3.75.44 \(\int e^{-4+e^{16} (1-x)+4 x+x^2-x^3+e^8 (-2 x+2 x^2)} (4-e^{16}+2 x-3 x^2+e^8 (-2+4 x)) \, dx\)

Optimal. Leaf size=19 \[ e^{(-1+x) \left (4-\left (-e^8+x\right )^2\right )} \]

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Rubi [A]  time = 0.21, antiderivative size = 36, normalized size of antiderivative = 1.89, number of steps used = 1, number of rules used = 1, integrand size = 62, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.016, Rules used = {6706} \begin {gather*} \exp \left (-x^3+x^2-2 e^8 \left (x-x^2\right )+4 x+e^{16} (1-x)-4\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[E^(-4 + E^16*(1 - x) + 4*x + x^2 - x^3 + E^8*(-2*x + 2*x^2))*(4 - E^16 + 2*x - 3*x^2 + E^8*(-2 + 4*x)),x]

[Out]

E^(-4 + E^16*(1 - x) + 4*x + x^2 - x^3 - 2*E^8*(x - x^2))

Rule 6706

Int[(F_)^(v_)*(u_), x_Symbol] :> With[{q = DerivativeDivides[v, u, x]}, Simp[(q*F^v)/Log[F], x] /;  !FalseQ[q]
] /; FreeQ[F, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\exp \left (-4+e^{16} (1-x)+4 x+x^2-x^3-2 e^8 \left (x-x^2\right )\right )\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.29, size = 32, normalized size = 1.68 \begin {gather*} e^{-4-e^{16} (-1+x)+4 x+2 e^8 (-1+x) x+x^2-x^3} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[E^(-4 + E^16*(1 - x) + 4*x + x^2 - x^3 + E^8*(-2*x + 2*x^2))*(4 - E^16 + 2*x - 3*x^2 + E^8*(-2 + 4*x
)),x]

[Out]

E^(-4 - E^16*(-1 + x) + 4*x + 2*E^8*(-1 + x)*x + x^2 - x^3)

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fricas [A]  time = 0.88, size = 32, normalized size = 1.68 \begin {gather*} e^{\left (-x^{3} + x^{2} - {\left (x - 1\right )} e^{16} + 2 \, {\left (x^{2} - x\right )} e^{8} + 4 \, x - 4\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-exp(8)^2+(4*x-2)*exp(8)-3*x^2+2*x+4)*exp((-x+1)*exp(8)^2+(2*x^2-2*x)*exp(8)-x^3+x^2+4*x-4),x, algo
rithm="fricas")

[Out]

e^(-x^3 + x^2 - (x - 1)*e^16 + 2*(x^2 - x)*e^8 + 4*x - 4)

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giac [B]  time = 0.23, size = 33, normalized size = 1.74 \begin {gather*} e^{\left (-x^{3} + 2 \, x^{2} e^{8} + x^{2} - x e^{16} - 2 \, x e^{8} + 4 \, x + e^{16} - 4\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-exp(8)^2+(4*x-2)*exp(8)-3*x^2+2*x+4)*exp((-x+1)*exp(8)^2+(2*x^2-2*x)*exp(8)-x^3+x^2+4*x-4),x, algo
rithm="giac")

[Out]

e^(-x^3 + 2*x^2*e^8 + x^2 - x*e^16 - 2*x*e^8 + 4*x + e^16 - 4)

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maple [A]  time = 0.03, size = 19, normalized size = 1.00

method	result	size
risch	\({\mathrm e}^{-\left (x -1\right ) \left (-2 x \,{\mathrm e}^{8}+x^{2}+{\mathrm e}^{16}-4\right )}\)	\(19\)
derivativedivides	\({\mathrm e}^{\left (1-x \right ) {\mathrm e}^{16}+\left (2 x^{2}-2 x \right ) {\mathrm e}^{8}-x^{3}+x^{2}+4 x -4}\)	\(37\)
default	\({\mathrm e}^{\left (1-x \right ) {\mathrm e}^{16}+\left (2 x^{2}-2 x \right ) {\mathrm e}^{8}-x^{3}+x^{2}+4 x -4}\)	\(37\)
norman	\({\mathrm e}^{\left (1-x \right ) {\mathrm e}^{16}+\left (2 x^{2}-2 x \right ) {\mathrm e}^{8}-x^{3}+x^{2}+4 x -4}\)	\(37\)
gosper	\({\mathrm e}^{2 x^{2} {\mathrm e}^{8}-x^{3}-2 x \,{\mathrm e}^{8}-x \,{\mathrm e}^{16}+x^{2}+{\mathrm e}^{16}+4 x -4}\)	\(38\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-exp(8)^2+(4*x-2)*exp(8)-3*x^2+2*x+4)*exp((1-x)*exp(8)^2+(2*x^2-2*x)*exp(8)-x^3+x^2+4*x-4),x,method=_RETU
RNVERBOSE)

[Out]

exp(-(x-1)*(-2*x*exp(8)+x^2+exp(16)-4))

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maxima [A]  time = 0.36, size = 32, normalized size = 1.68 \begin {gather*} e^{\left (-x^{3} + x^{2} - {\left (x - 1\right )} e^{16} + 2 \, {\left (x^{2} - x\right )} e^{8} + 4 \, x - 4\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-exp(8)^2+(4*x-2)*exp(8)-3*x^2+2*x+4)*exp((-x+1)*exp(8)^2+(2*x^2-2*x)*exp(8)-x^3+x^2+4*x-4),x, algo
rithm="maxima")

[Out]

e^(-x^3 + x^2 - (x - 1)*e^16 + 2*(x^2 - x)*e^8 + 4*x - 4)

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mupad [B]  time = 0.21, size = 40, normalized size = 2.11 \begin {gather*} {\mathrm {e}}^{2\,x^2\,{\mathrm {e}}^8}\,{\mathrm {e}}^{4\,x}\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{-4}\,{\mathrm {e}}^{-x^3}\,{\mathrm {e}}^{-2\,x\,{\mathrm {e}}^8}\,{\mathrm {e}}^{-x\,{\mathrm {e}}^{16}}\,{\mathrm {e}}^{{\mathrm {e}}^{16}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(4*x - exp(8)*(2*x - 2*x^2) - exp(16)*(x - 1) + x^2 - x^3 - 4)*(2*x - exp(16) - 3*x^2 + exp(8)*(4*x - 2
) + 4),x)

[Out]

exp(2*x^2*exp(8))*exp(4*x)*exp(x^2)*exp(-4)*exp(-x^3)*exp(-2*x*exp(8))*exp(-x*exp(16))*exp(exp(16))

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sympy [B]  time = 0.16, size = 31, normalized size = 1.63 \begin {gather*} e^{- x^{3} + x^{2} + 4 x + \left (1 - x\right ) e^{16} + \left (2 x^{2} - 2 x\right ) e^{8} - 4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-exp(8)**2+(4*x-2)*exp(8)-3*x**2+2*x+4)*exp((-x+1)*exp(8)**2+(2*x**2-2*x)*exp(8)-x**3+x**2+4*x-4),x
)

[Out]

exp(-x**3 + x**2 + 4*x + (1 - x)*exp(16) + (2*x**2 - 2*x)*exp(8) - 4)

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