3.89.72 $\int e^{-78+56x-13x^2+x^3+e^x(-16+8x-x^2)}(-55+82x-29x^2+3x^3+e^3(56-26x+3x^2)+e^x(8-14x+7x^2-x^3+e^3(-8+6x-x^2)))dx$

Optimal. Leaf size=29 $$e^{2-(4-x)(-4+x)(-5-e^x+x)}(-1+e^3+x)$$

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Rubi [F]  time = 4.72, 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 = {} $$\begin{array}{c}\int \exp (-78+56x-13x^2+x^3+e^x(-16+8x-x^2))(-55+82x-29x^2+3x^3+e^3(56-26x+3x^2)+e^x(8-14x+7x^2-x^3+e^3(-8+6x-x^2)))dx\end{array}$$

Verification is not applicable to the result.

[In]

Int[E^(-78 + 56*x - 13*x^2 + x^3 + E^x*(-16 + 8*x - x^2))*(-55 + 82*x - 29*x^2 + 3*x^3 + E^3*(56 - 26*x + 3*x^
2) + E^x*(8 - 14*x + 7*x^2 - x^3 + E^3*(-8 + 6*x - x^2))),x]

[Out]

-55*Defer[Int][E^(-78 + 56*x - 13*x^2 + x^3 + E^x*(-16 + 8*x - x^2)), x] + 56*Defer[Int][E^(-75 + 56*x - 13*x^
2 + x^3 + E^x*(-16 + 8*x - x^2)), x] + 8*(1 - E^3)*Defer[Int][E^(-78 + 57*x - 13*x^2 + x^3 + E^x*(-16 + 8*x -
x^2)), x] + 82*Defer[Int][E^(-78 + 56*x - 13*x^2 + x^3 + E^x*(-16 + 8*x - x^2))*x, x] - 26*Defer[Int][E^(-75 +
56*x - 13*x^2 + x^3 + E^x*(-16 + 8*x - x^2))*x, x] - 2*(7 - 3*E^3)*Defer[Int][E^(-78 + 57*x - 13*x^2 + x^3 +
E^x*(-16 + 8*x - x^2))*x, x] - 29*Defer[Int][E^(-78 + 56*x - 13*x^2 + x^3 + E^x*(-16 + 8*x - x^2))*x^2, x] + 3
*Defer[Int][E^(-75 + 56*x - 13*x^2 + x^3 + E^x*(-16 + 8*x - x^2))*x^2, x] + (7 - E^3)*Defer[Int][E^(-78 + 57*x
- 13*x^2 + x^3 + E^x*(-16 + 8*x - x^2))*x^2, x] + 3*Defer[Int][E^(-78 + 56*x - 13*x^2 + x^3 + E^x*(-16 + 8*x
- x^2))*x^3, x] - Defer[Int][E^(-78 + 57*x - 13*x^2 + x^3 + E^x*(-16 + 8*x - x^2))*x^3, x]

