3.14.82 \(\int \frac {e^{\frac {2 (189 x+198 x^2+111 x^3+30 x^4+3 x^5+e^8 (432 x+288 x^2+48 x^3)+e^4 (216 x+432 x^2+192 x^3+24 x^4))}{9+6 x+x^2}} (1134+1998 x+1998 x^2+942 x^3+210 x^4+18 x^5+e^8 (2592+2592 x+864 x^2+96 x^3)+e^4 (1296+4752 x+3456 x^2+960 x^3+96 x^4))}{27+27 x+9 x^2+x^3} \, dx\)

Optimal. Leaf size=24 \[ e^{6 x \left (6+\left (1+4 e^4+x+\frac {x}{3+x}\right )^2\right )} \]

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Rubi [F]  time = 12.36, 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 (\frac {2 \left (189 x+198 x^2+111 x^3+30 x^4+3 x^5+e^8 \left (432 x+288 x^2+48 x^3\right )+e^4 \left (216 x+432 x^2+192 x^3+24 x^4\right )\right )}{9+6 x+x^2}\right ) \left (1134+1998 x+1998 x^2+942 x^3+210 x^4+18 x^5+e^8 \left (2592+2592 x+864 x^2+96 x^3\right )+e^4 \left (1296+4752 x+3456 x^2+960 x^3+96 x^4\right )\right )}{27+27 x+9 x^2+x^3} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^((2*(189*x + 198*x^2 + 111*x^3 + 30*x^4 + 3*x^5 + E^8*(432*x + 288*x^2 + 48*x^3) + E^4*(216*x + 432*x^2
+ 192*x^3 + 24*x^4)))/(9 + 6*x + x^2))*(1134 + 1998*x + 1998*x^2 + 942*x^3 + 210*x^4 + 18*x^5 + E^8*(2592 + 2
592*x + 864*x^2 + 96*x^3) + E^4*(1296 + 4752*x + 3456*x^2 + 960*x^3 + 96*x^4)))/(27 + 27*x + 9*x^2 + x^3),x]

[Out]

