3.63.42 \(\int (1+e^{4 e^2-x}+18 x) \, dx\)

Optimal. Leaf size=20 \[ -e^{4 e^2-x}+x+9 x^2 \]

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Rubi [A]  time = 0.01, antiderivative size = 20, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {2194} \begin {gather*} 9 x^2+x-e^{4 e^2-x} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[1 + E^(4*E^2 - x) + 18*x,x]

[Out]

-E^(4*E^2 - x) + x + 9*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+9 x^2+\int e^{4 e^2-x} \, dx\\ &=-e^{4 e^2-x}+x+9 x^2\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.01, size = 20, normalized size = 1.00 \begin {gather*} -e^{4 e^2-x}+x+9 x^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[1 + E^(4*E^2 - x) + 18*x,x]

[Out]

-E^(4*E^2 - x) + x + 9*x^2

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fricas [A]  time = 0.60, size = 18, normalized size = 0.90 \begin {gather*} 9 \, x^{2} + x - e^{\left (-x + 4 \, e^{2}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(-x)*exp(4*exp(1)^2)+18*x+1,x, algorithm="fricas")

[Out]

9*x^2 + x - e^(-x + 4*e^2)

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giac [A]  time = 0.11, size = 18, normalized size = 0.90 \begin {gather*} 9 \, x^{2} + x - e^{\left (-x + 4 \, e^{2}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(-x)*exp(4*exp(1)^2)+18*x+1,x, algorithm="giac")

[Out]

9*x^2 + x - e^(-x + 4*e^2)

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maple [A]  time = 0.04, size = 19, normalized size = 0.95

method	result	size
risch	\(x +9 x^{2}-{\mathrm e}^{4 \,{\mathrm e}^{2}-x}\)	\(19\)
derivativedivides	\(x -{\mathrm e}^{4 \,{\mathrm e}^{2}} {\mathrm e}^{-x}+9 x^{2}\)	\(21\)
default	\(x -{\mathrm e}^{4 \,{\mathrm e}^{2}} {\mathrm e}^{-x}+9 x^{2}\)	\(21\)
norman	\(x -{\mathrm e}^{4 \,{\mathrm e}^{2}} {\mathrm e}^{-x}+9 x^{2}\)	\(21\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(-x)*exp(4*exp(1)^2)+18*x+1,x,method=_RETURNVERBOSE)

[Out]

x+9*x^2-exp(4*exp(2)-x)

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maxima [A]  time = 0.34, size = 18, normalized size = 0.90 \begin {gather*} 9 \, x^{2} + x - e^{\left (-x + 4 \, e^{2}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(-x)*exp(4*exp(1)^2)+18*x+1,x, algorithm="maxima")

[Out]

9*x^2 + x - e^(-x + 4*e^2)

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mupad [B]  time = 0.06, size = 18, normalized size = 0.90 \begin {gather*} x-{\mathrm {e}}^{4\,{\mathrm {e}}^2}\,{\mathrm {e}}^{-x}+9\,x^2 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(18*x + exp(4*exp(2))*exp(-x) + 1,x)

[Out]

x - exp(4*exp(2))*exp(-x) + 9*x^2

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sympy [A]  time = 0.09, size = 15, normalized size = 0.75 \begin {gather*} 9 x^{2} + x - e^{- x} e^{4 e^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(-x)*exp(4*exp(1)**2)+18*x+1,x)

[Out]

9*x**2 + x - exp(-x)*exp(4*exp(2))

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