3.23.91 \(\int (2+e^{-1+5 x-3 x^2} (-10+12 x)) \, dx\)

Optimal. Leaf size=22 \[ 2 \left (-e^{-1+2 x+3 \left (x-x^2\right )}+x\right ) \]

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Rubi [A]  time = 0.02, antiderivative size = 18, normalized size of antiderivative = 0.82, number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {2236} \begin {gather*} 2 x-2 e^{-3 x^2+5 x-1} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[2 + E^(-1 + 5*x - 3*x^2)*(-10 + 12*x),x]

[Out]

-2*E^(-1 + 5*x - 3*x^2) + 2*x

Rule 2236

Int[(F_)^((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)*((d_.) + (e_.)*(x_)), x_Symbol] :> Simp[(e*F^(a + b*x + c*x^2))/(
2*c*Log[F]), x] /; FreeQ[{F, a, b, c, d, e}, x] && EqQ[b*e - 2*c*d, 0]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=2 x+\int e^{-1+5 x-3 x^2} (-10+12 x) \, dx\\ &=-2 e^{-1+5 x-3 x^2}+2 x\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.04, size = 18, normalized size = 0.82 \begin {gather*} -2 e^{-1+5 x-3 x^2}+2 x \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[2 + E^(-1 + 5*x - 3*x^2)*(-10 + 12*x),x]

[Out]

-2*E^(-1 + 5*x - 3*x^2) + 2*x

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fricas [A]  time = 1.15, size = 17, normalized size = 0.77 \begin {gather*} 2 \, x - 2 \, e^{\left (-3 \, x^{2} + 5 \, x - 1\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((12*x-10)*exp(-3*x^2+5*x-1)+2,x, algorithm="fricas")

[Out]

2*x - 2*e^(-3*x^2 + 5*x - 1)

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giac [A]  time = 0.42, size = 17, normalized size = 0.77 \begin {gather*} 2 \, x - 2 \, e^{\left (-3 \, x^{2} + 5 \, x - 1\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((12*x-10)*exp(-3*x^2+5*x-1)+2,x, algorithm="giac")

[Out]

2*x - 2*e^(-3*x^2 + 5*x - 1)

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maple [A]  time = 0.04, size = 18, normalized size = 0.82

method	result	size
default	\(2 x -2 \,{\mathrm e}^{-3 x^{2}+5 x -1}\)	\(18\)
norman	\(2 x -2 \,{\mathrm e}^{-3 x^{2}+5 x -1}\)	\(18\)
risch	\(2 x -2 \,{\mathrm e}^{-3 x^{2}+5 x -1}\)	\(18\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((12*x-10)*exp(-3*x^2+5*x-1)+2,x,method=_RETURNVERBOSE)

[Out]

2*x-2*exp(-3*x^2+5*x-1)

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maxima [A]  time = 0.46, size = 17, normalized size = 0.77 \begin {gather*} 2 \, x - 2 \, e^{\left (-3 \, x^{2} + 5 \, x - 1\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((12*x-10)*exp(-3*x^2+5*x-1)+2,x, algorithm="maxima")

[Out]

2*x - 2*e^(-3*x^2 + 5*x - 1)

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mupad [B]  time = 0.09, size = 18, normalized size = 0.82 \begin {gather*} 2\,x-2\,{\mathrm {e}}^{5\,x}\,{\mathrm {e}}^{-1}\,{\mathrm {e}}^{-3\,x^2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(5*x - 3*x^2 - 1)*(12*x - 10) + 2,x)

[Out]

2*x - 2*exp(5*x)*exp(-1)*exp(-3*x^2)

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sympy [A]  time = 0.09, size = 15, normalized size = 0.68 \begin {gather*} 2 x - 2 e^{- 3 x^{2} + 5 x - 1} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((12*x-10)*exp(-3*x**2+5*x-1)+2,x)

[Out]

2*x - 2*exp(-3*x**2 + 5*x - 1)

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