24*(1 + 2*E^4)^2*Defer[Int][E^((6*x*(9*(7 + 8*E^4 + 16*E^8) + 6*(11 + 24*E^4 + 16*E^8)*x + (37 + 64*E^4 + 16*E
^8)*x^2 + 2*(5 + 4*E^4)*x^3 + x^4))/(9 + 6*x + x^2)), x] + 48*(1 + 2*E^4)*Defer[Int][E^((6*x*(9*(7 + 8*E^4 + 1
6*E^8) + 6*(11 + 24*E^4 + 16*E^8)*x + (37 + 64*E^4 + 16*E^8)*x^2 + 2*(5 + 4*E^4)*x^3 + x^4))/(9 + 6*x + x^2))*
x, x] + 18*Defer[Int][E^((6*x*(9*(7 + 8*E^4 + 16*E^8) + 6*(11 + 24*E^4 + 16*E^8)*x + (37 + 64*E^4 + 16*E^8)*x^
2 + 2*(5 + 4*E^4)*x^3 + x^4))/(9 + 6*x + x^2))*x^2, x] + 324*Defer[Int][E^((6*x*(9*(7 + 8*E^4 + 16*E^8) + 6*(1
1 + 24*E^4 + 16*E^8)*x + (37 + 64*E^4 + 16*E^8)*x^2 + 2*(5 + 4*E^4)*x^3 + x^4))/(9 + 6*x + x^2))/(3 + x)^3, x]
+ 54*(1 - 8*E^4)*Defer[Int][E^((6*x*(9*(7 + 8*E^4 + 16*E^8) + 6*(11 + 24*E^4 + 16*E^8)*x + (37 + 64*E^4 + 16*
E^8)*x^2 + 2*(5 + 4*E^4)*x^3 + x^4))/(9 + 6*x + x^2))/(3 + x)^2, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {\exp \left (\frac {6 x \left (9 \left (7+8 e^4+16 e^8\right )+6 \left (11+24 e^4+16 e^8\right ) x+\left (37+64 e^4+16 e^8\right ) x^2+2 \left (5+4 e^4\right ) x^3+x^4\right )}{9+6 x+x^2}\right ) \left (1134+1998 x+1998 x^2+942 x^3+210 x^4+18 x^5+e^8 \left (2592+2592 x+864 x^2+96 x^3\right )+e^4 \left (1296+4752 x+3456 x^2+960 x^3+96 x^4\right )\right )}{27+27 x+9 x^2+x^3} \, dx\\ &=\int \left (24 \exp \left (\frac {6 x \left (9 \left (7+8 e^4+16 e^8\right )+6 \left (11+24 e^4+16 e^8\right ) x+\left (37+64 e^4+16 e^8\right ) x^2+2 \left (5+4 e^4\right ) x^3+x^4\right )}{9+6 x+x^2}\right ) \left (1+2 e^4\right )^2+48 \exp \left (\frac {6 x \left (9 \left (7+8 e^4+16 e^8\right )+6 \left (11+24 e^4+16 e^8\right ) x+\left (37+64 e^4+16 e^8\right ) x^2+2 \left (5+4 e^4\right ) x^3+x^4\right )}{9+6 x+x^2}\right ) \left (1+2 e^4\right ) x+18 \exp \left (\frac {6 x \left (9 \left (7+8 e^4+16 e^8\right )+6 \left (11+24 e^4+16 e^8\right ) x+\left (37+64 e^4+16 e^8\right ) x^2+2 \left (5+4 e^4\right ) x^3+x^4\right )}{9+6 x+x^2}\right ) x^2-\frac {54 \exp \left (\frac {6 x \left (9 \left (7+8 e^4+16 e^8\right )+6 \left (11+24 e^4+16 e^8\right ) x+\left (37+64 e^4+16 e^8\right ) x^2+2 \left (5+4 e^4\right ) x^3+x^4\right )}{9+6 x+x^2}\right ) \left (-3 \left (3-8 e^4\right )-\left (1-8 e^4\right ) x\right )}{27+27 x+9 x^2+x^3}\right ) \, dx\\ &=18 \int \exp \left (\frac {6 x \left (9 \left (7+8 e^4+16 e^8\right )+6 \left (11+24 e^4+16 e^8\right ) x+\left (37+64 e^4+16 e^8\right ) x^2+2 \left (5+4 e^4\right ) x^3+x^4\right )}{9+6 x+x^2}\right ) x^2 \, dx-54 \int \frac {\exp \left (\frac {6 x \left (9 \left (7+8 e^4+16 e^8\right )+6 \left (11+24 e^4+16 e^8\right ) x+\left (37+64 e^4+16 e^8\right ) x^2+2 \left (5+4 e^4\right ) x^3+x^4\right )}{9+6 x+x^2}\right ) \left (-3 \left (3-8 e^4\right )-\left (1-8 e^4\right ) x\right )}{27+27 x+9 x^2+x^3} \, dx+\left (48 \left (1+2 e^4\right )\right ) \int \exp \left (\frac {6 x \left (9 \left (7+8 e^4+16 e^8\right )+6 \left (11+24 e^4+16 e^8\right ) x+\left (37+64 e^4+16 e^8\right ) x^2+2 \left (5+4 e^4\right ) x^3+x^4\right )}{9+6 x+x^2}\right ) x \, dx+\left (24 \left (1+2 e^4\right )^2\right ) \int \exp \left (\frac {6 x \left (9 \left (7+8 e^4+16 e^8\right )+6 \left (11+24 