Rubi steps

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =\int (-55\exp (-78+56x-13x^2+x^3+e^x(-16+8x-x^2))+82\exp (-78+56x-13x^2+x^3+e^x(-16+8x-x^2))x-29\exp (-78+56x-13x^2+x^3+e^x(-16+8x-x^2))x^2+3\exp (-78+56x-13x^2+x^3+e^x(-16+8x-x^2))x^3-\exp (-78+57x-13x^2+x^3+e^x(-16+8x-x^2))(-1+e^3+x)(8-6x+x^2)+\exp (-75+56x-13x^2+x^3+e^x(-16+8x-x^2))(56-26x+3x^2))dx\\ & =3\int \exp (-78+56x-13x^2+x^3+e^x(-16+8x-x^2))x^{3}dx-29\int \exp (-78+56x-13x^2+x^3+e^x(-16+8x-x^2))x^{2}dx-55\int \exp (-78+56x-13x^2+x^3+e^x(-16+8x-x^2))dx+82\int \exp (-78+56x-13x^2+x^3+e^x(-16+8x-x^2))xdx-\int \exp (-78+57x-13x^2+x^3+e^x(-16+8x-x^2))(-1+e^3+x)(8-6x+x^2)dx+\int \exp (-75+56x-13x^2+x^3+e^x(-16+8x-x^2))(56-26x+3x^2)dx\\ & =3\int \exp (-78+56x-13x^2+x^3+e^x(-16+8x-x^2))x^{3}dx-29\int \exp (-78+56x-13x^2+x^3+e^x(-16+8x-x^2))x^{2}dx-55\int \exp (-78+56x-13x^2+x^3+e^x(-16+8x-x^2))dx+82\int \exp (-78+56x-13x^2+x^3+e^x(-16+8x-x^2))xdx+\int (56\exp (-75+56x-13x^2+x^3+e^x(-16+8x-x^2))-26\exp (-75+56x-13x^2+x^3+e^x(-16+8x-x^2))x+3\exp (-75+56x-13x^2+x^3+e^x(-16+8x-x^2))x^2)dx-\int (8\exp (-78+57x-13x^2+x^3+e^x(-16+8x-x^2))(-1+e^3)-2\exp (-78+57x-13x^2+x^3+e^x(-16+8x-x^2))(-7+3e^3)x+\exp (-78+57x-13x^2+x^3+e^x(-16+8x-x^2))(-7+e^3)x^2+\exp (-78+57x-13x^2+x^3+e^x(-16+8x-x^2))x^3)dx\\ & =3\int \exp (-75+56x-13x^2+x^3+e^x(-16+8x-x^2))x^{2}dx+3\int \exp (-78+56x-13x^2+x^3+e^x(-16+8x-x^2))x^{3}dx-26\int \exp (-75+56x-13x^2+x^3+e^x(-16+8x-x^2))xdx-29\int \exp (-78+56x-13x^2+x^3+e^x(-16+8x-x^2))x^{2}dx-55\int \exp (-78+56x-13x^2+x^3+e^x(-16+8x-x^2))dx+56\int \exp (-75+56x-13x^2+x^3+e^x(-16+8x-x^2))dx+82\int \exp (-78+56x-13x^2+x^3+e^x(-16+8x-x^2))xdx-\left(2(7-3e^3)\right)\int \exp (-78+57x-13x^2+x^3+e^x(-16+8x-x^2))xdx+\left(8(1-e^3)\right)\int \exp (-78+57x-13x^2+x^3+e^x(-16+8x-x^2))dx-(-7+e^3)\int \exp (-78+57x-13x^2+x^3+e^x(-16+8x-x^2))x^{2}dx-\int \exp (-78+57x-13x^2+x^3+e^x(-16+8x-x^2))x^{3}dx\end{array}\end{array}$$

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Mathematica [A]  time = 0.08, size = 32, normalized size = 1.10 $$\begin{array}{c}{e}^{-78-e^x(-4+x{)}^2+56x-13x^2+x^3}(-1+e^3+x)\end{array}$$

Antiderivative was successfully verified.

[In]

Integrate[E^(-78 + 56*x - 13*x^2 + x^3 + E^x*(-16 + 8*x - x^2))*(-55 + 82*x - 29*x^2 + 3*x^3 + E^3*(56 - 26*x
+ 3*x^2) + E^x*(8 - 14*x + 7*x^2 - x^3 + E^3*(-8 + 6*x - x^2))),x]

[Out]

E^(-78 - E^x*(-4 + x)^2 + 56*x - 13*x^2 + x^3)*(-1 + E^3 + x)

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fricas [A]  time = 0.51, size = 32, normalized size = 1.10 $$\begin{array}{c}(x+e^3-1)e^{(x^3-13x^2-(x^2-8x+16)e^x+56x-78)}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-x^2+6*x-8)*exp(3)-x^3+7*x^2-14*x+8)*exp(x)+(3*x^2-26*x+56)*exp(3)+3*x^3-29*x^2+82*x-55)*exp((-x^
2+8*x-16)*exp(x)+x^3-13*x^2+56*x-78),x, algorithm="fricas")

[Out]

(x + e^3 - 1)*e^(x^3 - 13*x^2 - (x^2 - 8*x + 16)*e^x + 56*x - 78)

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 $$\begin{array}{c}\int (3x^3-29x^2+(3x^2-26x+56)e^3-(x^3-7x^2+(x^2-6x+8)e^3+14x-8)e^x+82x-55)e^{(x^3-13x^2-(x^2-8x+16)e^x+56x-78)}dx\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-x^2+6*x-8)*exp(3)-x^3+7*x^2-14*x+8)*exp(x)+(3*x^2-26*x+56)*exp(3)+3*x^3-29*x^2+82*x-55)*exp((-x^
2+8*x-16)*exp(x)+x^3-13*x^2+56*x-78),x, algorithm="giac")

[Out]

integrate((3*x^3 - 29*x^2 + (3*x^2 - 26*x + 56)*e^3 - (x^3 - 7*x^2 + (x^2 - 6*x + 8)*e^3 + 14*x - 8)*e^x + 82*
x - 55)*e^(x^3 - 13*x^2 - (x^2 - 8*x + 16)*e^x + 56*x - 78), x)

