3.8.81 \(\int e^{5-36 x^2+60 x^3-13 x^4-10 x^5-x^6+e^{4 x} (-9 x^4+18 x^5-9 x^6)+e^{2 x} (36 x^3-66 x^4+24 x^5+6 x^6)} (-72 x+180 x^2-52 x^3-50 x^4-6 x^5+e^{4 x} (-36 x^3+54 x^4+18 x^5-36 x^6)+e^{2 x} (108 x^2-192 x^3-12 x^4+84 x^5+12 x^6)) \, dx\)

Optimal. Leaf size=31 \[ e^{5-\left (x-x^2\right )^2 \left (x+3 \left (2-e^{2 x} x\right )\right )^2} \]

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Rubi [F]  time = 26.91, 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 \exp \left (5-36 x^2+60 x^3-13 x^4-10 x^5-x^6+e^{4 x} \left (-9 x^4+18 x^5-9 x^6\right )+e^{2 x} \left (36 x^3-66 x^4+24 x^5+6 x^6\right )\right ) \left (-72 x+180 x^2-52 x^3-50 x^4-6 x^5+e^{4 x} \left (-36 x^3+54 x^4+18 x^5-36 x^6\right )+e^{2 x} \left (108 x^2-192 x^3-12 x^4+84 x^5+12 x^6\right )\right ) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[E^(5 - 36*x^2 + 60*x^3 - 13*x^4 - 10*x^5 - x^6 + E^(4*x)*(-9*x^4 + 18*x^5 - 9*x^6) + E^(2*x)*(36*x^3 - 66*
x^4 + 24*x^5 + 6*x^6))*(-72*x + 180*x^2 - 52*x^3 - 50*x^4 - 6*x^5 + E^(4*x)*(-36*x^3 + 54*x^4 + 18*x^5 - 36*x^
6) + E^(2*x)*(108*x^2 - 192*x^3 - 12*x^4 + 84*x^5 + 12*x^6)),x]

[Out]

