3.4.19 \(\int (-2-12 x) \, dx\)

Optimal. Leaf size=14 \[ 2 (-1-3 x) x-\log (\log (5)) \]

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Rubi [A]  time = 0.00, antiderivative size = 9, normalized size of antiderivative = 0.64, number of steps used = 1, number of rules used = 0, integrand size = 5, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} -6 x^2-2 x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-2 - 12*x,x]

[Out]

-2*x - 6*x^2

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=-2 x-6 x^2\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 9, normalized size = 0.64 \begin {gather*} -2 x-6 x^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-2 - 12*x,x]

[Out]

-2*x - 6*x^2

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fricas [A]  time = 0.66, size = 9, normalized size = 0.64 \begin {gather*} -6 \, x^{2} - 2 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-6*x^2 - 2*x

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giac [A]  time = 0.27, size = 9, normalized size = 0.64 \begin {gather*} -6 \, x^{2} - 2 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-6*x^2 - 2*x

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maple [A]  time = 0.01, size = 9, normalized size = 0.64

method	result	size
gosper	\(-2 x \left (3 x +1\right )\)	\(9\)
default	\(-6 x^{2}-2 x\)	\(10\)
norman	\(-6 x^{2}-2 x\)	\(10\)
risch	\(-6 x^{2}-2 x\)	\(10\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maxima [A]  time = 0.43, size = 9, normalized size = 0.64 \begin {gather*} -6 \, x^{2} - 2 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-6*x^2 - 2*x

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mupad [B]  time = 0.03, size = 8, normalized size = 0.57 \begin {gather*} -2\,x\,\left (3\,x+1\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(- 12*x - 2,x)

[Out]

-2*x*(3*x + 1)

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sympy [A]  time = 0.04, size = 8, normalized size = 0.57 \begin {gather*} - 6 x^{2} - 2 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-12*x-2,x)

[Out]

-6*x**2 - 2*x

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