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maple [A]  time = 0.10, size = 37, normalized size = 1.28

method	result	size
risch	$({\mathrm{e}}^3+x-1){\mathrm{e}}^{-{\mathrm{e}}^x{x}^2+x^3+8{\mathrm{e}}^{x}x-13x^2-16{\mathrm{e}}^x+56x-78}$	$37$
norman	$x{\mathrm{e}}^{(-x^2+8x-16){\mathrm{e}}^x+x^3-13x^2+56x-78}+({\mathrm{e}}^3-1){\mathrm{e}}^{(-x^2+8x-16){\mathrm{e}}^x+x^3-13x^2+56x-78}$	$63$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((-x^2+6*x-8)*exp(3)-x^3+7*x^2-14*x+8)*exp(x)+(3*x^2-26*x+56)*exp(3)+3*x^3-29*x^2+82*x-55)*exp((-x^2+8*x-
16)*exp(x)+x^3-13*x^2+56*x-78),x,method=_RETURNVERBOSE)

[Out]

(exp(3)+x-1)*exp(-exp(x)*x^2+x^3+8*exp(x)*x-13*x^2-16*exp(x)+56*x-78)

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maxima [A]  time = 33.82, size = 36, normalized size = 1.24 $$\begin{array}{c}(x+e^3-1)e^{(x^3-x^2{e}^x-13x^2+8x{e}^x+56x-16e^x-78)}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-x^2+6*x-8)*exp(3)-x^3+7*x^2-14*x+8)*exp(x)+(3*x^2-26*x+56)*exp(3)+3*x^3-29*x^2+82*x-55)*exp((-x^
2+8*x-16)*exp(x)+x^3-13*x^2+56*x-78),x, algorithm="maxima")

[Out]

(x + e^3 - 1)*e^(x^3 - x^2*e^x - 13*x^2 + 8*x*e^x + 56*x - 16*e^x - 78)

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mupad [B]  time = 0.15, size = 111, normalized size = 3.83 $$\begin{array}{c}{\mathrm{e}}^{8x{\mathrm{e}}^x}{\mathrm{e}}^{56x}{\mathrm{e}}^{x^3}{\mathrm{e}}^{-75}{\mathrm{e}}^{-x^2{\mathrm{e}}^x}{\mathrm{e}}^{-13x^2}{\mathrm{e}}^{-16{\mathrm{e}}^x}-{\mathrm{e}}^{8x{\mathrm{e}}^x}{\mathrm{e}}^{56x}{\mathrm{e}}^{x^3}{\mathrm{e}}^{-78}{\mathrm{e}}^{-x^2{\mathrm{e}}^x}{\mathrm{e}}^{-13x^2}{\mathrm{e}}^{-16{\mathrm{e}}^x}+x{\mathrm{e}}^{8x{\mathrm{e}}^x}{\mathrm{e}}^{56x}{\mathrm{e}}^{x^3}{\mathrm{e}}^{-78}{\mathrm{e}}^{-x^2{\mathrm{e}}^x}{\mathrm{e}}^{-13x^2}{\mathrm{e}}^{-16{\mathrm{e}}^x}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(56*x - exp(x)*(x^2 - 8*x + 16) - 13*x^2 + x^3 - 78)*(82*x + exp(3)*(3*x^2 - 26*x + 56) - exp(x)*(14*x
+ exp(3)*(x^2 - 6*x + 8) - 7*x^2 + x^3 - 8) - 29*x^2 + 3*x^3 - 55),x)

[Out]

exp(8*x*exp(x))*exp(56*x)*exp(x^3)*exp(-75)*exp(-x^2*exp(x))*exp(-13*x^2)*exp(-16*exp(x)) - exp(8*x*exp(x))*ex
p(56*x)*exp(x^3)*exp(-78)*exp(-x^2*exp(x))*exp(-13*x^2)*exp(-16*exp(x)) + x*exp(8*x*exp(x))*exp(56*x)*exp(x^3)
*exp(-78)*exp(-x^2*exp(x))*exp(-13*x^2)*exp(-16*exp(x))

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sympy [A]  time = 0.33, size = 32, normalized size = 1.10 $$\begin{array}{c}(x-1+e^3)e^{x^3-13x^2+56x+(-x^2+8x-16)e^x-78}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-x**2+6*x-8)*exp(3)-x**3+7*x**2-14*x+8)*exp(x)+(3*x**2-26*x+56)*exp(3)+3*x**3-29*x**2+82*x-55)*ex
p((-x**2+8*x-16)*exp(x)+x**3-13*x**2+56*x-78),x)

[Out]

(x - 1 + exp(3))*exp(x**3 - 13*x**2 + 56*x + (-x**2 + 8*x - 16)*exp(x) - 78)

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