-72*Defer[Int][E^(5 - 36*x^2 + 60*x^3 - 13*x^4 - 10*x^5 - x^6 + E^(4*x)*(-9*x^4 + 18*x^5 - 9*x^6) + E^(2*x)*(3
6*x^3 - 66*x^4 + 24*x^5 + 6*x^6))*x, x] + 180*Defer[Int][E^(5 - 36*x^2 + 60*x^3 - 13*x^4 - 10*x^5 - x^6 + E^(4
*x)*(-9*x^4 + 18*x^5 - 9*x^6) + E^(2*x)*(36*x^3 - 66*x^4 + 24*x^5 + 6*x^6))*x^2, x] + 108*Defer[Int][E^(5 + 2*
x - 36*x^2 + 60*x^3 - 13*x^4 - 10*x^5 - x^6 + E^(4*x)*(-9*x^4 + 18*x^5 - 9*x^6) + E^(2*x)*(36*x^3 - 66*x^4 + 2
4*x^5 + 6*x^6))*x^2, x] - 52*Defer[Int][E^(5 - 36*x^2 + 60*x^3 - 13*x^4 - 10*x^5 - x^6 + E^(4*x)*(-9*x^4 + 18*
x^5 - 9*x^6) + E^(2*x)*(36*x^3 - 66*x^4 + 24*x^5 + 6*x^6))*x^3, x] - 192*Defer[Int][E^(5 + 2*x - 36*x^2 + 60*x
^3 - 13*x^4 - 10*x^5 - x^6 + E^(4*x)*(-9*x^4 + 18*x^5 - 9*x^6) + E^(2*x)*(36*x^3 - 66*x^4 + 24*x^5 + 6*x^6))*x
^3, x] - 36*Defer[Int][E^(5 + 4*x - 36*x^2 + 60*x^3 - 13*x^4 - 10*x^5 - x^6 + E^(4*x)*(-9*x^4 + 18*x^5 - 9*x^6
) + E^(2*x)*(36*x^3 - 66*x^4 + 24*x^5 + 6*x^6))*x^3, x] - 50*Defer[Int][E^(5 - 36*x^2 + 60*x^3 - 13*x^4 - 10*x
^5 - x^6 + E^(4*x)*(-9*x^4 + 18*x^5 - 9*x^6) + E^(2*x)*(36*x^3 - 66*x^4 + 24*x^5 + 6*x^6))*x^4, x] - 12*Defer[
Int][E^(5 + 2*x - 36*x^2 + 60*x^3 - 13*x^4 - 10*x^5 - x^6 + E^(4*x)*(-9*x^4 + 18*x^5 - 9*x^6) + E^(2*x)*(36*x^
3 - 66*x^4 + 24*x^5 + 6*x^6))*x^4, x] + 54*Defer[Int][E^(5 + 4*x - 36*x^2 + 60*x^3 - 13*x^4 - 10*x^5 - x^6 + E
^(4*x)*(-9*x^4 + 18*x^5 - 9*x^6) + E^(2*x)*(36*x^3 - 66*x^4 + 24*x^5 + 6*x^6))*x^4, x] - 6*Defer[Int][E^(5 - 3
6*x^2 + 60*x^3 - 13*x^4 - 10*x^5 - x^6 + E^(4*x)*(-9*x^4 + 18*x^5 - 9*x^6) + E^(2*x)*(36*x^3 - 66*x^4 + 24*x^5
+ 6*x^6))*x^5, x] + 84*Defer[Int][E^(5 + 2*x - 36*x^2 + 60*x^3 - 13*x^4 - 10*x^5 - x^6 + E^(4*x)*(-9*x^4 + 18
*x^5 - 9*x^6) + E^(2*x)*(36*x^3 - 66*x^4 + 24*x^5 + 6*x^6))*x^5, x] + 18*Defer[Int][E^(5 + 4*x - 36*x^2 + 60*x
^3 - 13*x^4 - 10*x^5 - x^6 + E^(4*x)*(-9*x^4 + 18*x^5 - 9*x^6) + E^(2*x)*(36*x^3 - 66*x^4 + 24*x^5 + 6*x^6))*x
^5, x] + 12*Defer[Int][E^(5 + 2*x - 36*x^2 + 60*x^3 - 13*x^4 - 10*x^5 - x^6 + E^(4*x)*(-9*x^4 + 18*x^5 - 9*x^6
) + E^(2*x)*(36*x^3 - 66*x^4 + 24*x^5 + 6*x^6))*x^6, x] - 36*Defer[Int][E^(5 + 4*x - 36*x^2 + 60*x^3 - 13*x^4
- 10*x^5 - x^6 + E^(4*x)*(-9*x^4 + 18*x^5 - 9*x^6) + E^(2*x)*(36*x^3 - 66*x^4 + 24*x^5 + 6*x^6))*x^6, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-72 \exp \left (5-36 x^2+60 x^3-13 x^4-10 x^5-x^6+e^{4 x} \left (-9 x^4+18 x^5-9 x^6\right )+e^{2 x} \left (36 x^3-66 x^4+24 x^5+6 x^6\right )\right ) x+180 \exp \left (5-36 x^2+60 x^3-13 x^4-10 x^5-x^6+e^{4 x} \left (-9 x^4+18 x^5-9 x^6\right )+e^{2 x} \left (36 x^3-66 x^4+24 x^5+6 x^6\right )\right ) x^2-52 \exp \left (5-36 x^2+60 x^3-13 x^4-10 x^5-x^6+e^{4 x} \left (-9 x^4+18 x^5-9 x^6\right )+e^{2 x} \left (36 x^3-66 x^4+24 x^5+6 x^6\right )\right ) x^3-50 \exp \left (5-36 x^2+60 x^3-13 x^4-10 x^5-x^6+e^{4 x} \left (-9 x^4+18 x^5-9 x^6\right )+e^{2 x} \left (36 x^3-66 x^4+24 x^5+6 x^6\right )\right ) x^4-6 \exp \left (5-36 x^2+60 x^3-13 x^4-10 x^5-x^6+e^{4 x} \left (-9 x^4+18 x^5-9 x^6\right )+e^{2 x} \left (36 x^3-66 x^4+24 x^5+6 x^6\right )\right ) x^5-18 \exp \left (5+4 x-36 x^2+60 x^3-13 x^4-10 x^5-x^6+e^{4 x} \left (-9 x^4+18 x^5-9 x^6\right )+e^{2 x} \left (36 x^3-66 x^4+24 x^5+6 x^6\right )\right ) x^3 \left (2-3 x-x^2+2 x^3\right )+12 \exp \left (5+2 x-36 x^2+60 x^3-13 x^4-10 x^5-x^6+e^{4 x} \left (-9 x^4+18 x^5-9 x^6\right )+e^{2 x} \left (36 x^3-66 x^4+24 x^5+6 x^6\right )\right ) x^2 \left (9-16 x-x^2+7 x^3+x^4\right )\right ) \, dx\\ &=-\left (6 \int \exp \left (5-36 x^2+60 x^3-13 x^4-10 x^5-x^6+e^{4 x} \left (-9 x^4+18 x^5-9 x^6\right )+e^{2 x} \left (36 x^3-66 x^4+24 x^5+6 x^6\right )\right ) x^5 \, dx\right )+12 \int \exp \left (5+2 x-36 x^2+60 x^3-13 x^4-10 x^5-x^6+e^{4 x} \left (-9 x^4+18 x^5-9 x^6\right )+e^{2 x} \left (36 x^3-66 x^4+24 x^5+6 x^6\right )\right ) x^2 \left (9-16 x-x^2+7 x^3+x^4\right ) \, dx-18 \int \exp \left (5+4 x-36 x^2+60 x^3-13 x^4-10 x^5-x^6+e^{4 x} \left (-9 x^4+18 x^5-9 x^6\right )+e^{2 x} \left (36 x^3-66 x^4+24 x^5+6 x^6\right )\right ) x^3 \left (2-3 x-x^2+2 x^3\right ) \, dx-50 \int \exp \left (5-36 x^2+60 x^3-13 x^4-10 x^5-x^6+e^{4 x} \left (-9 x^4+18 x^5-9 x^6\right )+e^{2 x} \left (36 x^3-66 x^4+24 x^5+6 x^6\right )\right ) x^4 \, dx-52 \int \exp \left (5-36 x^2+60 x^3-13 x^4-10 x^5-x^6+e^{4 x} \left (-9 x^4+18 x^5-9 x^6\right )+e^{2 x} \left (36 x^3-66 x^4+24 x^5+6 x^6\right )\right ) x^3 \, dx-72 \int \exp \left (5-36 x^2+60 x^3-13 x^4-10 x^5-x^6+e^{4 x} \left (-9 x^4+18 x^5-9 x^6\right )+e^{2 x} \left (36 x^3-66 x^4+24 x^5+6 x^6\right )\right ) x \, dx+180 \int \exp \left (5-36 x^2+60 x^3-13 x^4-10 x^5-x^6+e^{4 x} \left (-9 x^4+18 x^5-9 x^6\right )+e^{2 x} \left (36 x^3-66 x^4+24 x^5+6 x^6\right )\right ) x^2 \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.16, size = 62, normalized size = 2.00 \begin {gather*} e^{5-36 x^2+60 x^3-13 x^4-9 e^{4 x} (-1+x)^2 x^4-10 x^5-x^6+6 e^{2 x} (-1+x)^2 x^3 (6+x)} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[E^(5 - 36*x^2 + 60*x^3 - 13*x^4 - 10*x^5 - x^6 + E^(4*x)*(-9*x^4 + 18*x^5 - 9*x^6) + E^(2*x)*(36*x^3
- 66*x^4 + 24*x^5 + 6*x^6))*(-72*x + 180*x^2 - 52*x^3 - 50*x^4 - 6*x^5 + E^(4*x)*(-36*x^3 + 54*x^4 + 18*x^5 -
36*x^6) + E^(2*x)*(108*x^2 - 192*x^3 - 12*x^4 + 84*x^5 + 12*x^6)),x]