e^4+16 e^8\right ) x+\left (37+64 e^4+16 e^8\right ) x^2+2 \left (5+4 e^4\right ) x^3+x^4\right )}{9+6 x+x^2}\right ) \, dx\\ &=18 \int \exp \left (\frac {6 x \left (9 \left (7+8 e^4+16 e^8\right )+6 \left (11+24 e^4+16 e^8\right ) x+\left (37+64 e^4+16 e^8\right ) x^2+2 \left (5+4 e^4\right ) x^3+x^4\right )}{9+6 x+x^2}\right ) x^2 \, dx-54 \int \left (-\frac {6 \exp \left (\frac {6 x \left (9 \left (7+8 e^4+16 e^8\right )+6 \left (11+24 e^4+16 e^8\right ) x+\left (37+64 e^4+16 e^8\right ) x^2+2 \left (5+4 e^4\right ) x^3+x^4\right )}{9+6 x+x^2}\right )}{(3+x)^3}+\frac {\exp \left (\frac {6 x \left (9 \left (7+8 e^4+16 e^8\right )+6 \left (11+24 e^4+16 e^8\right ) x+\left (37+64 e^4+16 e^8\right ) x^2+2 \left (5+4 e^4\right ) x^3+x^4\right )}{9+6 x+x^2}\right ) \left (-1+8 e^4\right )}{(3+x)^2}\right ) \, dx+\left (48 \left (1+2 e^4\right )\right ) \int \exp \left (\frac {6 x \left (9 \left (7+8 e^4+16 e^8\right )+6 \left (11+24 e^4+16 e^8\right ) x+\left (37+64 e^4+16 e^8\right ) x^2+2 \left (5+4 e^4\right ) x^3+x^4\right )}{9+6 x+x^2}\right ) x \, dx+\left (24 \left (1+2 e^4\right )^2\right ) \int \exp \left (\frac {6 x \left (9 \left (7+8 e^4+16 e^8\right )+6 \left (11+24 e^4+16 e^8\right ) x+\left (37+64 e^4+16 e^8\right ) x^2+2 \left (5+4 e^4\right ) x^3+x^4\right )}{9+6 x+x^2}\right ) \, dx\\ &=18 \int \exp \left (\frac {6 x \left (9 \left (7+8 e^4+16 e^8\right )+6 \left (11+24 e^4+16 e^8\right ) x+\left (37+64 e^4+16 e^8\right ) x^2+2 \left (5+4 e^4\right ) x^3+x^4\right )}{9+6 x+x^2}\right ) x^2 \, dx+324 \int \frac {\exp \left (\frac {6 x \left (9 \left (7+8 e^4+16 e^8\right )+6 \left (11+24 e^4+16 e^8\right ) x+\left (37+64 e^4+16 e^8\right ) x^2+2 \left (5+4 e^4\right ) x^3+x^4\right )}{9+6 x+x^2}\right )}{(3+x)^3} \, dx+\left (54 \left (1-8 e^4\right )\right ) \int \frac {\exp \left (\frac {6 x \left (9 \left (7+8 e^4+16 e^8\right )+6 \left (11+24 e^4+16 e^8\right ) x+\left (37+64 e^4+16 e^8\right ) x^2+2 \left (5+4 e^4\right ) x^3+x^4\right )}{9+6 x+x^2}\right )}{(3+x)^2} \, dx+\left (48 \left (1+2 e^4\right )\right ) \int \exp \left (\frac {6 x \left (9 \left (7+8 e^4+16 e^8\right )+6 \left (11+24 e^4+16 e^8\right ) x+\left (37+64 e^4+16 e^8\right ) x^2+2 \left (5+4 e^4\right ) x^3+x^4\right )}{9+6 x+x^2}\right ) x \, dx+\left (24 \left (1+2 e^4\right )^2\right ) \int \exp \left (\frac {6 x \left (9 \left (7+8 e^4+16 e^8\right )+6 \left (11+24 e^4+16 e^8\right ) x+\left (37+64 e^4+16 e^8\right ) x^2+2 \left (5+4 e^4\right ) x^3+x^4\right )}{9+6 x+x^2}\right ) \, dx\\ \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.11, size = 56, normalized size = 2.33 \begin {gather*} e^{\frac {6 x \left (63+66 x+37 x^2+10 x^3+x^4+16 e^8 (3+x)^2+8 e^4 \left (9+18 x+8 x^2+x^3\right )\right )}{(3+x)^2}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^((2*(189*x + 198*x^2 + 111*x^3 + 30*x^4 + 3*x^5 + E^8*(432*x + 288*x^2 + 48*x^3) + E^4*(216*x + 4
32*x^2 + 192*x^3 + 24*x^4)))/(9 + 6*x + x^2))*(1134 + 1998*x + 1998*x^2 + 942*x^3 + 210*x^4 + 18*x^5 + E^8*(25
92 + 2592*x + 864*x^2 + 96*x^3) + E^4*(1296 + 4752*x + 3456*x^2 + 960*x^3 + 96*x^4)))/(27 + 27*x + 9*x^2 + x^3
),x]

