108 \, x + e^{2} + 81\right )} e^{10} - 2 \, {\left (x^{5} + 12 \, x^{4} + 54 \, x^{3} + 108 \, x^{2} + x e^{2} + 2 \, {\left (x^{3} + 6 \, x^{2} + 9 \, x\right )} e + 81 \, x\right )} e^{5} + 2 \, {\left (x^{4} + 6 \, x^{3} + 9 \, x^{2}\right )} e}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((5*exp(1)^2+(10*x^2+60*x+90)*exp(1)+5*x^4+60*x^3+270*x^2+540*x+405)*exp(exp(4)/(5*exp(1)+5*x^2+30*x
+45))+(4*x+12)*exp(4)*exp(5)+(-4*x^2-12*x)*exp(4))*exp(2/exp(exp(4)/(5*exp(1)+5*x^2+30*x+45)))/((5*exp(1)^2+(1
0*x^2+60*x+90)*exp(1)+5*x^4+60*x^3+270*x^2+540*x+405)*exp(5)^2+(-10*x*exp(1)^2+(-20*x^3-120*x^2-180*x)*exp(1)-
10*x^5-120*x^4-540*x^3-1080*x^2-810*x)*exp(5)+5*x^2*exp(1)^2+(10*x^4+60*x^3+90*x^2)*exp(1)+5*x^6+60*x^5+270*x^
4+540*x^3+405*x^2)/exp(exp(4)/(5*exp(1)+5*x^2+30*x+45)),x, algorithm="maxima")

[Out]

1/5*integrate((4*(x + 3)*e^9 - 4*(x^2 + 3*x)*e^4 + 5*(x^4 + 12*x^3 + 54*x^2 + 2*(x^2 + 6*x + 9)*e + 108*x + e^
2 + 81)*e^(1/5*e^4/(x^2 + 6*x + e + 9)))*e^(-1/5*e^4/(x^2 + 6*x + e + 9) + 2*e^(-1/5*e^4/(x^2 + 6*x + e + 9)))
/(x^6 + 12*x^5 + 54*x^4 + 108*x^3 + x^2*e^2 + 81*x^2 + (x^4 + 12*x^3 + 54*x^2 + 2*(x^2 + 6*x + 9)*e + 108*x +
e^2 + 81)*e^10 - 2*(x^5 + 12*x^4 + 54*x^3 + 108*x^2 + x*e^2 + 2*(x^3 + 6*x^2 + 9*x)*e + 81*x)*e^5 + 2*(x^4 + 6
*x^3 + 9*x^2)*e), x)

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mupad [B]  time = 9.06, size = 34, normalized size = 1.06 \begin {gather*} -\frac {{\mathrm {e}}^{2\,{\mathrm {e}}^{-\frac {{\mathrm {e}}^4}{5\,\left (x^2+6\,x+\mathrm {e}+9\right )}}}}{x-{\mathrm {e}}^5} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(2*exp(-exp(4)/(30*x + 5*exp(1) + 5*x^2 + 45)))*exp(-exp(4)/(30*x + 5*exp(1) + 5*x^2 + 45))*(exp(exp(4
)/(30*x + 5*exp(1) + 5*x^2 + 45))*(540*x + 5*exp(2) + exp(1)*(60*x + 10*x^2 + 90) + 270*x^2 + 60*x^3 + 5*x^4 +
405) - exp(4)*(12*x + 4*x^2) + exp(9)*(4*x + 12)))/(exp(10)*(540*x + 5*exp(2) + exp(1)*(60*x + 10*x^2 + 90) +
270*x^2 + 60*x^3 + 5*x^4 + 405) - exp(5)*(810*x + 10*x*exp(2) + exp(1)*(180*x + 120*x^2 + 20*x^3) + 1080*x^2
+ 540*x^3 + 120*x^4 + 10*x^5) + 5*x^2*exp(2) + exp(1)*(90*x^2 + 60*x^3 + 10*x^4) + 405*x^2 + 540*x^3 + 270*x^4
+ 60*x^5 + 5*x^6),x)

[Out]

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

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sympy [A]  time = 1.03, size = 29, normalized size = 0.91 \begin {gather*} - \frac {e^{2 e^{- \frac {e^{4}}{5 x^{2} + 30 x + 5 e + 45}}}}{x - e^{5}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((5*exp(1)**2+(10*x**2+60*x+90)*exp(1)+5*x**4+60*x**3+270*x**2+540*x+405)*exp(exp(4)/(5*exp(1)+5*x**
2+30*x+45))+(4*x+12)*exp(4)*exp(5)+(-4*x**2-12*x)*exp(4))*exp(2/exp(exp(4)/(5*exp(1)+5*x**2+30*x+45)))/((5*exp
(1)**2+(10*x**2+60*x+90)*exp(1)+5*x**4+60*x**3+270*x**2+540*x+405)*exp(5)**2+(-10*x*exp(1)**2+(-20*x**3-120*x*
*2-180*x)*exp(1)-10*x**5-120*x**4-540*x**3-1080*x**2-810*x)*exp(5)+5*x**2*exp(1)**2+(10*x**4+60*x**3+90*x**2)*
exp(1)+5*x**6+60*x**5+270*x**4+540*x**3+405*x**2)/exp(exp(4)/(5*exp(1)+5*x**2+30*x+45)),x)

[Out]

-exp(2*exp(-exp(4)/(5*x**2 + 30*x + 5*E + 45)))/(x - exp(5))

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