[Out]

E^(5 - 36*x^2 + 60*x^3 - 13*x^4 - 9*E^(4*x)*(-1 + x)^2*x^4 - 10*x^5 - x^6 + 6*E^(2*x)*(-1 + x)^2*x^3*(6 + x))

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fricas [B]  time = 1.16, size = 71, normalized size = 2.29 \begin {gather*} e^{\left (-x^{6} - 10 \, x^{5} - 13 \, x^{4} + 60 \, x^{3} - 36 \, x^{2} - 9 \, {\left (x^{6} - 2 \, x^{5} + x^{4}\right )} e^{\left (4 \, x\right )} + 6 \, {\left (x^{6} + 4 \, x^{5} - 11 \, x^{4} + 6 \, x^{3}\right )} e^{\left (2 \, x\right )} + 5\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-36*x^6+18*x^5+54*x^4-36*x^3)*exp(2*x)^2+(12*x^6+84*x^5-12*x^4-192*x^3+108*x^2)*exp(2*x)-6*x^5-50*
x^4-52*x^3+180*x^2-72*x)*exp((-9*x^6+18*x^5-9*x^4)*exp(2*x)^2+(6*x^6+24*x^5-66*x^4+36*x^3)*exp(2*x)-x^6-10*x^5
-13*x^4+60*x^3-36*x^2+5),x, algorithm="fricas")

