3.69.23 $\int e^{4+8x+4x^2}(-24-24x)dx$

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

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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 = {2236} $$\begin{array}{c}-3e^{4x^2+8x+4}\end{array}$$

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 2236

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

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =-3e^{4+8x+4x^2}\end{array}\end{array}$$

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Mathematica [A]  time = 0.00, size = 11, normalized size = 0.50 $$\begin{array}{c}-3e^{4(1+x{)}^2}\end{array}$$

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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fricas [A]  time = 0.68, size = 13, normalized size = 0.59 $$\begin{array}{c}-3e^{(4x^2+8x+4)}\end{array}$$

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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giac [A]  time = 0.12, size = 13, normalized size = 0.59 $$\begin{array}{c}-3e^{(4x^2+8x+4)}\end{array}$$

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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maple [A]  time = 0.03, size = 11, normalized size = 0.50

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

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+1)^2)

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maxima [A]  time = 0.37, size = 13, normalized size = 0.59 $$\begin{array}{c}-3e^{(4x^2+8x+4)}\end{array}$$

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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mupad [B]  time = 0.05, size = 14, normalized size = 0.64 $$\begin{array}{c}-3{\mathrm{e}}^{8x}{\mathrm{e}}^4{\mathrm{e}}^{4x^2}\end{array}$$

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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sympy [A]  time = 0.11, size = 14, normalized size = 0.64 $$\begin{array}{c}-3e^{4x^2+8x+4}\end{array}$$

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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