3.31.97 \(\int (-2 e^{-3+2 x}+e^{-22+x-x^2} (1-2 x)) \, dx\)

Optimal. Leaf size=24 \[ -5-e^{-3+2 x}+e^{-22-x-(-2+x) x} \]

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Rubi [A]  time = 0.02, antiderivative size = 20, normalized size of antiderivative = 0.83, number of steps used = 3, number of rules used = 2, integrand size = 26, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {2194, 2236} \begin {gather*} e^{-x^2+x-22}-e^{2 x-3} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-2*E^(-3 + 2*x) + E^(-22 + x - x^2)*(1 - 2*x),x]

[Out]

-E^(-3 + 2*x) + E^(-22 + x - x^2)

Rule 2194

Int[((F_)^((c_.)*((a_.) + (b_.)*(x_))))^(n_.), x_Symbol] :> Simp[(F^(c*(a + b*x)))^n/(b*c*n*Log[F]), x] /; Fre
eQ[{F, a, b, c, n}, 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} &=-\left (2 \int e^{-3+2 x} \, dx\right )+\int e^{-22+x-x^2} (1-2 x) \, dx\\ &=-e^{-3+2 x}+e^{-22+x-x^2}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.04, size = 20, normalized size = 0.83 \begin {gather*} -e^{-3+2 x}+e^{-22+x-x^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-2*E^(-3 + 2*x) + E^(-22 + x - x^2)*(1 - 2*x),x]

[Out]

-E^(-3 + 2*x) + E^(-22 + x - x^2)

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fricas [A]  time = 0.56, size = 18, normalized size = 0.75 \begin {gather*} e^{\left (-x^{2} + x - 22\right )} - e^{\left (2 \, x - 3\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-2*exp(2*x-3)+(1-2*x)*exp(-x^2+x-22),x, algorithm="fricas")

[Out]

e^(-x^2 + x - 22) - e^(2*x - 3)

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giac [A]  time = 0.25, size = 18, normalized size = 0.75 \begin {gather*} e^{\left (-x^{2} + x - 22\right )} - e^{\left (2 \, x - 3\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-2*exp(2*x-3)+(1-2*x)*exp(-x^2+x-22),x, algorithm="giac")

[Out]

e^(-x^2 + x - 22) - e^(2*x - 3)

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maple [A]  time = 0.02, size = 19, normalized size = 0.79

method	result	size
default	\({\mathrm e}^{-x^{2}+x -22}-{\mathrm e}^{2 x -3}\)	\(19\)
norman	\({\mathrm e}^{-x^{2}+x -22}-{\mathrm e}^{2 x -3}\)	\(19\)
risch	\({\mathrm e}^{-x^{2}+x -22}-{\mathrm e}^{2 x -3}\)	\(19\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-2*exp(2*x-3)+(1-2*x)*exp(-x^2+x-22),x,method=_RETURNVERBOSE)

[Out]

exp(-x^2+x-22)-exp(2*x-3)

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maxima [A]  time = 0.46, size = 18, normalized size = 0.75 \begin {gather*} e^{\left (-x^{2} + x - 22\right )} - e^{\left (2 \, x - 3\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-2*exp(2*x-3)+(1-2*x)*exp(-x^2+x-22),x, algorithm="maxima")

[Out]

e^(-x^2 + x - 22) - e^(2*x - 3)

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mupad [B]  time = 0.11, size = 20, normalized size = 0.83 \begin {gather*} {\mathrm {e}}^{-22}\,{\mathrm {e}}^{-x^2}\,{\mathrm {e}}^x-{\mathrm {e}}^{2\,x}\,{\mathrm {e}}^{-3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(- 2*exp(2*x - 3) - exp(x - x^2 - 22)*(2*x - 1),x)

[Out]

exp(-22)*exp(-x^2)*exp(x) - exp(2*x)*exp(-3)

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sympy [A]  time = 0.13, size = 14, normalized size = 0.58 \begin {gather*} - e^{2 x - 3} + e^{- x^{2} + x - 22} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-2*exp(2*x-3)+(1-2*x)*exp(-x**2+x-22),x)

[Out]

-exp(2*x - 3) + exp(-x**2 + x - 22)

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