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

Optimal. Leaf size=18 \[ -1+e^{-6 e^3+x} (-3+x)-x \]

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Rubi [A]  time = 0.02, antiderivative size = 31, normalized size of antiderivative = 1.72, number of steps used = 3, number of rules used = 2, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.133, Rules used = {2176, 2194} \begin {gather*} -e^{x-6 e^3} (2-x)-e^{x-6 e^3}-x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-1 + E^(-6*E^3 + x)*(-2 + x),x]

[Out]

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

Rule 2176

Int[((b_.)*(F_)^((g_.)*((e_.) + (f_.)*(x_))))^(n_.)*((c_.) + (d_.)*(x_))^(m_.), x_Symbol] :> Simp[((c + d*x)^m
*(b*F^(g*(e + f*x)))^n)/(f*g*n*Log[F]), x] - Dist[(d*m)/(f*g*n*Log[F]), Int[(c + d*x)^(m - 1)*(b*F^(g*(e + f*x
)))^n, x], x] /; FreeQ[{F, b, c, d, e, f, g, n}, x] && GtQ[m, 0] && IntegerQ[2*m] &&  !$UseGamma === True

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]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=-x+\int e^{-6 e^3+x} (-2+x) \, dx\\ &=-e^{-6 e^3+x} (2-x)-x-\int e^{-6 e^3+x} \, dx\\ &=-e^{-6 e^3+x}-e^{-6 e^3+x} (2-x)-x\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.03, size = 27, normalized size = 1.50 \begin {gather*} -x+e^x \left (-3 e^{-6 e^3}+e^{-6 e^3} x\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

-x + E^x*(-3/E^(6*E^3) + x/E^(6*E^3))

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fricas [A]  time = 0.96, size = 15, normalized size = 0.83 \begin {gather*} {\left (x - 3\right )} e^{\left (x - 6 \, e^{3}\right )} - x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

(x - 3)*e^(x - 6*e^3) - x

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giac [A]  time = 0.22, size = 15, normalized size = 0.83 \begin {gather*} {\left (x - 3\right )} e^{\left (x - 6 \, e^{3}\right )} - x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

(x - 3)*e^(x - 6*e^3) - x

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maple [A]  time = 0.02, size = 16, normalized size = 0.89

method	result	size
risch	\(\left (x -3\right ) {\mathrm e}^{-6 \,{\mathrm e}^{3}+x}-x\)	\(16\)
norman	\({\mathrm e}^{-6 \,{\mathrm e}^{3}+x} x -x -3 \,{\mathrm e}^{-6 \,{\mathrm e}^{3}+x}\)	\(23\)
default	\(-x +{\mathrm e}^{-6 \,{\mathrm e}^{3}+x} \left (-6 \,{\mathrm e}^{3}+x \right )-3 \,{\mathrm e}^{-6 \,{\mathrm e}^{3}+x}+6 \,{\mathrm e}^{-6 \,{\mathrm e}^{3}+x} {\mathrm e}^{3}\)	\(39\)
derivativedivides	\(6 \,{\mathrm e}^{3}-x +{\mathrm e}^{-6 \,{\mathrm e}^{3}+x} \left (-6 \,{\mathrm e}^{3}+x \right )-3 \,{\mathrm e}^{-6 \,{\mathrm e}^{3}+x}+6 \,{\mathrm e}^{-6 \,{\mathrm e}^{3}+x} {\mathrm e}^{3}\)	\(43\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maxima [A]  time = 0.37, size = 24, normalized size = 1.33 \begin {gather*} {\left (x - 1\right )} e^{\left (x - 6 \, e^{3}\right )} - x - 2 \, e^{\left (x - 6 \, e^{3}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

(x - 1)*e^(x - 6*e^3) - x - 2*e^(x - 6*e^3)

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mupad [B]  time = 0.06, size = 22, normalized size = 1.22 \begin {gather*} x\,{\mathrm {e}}^{-6\,{\mathrm {e}}^3}\,{\mathrm {e}}^x-3\,{\mathrm {e}}^{-6\,{\mathrm {e}}^3}\,{\mathrm {e}}^x-x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(x - 6*exp(3))*(x - 2) - 1,x)

[Out]

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

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sympy [A]  time = 0.08, size = 12, normalized size = 0.67 \begin {gather*} - x + \left (x - 3\right ) e^{x - 6 e^{3}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-x + (x - 3)*exp(x - 6*exp(3))

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