3.69.23 \(\int e^{4+8 x+4 x^2} (-24-24 x) \, dx\) [6823]

Optimal. Leaf size=22 \[ 3 \left (-e^{(2+2 x)^2}+\frac {1}{4 \log ^2(2)}\right ) \]

[Out]

3/4/ln(2)^2-3*exp((2+2*x)^2)

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Rubi [A]
time = 0.01, antiderivative size = 14, normalized size of antiderivative = 0.64, number of steps used = 1, number of rules used = 1, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {2268} \begin {gather*} -3 e^{4 x^2+8 x+4} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[E^(4 + 8*x + 4*x^2)*(-24 - 24*x),x]

[Out]

-3*E^(4 + 8*x + 4*x^2)

Rule 2268

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} &=-3 e^{4+8 x+4 x^2}\\ \end {aligned} \end {gather*}

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Mathematica [A]
time = 0.02, size = 11, normalized size = 0.50 \begin {gather*} -3 e^{4 (1+x)^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[E^(4 + 8*x + 4*x^2)*(-24 - 24*x),x]

[Out]

-3*E^(4*(1 + x)^2)

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Maple [A]
time = 0.03, size = 14, normalized size = 0.64

method	result	size
risch	\(-3 \,{\mathrm e}^{4 \left (x +1\right )^{2}}\)	\(11\)
gosper	\(-3 \,{\mathrm e}^{4 x^{2}+8 x +4}\)	\(14\)
default	\(-3 \,{\mathrm e}^{4 x^{2}+8 x +4}\)	\(14\)
norman	\(-3 \,{\mathrm e}^{4 x^{2}+8 x +4}\)	\(14\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-24*x-24)*exp(4*x^2+8*x+4),x,method=_RETURNVERBOSE)

[Out]

-3*exp(4*x^2+8*x+4)

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Maxima [A]
time = 0.29, size = 13, normalized size = 0.59 \begin {gather*} -3 \, e^{\left (4 \, x^{2} + 8 \, x + 4\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-24*x-24)*exp(4*x^2+8*x+4),x, algorithm="maxima")

[Out]

-3*e^(4*x^2 + 8*x + 4)

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Fricas [A]
time = 0.42, size = 13, normalized size = 0.59 \begin {gather*} -3 \, e^{\left (4 \, x^{2} + 8 \, x + 4\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-24*x-24)*exp(4*x^2+8*x+4),x, algorithm="fricas")

[Out]

-3*e^(4*x^2 + 8*x + 4)

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Sympy [A]
time = 0.03, size = 14, normalized size = 0.64 \begin {gather*} - 3 e^{4 x^{2} + 8 x + 4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-24*x-24)*exp(4*x**2+8*x+4),x)

[Out]

-3*exp(4*x**2 + 8*x + 4)

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Giac [A]
time = 0.41, size = 13, normalized size = 0.59 \begin {gather*} -3 \, e^{\left (4 \, x^{2} + 8 \, x + 4\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-24*x-24)*exp(4*x^2+8*x+4),x, algorithm="giac")

[Out]

-3*e^(4*x^2 + 8*x + 4)

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Mupad [B]
time = 0.05, size = 14, normalized size = 0.64 \begin {gather*} -3\,{\mathrm {e}}^{8\,x}\,{\mathrm {e}}^4\,{\mathrm {e}}^{4\,x^2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-exp(8*x + 4*x^2 + 4)*(24*x + 24),x)

[Out]

-3*exp(8*x)*exp(4)*exp(4*x^2)

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