3.22.73 \(\int (1-2 e^{2 e^2+2 x}+2 x) \, dx\)

Optimal. Leaf size=18 \[ -e^{2 e^2+2 x}+x+x^2 \]

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Rubi [A]  time = 0.01, antiderivative size = 18, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {2194} \begin {gather*} x^2+x-e^{2 x+2 e^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[1 - 2*E^(2*E^2 + 2*x) + 2*x,x]

[Out]

-E^(2*E^2 + 2*x) + 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]

Rubi steps

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

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Mathematica [A]  time = 0.01, size = 18, normalized size = 1.00 \begin {gather*} -e^{2 e^2+2 x}+x+x^2 \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

-E^(2*E^2 + 2*x) + x + x^2

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fricas [A]  time = 0.60, size = 16, normalized size = 0.89 \begin {gather*} x^{2} + x - e^{\left (2 \, x + 2 \, e^{2}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x^2 + x - e^(2*x + 2*e^2)

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giac [A]  time = 0.17, size = 16, normalized size = 0.89 \begin {gather*} x^{2} + x - e^{\left (2 \, x + 2 \, e^{2}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x^2 + x - e^(2*x + 2*e^2)

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maple [A]  time = 0.06, size = 15, normalized size = 0.83

method	result	size
default	\(x -{\mathrm e}^{2 x +2 \,{\mathrm e}^{2}}+x^{2}\)	\(15\)
norman	\(x -{\mathrm e}^{2 x +2 \,{\mathrm e}^{2}}+x^{2}\)	\(15\)
risch	\(x -{\mathrm e}^{2 x +2 \,{\mathrm e}^{2}}+x^{2}\)	\(17\)
derivativedivides	\(\left (x +{\mathrm e}^{2}\right )^{2}+x +{\mathrm e}^{2}-{\mathrm e}^{2 x +2 \,{\mathrm e}^{2}}-2 \,{\mathrm e}^{2} \left (x +{\mathrm e}^{2}\right )\)	\(28\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x-exp(x+exp(2))^2+x^2

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maxima [A]  time = 0.35, size = 16, normalized size = 0.89 \begin {gather*} x^{2} + x - e^{\left (2 \, x + 2 \, e^{2}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x^2 + x - e^(2*x + 2*e^2)

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mupad [B]  time = 0.08, size = 16, normalized size = 0.89 \begin {gather*} x-{\mathrm {e}}^{2\,{\mathrm {e}}^2}\,{\mathrm {e}}^{2\,x}+x^2 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(2*x - 2*exp(2*x + 2*exp(2)) + 1,x)

[Out]

x - exp(2*exp(2))*exp(2*x) + x^2

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sympy [A]  time = 0.09, size = 14, normalized size = 0.78 \begin {gather*} x^{2} + x - e^{2 x + 2 e^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x**2 + x - exp(2*x + 2*exp(2))

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