3.58.49 \(\int e^{24 x-48 x^2} (288-1152 x) \, dx\)

Optimal. Leaf size=18 \[ -e^4+12 e^{-12 x (-2+4 x)} \]

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Rubi [A]  time = 0.01, antiderivative size = 13, normalized size of antiderivative = 0.72, number of steps used = 1, number of rules used = 1, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.059, Rules used = {2236} \begin {gather*} 12 e^{24 x-48 x^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[E^(24*x - 48*x^2)*(288 - 1152*x),x]

[Out]

12*E^(24*x - 48*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 {gather*} \begin {aligned} \text {integral} &=12 e^{24 x-48 x^2}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.03, size = 13, normalized size = 0.72 \begin {gather*} 12 e^{24 x-48 x^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[E^(24*x - 48*x^2)*(288 - 1152*x),x]

[Out]

12*E^(24*x - 48*x^2)

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fricas [A]  time = 0.75, size = 12, normalized size = 0.67 \begin {gather*} 12 \, e^{\left (-48 \, x^{2} + 24 \, x\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-1152*x+288)/exp(48*x^2-24*x),x, algorithm="fricas")

[Out]

12*e^(-48*x^2 + 24*x)

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giac [A]  time = 0.23, size = 12, normalized size = 0.67 \begin {gather*} 12 \, e^{\left (-48 \, x^{2} + 24 \, x\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-1152*x+288)/exp(48*x^2-24*x),x, algorithm="giac")

[Out]

12*e^(-48*x^2 + 24*x)

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maple [A]  time = 0.03, size = 12, normalized size = 0.67

method	result	size
risch	\(12 \,{\mathrm e}^{-24 x \left (2 x -1\right )}\)	\(12\)
default	\(12 \,{\mathrm e}^{-48 x^{2}+24 x}\)	\(13\)
gosper	\(12 \,{\mathrm e}^{-48 x^{2}+24 x}\)	\(15\)
norman	\(12 \,{\mathrm e}^{-48 x^{2}+24 x}\)	\(15\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-1152*x+288)/exp(48*x^2-24*x),x,method=_RETURNVERBOSE)

[Out]

12*exp(-24*x*(2*x-1))

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maxima [A]  time = 0.41, size = 12, normalized size = 0.67 \begin {gather*} 12 \, e^{\left (-48 \, x^{2} + 24 \, x\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-1152*x+288)/exp(48*x^2-24*x),x, algorithm="maxima")

[Out]

12*e^(-48*x^2 + 24*x)

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mupad [B]  time = 3.76, size = 12, normalized size = 0.67 \begin {gather*} 12\,{\mathrm {e}}^{24\,x-48\,x^2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-exp(24*x - 48*x^2)*(1152*x - 288),x)

[Out]

12*exp(24*x - 48*x^2)

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sympy [A]  time = 0.09, size = 10, normalized size = 0.56 \begin {gather*} 12 e^{- 48 x^{2} + 24 x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-1152*x+288)/exp(48*x**2-24*x),x)

[Out]

12*exp(-48*x**2 + 24*x)

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