[Out]

E^((6*x*(63 + 66*x + 37*x^2 + 10*x^3 + x^4 + 16*E^8*(3 + x)^2 + 8*E^4*(9 + 18*x + 8*x^2 + x^3)))/(3 + x)^2)

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fricas [B]  time = 1.32, size = 72, normalized size = 3.00 \begin {gather*} e^{\left (\frac {6 \, {\left (x^{5} + 10 \, x^{4} + 37 \, x^{3} + 66 \, x^{2} + 16 \, {\left (x^{3} + 6 \, x^{2} + 9 \, x\right )} e^{8} + 8 \, {\left (x^{4} + 8 \, x^{3} + 18 \, x^{2} + 9 \, x\right )} e^{4} + 63 \, x\right )}}{x^{2} + 6 \, x + 9}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((96*x^3+864*x^2+2592*x+2592)*exp(4)^2+(96*x^4+960*x^3+3456*x^2+4752*x+1296)*exp(4)+18*x^5+210*x^4+9
42*x^3+1998*x^2+1998*x+1134)*exp(((48*x^3+288*x^2+432*x)*exp(4)^2+(24*x^4+192*x^3+432*x^2+216*x)*exp(4)+3*x^5+
30*x^4+111*x^3+198*x^2+189*x)/(x^2+6*x+9))^2/(x^3+9*x^2+27*x+27),x, algorithm="fricas")

[Out]

e^(6*(x^5 + 10*x^4 + 37*x^3 + 66*x^2 + 16*(x^3 + 6*x^2 + 9*x)*e^8 + 8*(x^4 + 8*x^3 + 18*x^2 + 9*x)*e^4 + 63*x)
/(x^2 + 6*x + 9))

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giac [B]  time = 0.52, size = 190, normalized size = 7.92 \begin {gather*} e^{\left (\frac {6 \, x^{5}}{x^{2} + 6 \, x + 9} + \frac {48 \, x^{4} e^{4}}{x^{2} + 6 \, x + 9} + \frac {60 \, x^{4}}{x^{2} + 6 \, x + 9} + \frac {96 \, x^{3} e^{8}}{x^{2} + 6 \, x + 9} + \frac {384 \, x^{3} e^{4}}{x^{2} + 6 \, x + 9} + \frac {222 \, x^{3}}{x^{2} + 6 \, x + 9} + \frac {576 \, x^{2} e^{8}}{x^{2} + 6 \, x + 9} + \frac {864 \, x^{2} e^{4}}{x^{2} + 6 \, x + 9} + \frac {396 \, x^{2}}{x^{2} + 6 \, x + 9} + \frac {864 \, x e^{8}}{x^{2} + 6 \, x + 9} + \frac {432 \, x e^{4}}{x^{2} + 6 \, x + 9} + \frac {378 \, x}{x^{2} + 6 \, x + 9}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((96*x^3+864*x^2+2592*x+2592)*exp(4)^2+(96*x^4+960*x^3+3456*x^2+4752*x+1296)*exp(4)+18*x^5+210*x^4+9
42*x^3+1998*x^2+1998*x+1134)*exp(((48*x^3+288*x^2+432*x)*exp(4)^2+(24*x^4+192*x^3+432*x^2+216*x)*exp(4)+3*x^5+
30*x^4+111*x^3+198*x^2+189*x)/(x^2+6*x+9))^2/(x^3+9*x^2+27*x+27),x, algorithm="giac")

[Out]

e^(6*x^5/(x^2 + 6*x + 9) + 48*x^4*e^4/(x^2 + 6*x + 9) + 60*x^4/(x^2 + 6*x + 9) + 96*x^3*e^8/(x^2 + 6*x + 9) +
384*x^3*e^4/(x^2 + 6*x + 9) + 222*x^3/(x^2 + 6*x + 9) + 576*x^2*e^8/(x^2 + 6*x + 9) + 864*x^2*e^4/(x^2 + 6*x +
9) + 396*x^2/(x^2 + 6*x + 9) + 864*x*e^8/(x^2 + 6*x + 9) + 432*x*e^4/(x^2 + 6*x + 9) + 378*x/(x^2 + 6*x + 9))

