3.66.10 \(\int (-2+4 e^2-12 x) \, dx\)

Optimal. Leaf size=13 \[ 2 \left (-1+2 e^2-3 x\right ) x \]

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Rubi [A]  time = 0.01, antiderivative size = 16, normalized size of antiderivative = 1.23, number of steps used = 1, number of rules used = 0, integrand size = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} -6 x^2-2 \left (1-2 e^2\right ) x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-2 + 4*E^2 - 12*x,x]

[Out]

-2*(1 - 2*E^2)*x - 6*x^2

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=-2 \left (1-2 e^2\right ) x-6 x^2\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 15, normalized size = 1.15 \begin {gather*} -2 x+4 e^2 x-6 x^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-2 + 4*E^2 - 12*x,x]

[Out]

-2*x + 4*E^2*x - 6*x^2

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fricas [A]  time = 1.32, size = 14, normalized size = 1.08 \begin {gather*} -6 \, x^{2} + 4 \, x e^{2} - 2 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(4*exp(2)-12*x-2,x, algorithm="fricas")

[Out]

-6*x^2 + 4*x*e^2 - 2*x

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giac [A]  time = 0.14, size = 14, normalized size = 1.08 \begin {gather*} -6 \, x^{2} + 4 \, x e^{2} - 2 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(4*exp(2)-12*x-2,x, algorithm="giac")

[Out]

-6*x^2 + 4*x*e^2 - 2*x

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maple [A]  time = 0.04, size = 13, normalized size = 1.00

method	result	size
gosper	\(2 \left (-1-3 x +2 \,{\mathrm e}^{2}\right ) x\)	\(13\)
default	\(4 \,{\mathrm e}^{2} x -6 x^{2}-2 x\)	\(15\)
norman	\(\left (4 \,{\mathrm e}^{2}-2\right ) x -6 x^{2}\)	\(15\)
risch	\(4 \,{\mathrm e}^{2} x -6 x^{2}-2 x\)	\(15\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(4*exp(2)-12*x-2,x,method=_RETURNVERBOSE)

[Out]

2*(-1-3*x+2*exp(2))*x

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maxima [A]  time = 0.39, size = 14, normalized size = 1.08 \begin {gather*} -6 \, x^{2} + 4 \, x e^{2} - 2 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(4*exp(2)-12*x-2,x, algorithm="maxima")

[Out]

-6*x^2 + 4*x*e^2 - 2*x

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mupad [B]  time = 0.04, size = 12, normalized size = 0.92 \begin {gather*} -2\,x\,\left (3\,x-2\,{\mathrm {e}}^2+1\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(4*exp(2) - 12*x - 2,x)

[Out]

-2*x*(3*x - 2*exp(2) + 1)

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sympy [A]  time = 0.05, size = 12, normalized size = 0.92 \begin {gather*} - 6 x^{2} + x \left (-2 + 4 e^{2}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(4*exp(2)-12*x-2,x)

[Out]

-6*x**2 + x*(-2 + 4*exp(2))

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