[Out]

e^(-x^6 - 10*x^5 - 13*x^4 + 60*x^3 - 36*x^2 - 9*(x^6 - 2*x^5 + x^4)*e^(4*x) + 6*(x^6 + 4*x^5 - 11*x^4 + 6*x^3)
*e^(2*x) + 5)

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giac [B]  time = 1.82, size = 91, normalized size = 2.94 \begin {gather*} e^{\left (-9 \, x^{6} e^{\left (4 \, x\right )} + 6 \, x^{6} e^{\left (2 \, x\right )} - x^{6} + 18 \, x^{5} e^{\left (4 \, x\right )} + 24 \, x^{5} e^{\left (2 \, x\right )} - 10 \, x^{5} - 9 \, x^{4} e^{\left (4 \, x\right )} - 66 \, x^{4} e^{\left (2 \, x\right )} - 13 \, x^{4} + 36 \, x^{3} e^{\left (2 \, x\right )} + 60 \, x^{3} - 36 \, x^{2} + 5\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-36*x^6+18*x^5+54*x^4-36*x^3)*exp(2*x)^2+(12*x^6+84*x^5-12*x^4-192*x^3+108*x^2)*exp(2*x)-6*x^5-50*
x^4-52*x^3+180*x^2-72*x)*exp((-9*x^6+18*x^5-9*x^4)*exp(2*x)^2+(6*x^6+24*x^5-66*x^4+36*x^3)*exp(2*x)-x^6-10*x^5
-13*x^4+60*x^3-36*x^2+5),x, algorithm="giac")

[Out]

e^(-9*x^6*e^(4*x) + 6*x^6*e^(2*x) - x^6 + 18*x^5*e^(4*x) + 24*x^5*e^(2*x) - 10*x^5 - 9*x^4*e^(4*x) - 66*x^4*e^
(2*x) - 13*x^4 + 36*x^3*e^(2*x) + 60*x^3 - 36*x^2 + 5)

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maple [B]  time = 0.15, size = 92, normalized size = 2.97

method	result	size
risch	\({\mathrm e}^{-9 \,{\mathrm e}^{4 x} x^{6}+6 \,{\mathrm e}^{2 x} x^{6}+18 \,{\mathrm e}^{4 x} x^{5}+24 x^{5} {\mathrm e}^{2 x}-x^{6}-9 \,{\mathrm e}^{4 x} x^{4}-66 \,{\mathrm e}^{2 x} x^{4}-10 x^{5}+36 \,{\mathrm e}^{2 x} x^{3}-13 x^{4}+60 x^{3}-36 x^{2}+5}\)	\(92\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-36*x^6+18*x^5+54*x^4-36*x^3)*exp(2*x)^2+(12*x^6+84*x^5-12*x^4-192*x^3+108*x^2)*exp(2*x)-6*x^5-50*x^4-52
*x^3+180*x^2-72*x)*exp((-9*x^6+18*x^5-9*x^4)*exp(2*x)^2+(6*x^6+24*x^5-66*x^4+36*x^3)*exp(2*x)-x^6-10*x^5-13*x^
4+60*x^3-36*x^2+5),x,method=_RETURNVERBOSE)

[Out]

exp(-9*exp(4*x)*x^6+6*exp(2*x)*x^6+18*exp(4*x)*x^5+24*x^5*exp(2*x)-x^6-9*exp(4*x)*x^4-66*exp(2*x)*x^4-10*x^5+3
6*exp(2*x)*x^3-13*x^4+60*x^3-36*x^2+5)

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maxima [B]  time = 1.12, size = 91, normalized size = 2.94 \begin {gather*} e^{\left (-9 \, x^{6} e^{\left (4 \, x\right )} + 6 \, x^{6} e^{\left (2 \, x\right )} - x^{6} + 18 \, x^{5} e^{\left (4 \, x\right )} + 24 \, x^{5} e^{\left (2 \, x\right )} - 10 \, x^{5} - 9 \, x^{4} e^{\left (4 \, x\right )} - 66 \, x^{4} e^{\left (2 \, x\right )} - 13 \, x^{4} + 36 \, x^{3} e^{\left (2 \, x\right )} + 60 \, x^{3} - 36 \, x^{2} + 5\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-36*x^6+18*x^5+54*x^4-36*x^3)*exp(2*x)^2+(12*x^6+84*x^5-12*x^4-192*x^3+108*x^2)*exp(2*x)-6*x^5-50*
x^4-52*x^3+180*x^2-72*x)*exp((-9*x^6+18*x^5-9*x^4)*exp(2*x)^2+(6*x^6+24*x^5-66*x^4+36*x^3)*exp(2*x)-x^6-10*x^5
-13*x^4+60*x^3-36*x^2+5),x, algorithm="maxima")

