3.57.82 \(\int (e^{-16+x}-8 x) \, dx\)

Optimal. Leaf size=23 \[ e^{-16+x}-4 x^2-4 \left (1+e^4-\log (\log (2))\right ) \]

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Rubi [A]  time = 0.00, antiderivative size = 11, normalized size of antiderivative = 0.48, number of steps used = 2, number of rules used = 1, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {2194} \begin {gather*} e^{x-16}-4 x^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Int[E^(-16 + x) - 8*x,x]

[Out]

E^(-16 + x) - 4*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} &=-4 x^2+\int e^{-16+x} \, dx\\ &=e^{-16+x}-4 x^2\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 11, normalized size = 0.48 \begin {gather*} e^{-16+x}-4 x^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[E^(-16 + x) - 8*x,x]

[Out]

E^(-16 + x) - 4*x^2

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fricas [A]  time = 0.99, size = 10, normalized size = 0.43 \begin {gather*} -4 \, x^{2} + e^{\left (x - 16\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(x-16)-8*x,x, algorithm="fricas")

[Out]

-4*x^2 + e^(x - 16)

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giac [A]  time = 0.13, size = 10, normalized size = 0.43 \begin {gather*} -4 \, x^{2} + e^{\left (x - 16\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(x-16)-8*x,x, algorithm="giac")

[Out]

-4*x^2 + e^(x - 16)

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maple [A]  time = 0.03, size = 11, normalized size = 0.48

method	result	size
default	\(-4 x^{2}+{\mathrm e}^{x -16}\)	\(11\)
norman	\(-4 x^{2}+{\mathrm e}^{x -16}\)	\(11\)
risch	\(-4 x^{2}+{\mathrm e}^{x -16}\)	\(11\)
derivativedivides	\(-4 \left (x -16\right )^{2}-128 x +2048+{\mathrm e}^{x -16}\)	\(17\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(x-16)-8*x,x,method=_RETURNVERBOSE)

[Out]

-4*x^2+exp(x-16)

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maxima [A]  time = 0.35, size = 10, normalized size = 0.43 \begin {gather*} -4 \, x^{2} + e^{\left (x - 16\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(x-16)-8*x,x, algorithm="maxima")

[Out]

-4*x^2 + e^(x - 16)

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mupad [B]  time = 0.05, size = 11, normalized size = 0.48 \begin {gather*} {\mathrm {e}}^{-16}\,{\mathrm {e}}^x-4\,x^2 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(x - 16) - 8*x,x)

[Out]

exp(-16)*exp(x) - 4*x^2

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sympy [A]  time = 0.07, size = 8, normalized size = 0.35 \begin {gather*} - 4 x^{2} + e^{x - 16} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(x-16)-8*x,x)

[Out]

-4*x**2 + exp(x - 16)

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