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maple [B]  time = 115.96, size = 67, normalized size = 2.79

method	result	size
risch	\({\mathrm e}^{\frac {6 x \left (8 x^{3} {\mathrm e}^{4}+x^{4}+64 x^{2} {\mathrm e}^{4}+16 x^{2} {\mathrm e}^{8}+10 x^{3}+144 x \,{\mathrm e}^{4}+96 x \,{\mathrm e}^{8}+37 x^{2}+72 \,{\mathrm e}^{4}+144 \,{\mathrm e}^{8}+66 x +63\right )}{\left (3+x \right )^{2}}}\)	\(67\)
gosper	\({\mathrm e}^{\frac {6 x \left (8 x^{3} {\mathrm e}^{4}+x^{4}+64 x^{2} {\mathrm e}^{4}+16 x^{2} {\mathrm e}^{8}+10 x^{3}+144 x \,{\mathrm e}^{4}+96 x \,{\mathrm e}^{8}+37 x^{2}+72 \,{\mathrm e}^{4}+144 \,{\mathrm e}^{8}+66 x +63\right )}{x^{2}+6 x +9}}\)	\(80\)
norman	\(\frac {x^{2} {\mathrm e}^{\frac {2 \left (48 x^{3}+288 x^{2}+432 x \right ) {\mathrm e}^{8}+2 \left (24 x^{4}+192 x^{3}+432 x^{2}+216 x \right ) {\mathrm e}^{4}+6 x^{5}+60 x^{4}+222 x^{3}+396 x^{2}+378 x}{x^{2}+6 x +9}}+9 \,{\mathrm e}^{\frac {2 \left (48 x^{3}+288 x^{2}+432 x \right ) {\mathrm e}^{8}+2 \left (24 x^{4}+192 x^{3}+432 x^{2}+216 x \right ) {\mathrm e}^{4}+6 x^{5}+60 x^{4}+222 x^{3}+396 x^{2}+378 x}{x^{2}+6 x +9}}+6 x \,{\mathrm e}^{\frac {2 \left (48 x^{3}+288 x^{2}+432 x \right ) {\mathrm e}^{8}+2 \left (24 x^{4}+192 x^{3}+432 x^{2}+216 x \right ) {\mathrm e}^{4}+6 x^{5}+60 x^{4}+222 x^{3}+396 x^{2}+378 x}{x^{2}+6 x +9}}}{\left (3+x \right )^{2}}\)	\(254\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((96*x^3+864*x^2+2592*x+2592)*exp(4)^2+(96*x^4+960*x^3+3456*x^2+4752*x+1296)*exp(4)+18*x^5+210*x^4+942*x^3
+1998*x^2+1998*x+1134)*exp(((48*x^3+288*x^2+432*x)*exp(4)^2+(24*x^4+192*x^3+432*x^2+216*x)*exp(4)+3*x^5+30*x^4
+111*x^3+198*x^2+189*x)/(x^2+6*x+9))^2/(x^3+9*x^2+27*x+27),x,method=_RETURNVERBOSE)

[Out]

exp(6*x*(8*x^3*exp(4)+x^4+64*x^2*exp(4)+16*x^2*exp(8)+10*x^3+144*x*exp(4)+96*x*exp(8)+37*x^2+72*exp(4)+144*exp
(8)+66*x+63)/(3+x)^2)

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maxima [B]  time = 1.69, size = 65, normalized size = 2.71 \begin {gather*} e^{\left (6 \, x^{3} + 48 \, x^{2} e^{4} + 24 \, x^{2} + 96 \, x e^{8} + 96 \, x e^{4} + 24 \, x + \frac {432 \, e^{4}}{x + 3} - \frac {162}{x^{2} + 6 \, x + 9} - \frac {54}{x + 3} - 144 \, e^{4} + 36\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((96*x^3+864*x^2+2592*x+2592)*exp(4)^2+(96*x^4+960*x^3+3456*x^2+4752*x+1296)*exp(4)+18*x^5+210*x^4+9
42*x^3+1998*x^2+1998*x+1134)*exp(((48*x^3+288*x^2+432*x)*exp(4)^2+(24*x^4+192*x^3+432*x^2+216*x)*exp(4)+3*x^5+
30*x^4+111*x^3+198*x^2+189*x)/(x^2+6*x+9))^2/(x^3+9*x^2+27*x+27),x, algorithm="maxima")

[Out]

e^(6*x^3 + 48*x^2*e^4 + 24*x^2 + 96*x*e^8 + 96*x*e^4 + 24*x + 432*e^4/(x + 3) - 162/(x^2 + 6*x + 9) - 54/(x +
3) - 144*e^4 + 36)