[Out]

e^(-9*x^6*e^(4*x) + 6*x^6*e^(2*x) - x^6 + 18*x^5*e^(4*x) + 24*x^5*e^(2*x) - 10*x^5 - 9*x^4*e^(4*x) - 66*x^4*e^
(2*x) - 13*x^4 + 36*x^3*e^(2*x) + 60*x^3 - 36*x^2 + 5)

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mupad [B]  time = 0.93, size = 103, normalized size = 3.32 \begin {gather*} {\mathrm {e}}^5\,{\mathrm {e}}^{-x^6}\,{\mathrm {e}}^{-10\,x^5}\,{\mathrm {e}}^{-13\,x^4}\,{\mathrm {e}}^{-36\,x^2}\,{\mathrm {e}}^{60\,x^3}\,{\mathrm {e}}^{6\,x^6\,{\mathrm {e}}^{2\,x}}\,{\mathrm {e}}^{-9\,x^4\,{\mathrm {e}}^{4\,x}}\,{\mathrm {e}}^{-9\,x^6\,{\mathrm {e}}^{4\,x}}\,{\mathrm {e}}^{18\,x^5\,{\mathrm {e}}^{4\,x}}\,{\mathrm {e}}^{24\,x^5\,{\mathrm {e}}^{2\,x}}\,{\mathrm {e}}^{36\,x^3\,{\mathrm {e}}^{2\,x}}\,{\mathrm {e}}^{-66\,x^4\,{\mathrm {e}}^{2\,x}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-exp(exp(2*x)*(36*x^3 - 66*x^4 + 24*x^5 + 6*x^6) - exp(4*x)*(9*x^4 - 18*x^5 + 9*x^6) - 36*x^2 + 60*x^3 - 1
3*x^4 - 10*x^5 - x^6 + 5)*(72*x - exp(2*x)*(108*x^2 - 192*x^3 - 12*x^4 + 84*x^5 + 12*x^6) + exp(4*x)*(36*x^3 -
54*x^4 - 18*x^5 + 36*x^6) - 180*x^2 + 52*x^3 + 50*x^4 + 6*x^5),x)

[Out]

exp(5)*exp(-x^6)*exp(-10*x^5)*exp(-13*x^4)*exp(-36*x^2)*exp(60*x^3)*exp(6*x^6*exp(2*x))*exp(-9*x^4*exp(4*x))*e
xp(-9*x^6*exp(4*x))*exp(18*x^5*exp(4*x))*exp(24*x^5*exp(2*x))*exp(36*x^3*exp(2*x))*exp(-66*x^4*exp(2*x))

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sympy [B]  time = 0.50, size = 71, normalized size = 2.29 \begin {gather*} e^{- x^{6} - 10 x^{5} - 13 x^{4} + 60 x^{3} - 36 x^{2} + \left (- 9 x^{6} + 18 x^{5} - 9 x^{4}\right ) e^{4 x} + \left (6 x^{6} + 24 x^{5} - 66 x^{4} + 36 x^{3}\right ) e^{2 x} + 5} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-36*x**6+18*x**5+54*x**4-36*x**3)*exp(2*x)**2+(12*x**6+84*x**5-12*x**4-192*x**3+108*x**2)*exp(2*x)
-6*x**5-50*x**4-52*x**3+180*x**2-72*x)*exp((-9*x**6+18*x**5-9*x**4)*exp(2*x)**2+(6*x**6+24*x**5-66*x**4+36*x**
3)*exp(2*x)-x**6-10*x**5-13*x**4+60*x**3-36*x**2+5),x)

[Out]

exp(-x**6 - 10*x**5 - 13*x**4 + 60*x**3 - 36*x**2 + (-9*x**6 + 18*x**5 - 9*x**4)*exp(4*x) + (6*x**6 + 24*x**5
- 66*x**4 + 36*x**3)*exp(2*x) + 5)

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