3.76.65 \(\int e^{e^x+3 x-6 x^2} (-1-3 x-e^x x+12 x^2) \, dx\)

Optimal. Leaf size=19 \[ 3-e^{e^x+3 x-6 x^2} x \]

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Rubi [B]  time = 0.11, antiderivative size = 40, normalized size of antiderivative = 2.11, number of steps used = 1, number of rules used = 1, integrand size = 31, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.032, Rules used = {2288} \begin {gather*} -\frac {e^{-6 x^2+3 x+e^x} \left (-12 x^2+e^x x+3 x\right )}{-12 x+e^x+3} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[E^(E^x + 3*x - 6*x^2)*(-1 - 3*x - E^x*x + 12*x^2),x]

[Out]

-((E^(E^x + 3*x - 6*x^2)*(3*x + E^x*x - 12*x^2))/(3 + E^x - 12*x))

Rule 2288

Int[(y_.)*(F_)^(u_)*((v_) + (w_)), x_Symbol] :> With[{z = (v*y)/(Log[F]*D[u, x])}, Simp[F^u*z, x] /; EqQ[D[z,
x], w*y]] /; FreeQ[F, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=-\frac {e^{e^x+3 x-6 x^2} \left (3 x+e^x x-12 x^2\right )}{3+e^x-12 x}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.05, size = 17, normalized size = 0.89 \begin {gather*} -e^{e^x+3 x-6 x^2} x \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[E^(E^x + 3*x - 6*x^2)*(-1 - 3*x - E^x*x + 12*x^2),x]

[Out]

-(E^(E^x + 3*x - 6*x^2)*x)

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fricas [A]  time = 0.50, size = 15, normalized size = 0.79 \begin {gather*} -x e^{\left (-6 \, x^{2} + 3 \, x + e^{x}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-exp(x)*x+12*x^2-3*x-1)*exp(exp(x)-6*x^2+3*x),x, algorithm="fricas")

[Out]

-x*e^(-6*x^2 + 3*x + e^x)

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giac [A]  time = 0.28, size = 15, normalized size = 0.79 \begin {gather*} -x e^{\left (-6 \, x^{2} + 3 \, x + e^{x}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-exp(x)*x+12*x^2-3*x-1)*exp(exp(x)-6*x^2+3*x),x, algorithm="giac")

[Out]

-x*e^(-6*x^2 + 3*x + e^x)

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maple [A]  time = 0.03, size = 16, normalized size = 0.84

method	result	size
norman	\(-{\mathrm e}^{{\mathrm e}^{x}-6 x^{2}+3 x} x\)	\(16\)
risch	\(-{\mathrm e}^{{\mathrm e}^{x}-6 x^{2}+3 x} x\)	\(16\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-exp(x)*x+12*x^2-3*x-1)*exp(exp(x)-6*x^2+3*x),x,method=_RETURNVERBOSE)

[Out]

-exp(exp(x)-6*x^2+3*x)*x

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maxima [A]  time = 0.42, size = 15, normalized size = 0.79 \begin {gather*} -x e^{\left (-6 \, x^{2} + 3 \, x + e^{x}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-exp(x)*x+12*x^2-3*x-1)*exp(exp(x)-6*x^2+3*x),x, algorithm="maxima")

[Out]

-x*e^(-6*x^2 + 3*x + e^x)

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mupad [B]  time = 4.54, size = 16, normalized size = 0.84 \begin {gather*} -x\,{\mathrm {e}}^{3\,x}\,{\mathrm {e}}^{{\mathrm {e}}^x}\,{\mathrm {e}}^{-6\,x^2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-exp(3*x + exp(x) - 6*x^2)*(3*x + x*exp(x) - 12*x^2 + 1),x)

[Out]

-x*exp(3*x)*exp(exp(x))*exp(-6*x^2)

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sympy [A]  time = 0.16, size = 15, normalized size = 0.79 \begin {gather*} - x e^{- 6 x^{2} + 3 x + e^{x}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-exp(x)*x+12*x**2-3*x-1)*exp(exp(x)-6*x**2+3*x),x)

[Out]

-x*exp(-6*x**2 + 3*x + exp(x))

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