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mupad [B]  time = 1.67, size = 201, normalized size = 8.38 \begin {gather*} {\mathrm {e}}^{\frac {6\,x^5}{x^2+6\,x+9}}\,{\mathrm {e}}^{\frac {60\,x^4}{x^2+6\,x+9}}\,{\mathrm {e}}^{\frac {222\,x^3}{x^2+6\,x+9}}\,{\mathrm {e}}^{\frac {396\,x^2}{x^2+6\,x+9}}\,{\mathrm {e}}^{\frac {432\,x\,{\mathrm {e}}^4}{x^2+6\,x+9}}\,{\mathrm {e}}^{\frac {864\,x\,{\mathrm {e}}^8}{x^2+6\,x+9}}\,{\mathrm {e}}^{\frac {48\,x^4\,{\mathrm {e}}^4}{x^2+6\,x+9}}\,{\mathrm {e}}^{\frac {96\,x^3\,{\mathrm {e}}^8}{x^2+6\,x+9}}\,{\mathrm {e}}^{\frac {384\,x^3\,{\mathrm {e}}^4}{x^2+6\,x+9}}\,{\mathrm {e}}^{\frac {576\,x^2\,{\mathrm {e}}^8}{x^2+6\,x+9}}\,{\mathrm {e}}^{\frac {864\,x^2\,{\mathrm {e}}^4}{x^2+6\,x+9}}\,{\mathrm {e}}^{\frac {378\,x}{x^2+6\,x+9}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp((2*(189*x + exp(8)*(432*x + 288*x^2 + 48*x^3) + exp(4)*(216*x + 432*x^2 + 192*x^3 + 24*x^4) + 198*x^2
+ 111*x^3 + 30*x^4 + 3*x^5))/(6*x + x^2 + 9))*(1998*x + exp(8)*(2592*x + 864*x^2 + 96*x^3 + 2592) + exp(4)*(4
752*x + 3456*x^2 + 960*x^3 + 96*x^4 + 1296) + 1998*x^2 + 942*x^3 + 210*x^4 + 18*x^5 + 1134))/(27*x + 9*x^2 + x
^3 + 27),x)

[Out]

exp((6*x^5)/(6*x + x^2 + 9))*exp((60*x^4)/(6*x + x^2 + 9))*exp((222*x^3)/(6*x + x^2 + 9))*exp((396*x^2)/(6*x +
x^2 + 9))*exp((432*x*exp(4))/(6*x + x^2 + 9))*exp((864*x*exp(8))/(6*x + x^2 + 9))*exp((48*x^4*exp(4))/(6*x +
x^2 + 9))*exp((96*x^3*exp(8))/(6*x + x^2 + 9))*exp((384*x^3*exp(4))/(6*x + x^2 + 9))*exp((576*x^2*exp(8))/(6*x
+ x^2 + 9))*exp((864*x^2*exp(4))/(6*x + x^2 + 9))*exp((378*x)/(6*x + x^2 + 9))

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sympy [B]  time = 0.61, size = 75, normalized size = 3.12 \begin {gather*} e^{\frac {2 \left (3 x^{5} + 30 x^{4} + 111 x^{3} + 198 x^{2} + 189 x + \left (48 x^{3} + 288 x^{2} + 432 x\right ) e^{8} + \left (24 x^{4} + 192 x^{3} + 432 x^{2} + 216 x\right ) e^{4}\right )}{x^{2} + 6 x + 9}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((96*x**3+864*x**2+2592*x+2592)*exp(4)**2+(96*x**4+960*x**3+3456*x**2+4752*x+1296)*exp(4)+18*x**5+21
0*x**4+942*x**3+1998*x**2+1998*x+1134)*exp(((48*x**3+288*x**2+432*x)*exp(4)**2+(24*x**4+192*x**3+432*x**2+216*
x)*exp(4)+3*x**5+30*x**4+111*x**3+198*x**2+189*x)/(x**2+6*x+9))**2/(x**3+9*x**2+27*x+27),x)

[Out]

exp(2*(3*x**5 + 30*x**4 + 111*x**3 + 198*x**2 + 189*x + (48*x**3 + 288*x**2 + 432*x)*exp(8) + (24*x**4 + 192*x
**3 + 432*x**2 + 216*x)*exp(4))/(x**2 + 6*x + 9))

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