\(\int (-2-12 x) \, dx\) [319]

Optimal result

Integrand size = 5, antiderivative size = 14 \[ \int (-2-12 x) \, dx=2 (-1-3 x) x-\log (\log (5)) \]

[Out]

2*(-3*x-1)*x-ln(ln(5))

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.64, number of steps used = 1, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int (-2-12 x) \, dx=-6 x^2-2 x \]

[In]

Int[-2 - 12*x,x]

[Out]

-2*x - 6*x^2

Rubi steps \begin{align*} \text {integral}& = -2 x-6 x^2 \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.64 \[ \int (-2-12 x) \, dx=-2 x-6 x^2 \]

[In]

Integrate[-2 - 12*x,x]

[Out]

-2*x - 6*x^2

Maple [A] (verified)

Time = 0.01 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.64

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

[In]

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

[Out]

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

Fricas [A] (verification not implemented)

none

Time = 0.22 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.64 \[ \int (-2-12 x) \, dx=-6 \, x^{2} - 2 \, x \]

[In]

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

[Out]

-6*x^2 - 2*x

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.57 \[ \int (-2-12 x) \, dx=- 6 x^{2} - 2 x \]

[In]

integrate(-12*x-2,x)

[Out]

-6*x**2 - 2*x

Maxima [A] (verification not implemented)

none

Time = 0.21 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.64 \[ \int (-2-12 x) \, dx=-6 \, x^{2} - 2 \, x \]

[In]

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

[Out]

-6*x^2 - 2*x

Giac [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.64 \[ \int (-2-12 x) \, dx=-6 \, x^{2} - 2 \, x \]

[In]

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

[Out]

-6*x^2 - 2*x

Mupad [B] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.57 \[ \int (-2-12 x) \, dx=-2\,x\,\left (3\,x+1\right ) \]

[In]

int(- 12*x - 2,x)

[Out]

-2*x*(3*x + 1)