\(\int (-2+4 e^2-12 x) \, dx\) [6510]

Optimal result

Integrand size = 10, antiderivative size = 13 \[ \int \left (-2+4 e^2-12 x\right ) \, dx=2 \left (-1+2 e^2-3 x\right ) x \]

[Out]

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

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.23, number of steps used = 1, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \left (-2+4 e^2-12 x\right ) \, dx=-6 x^2-2 \left (1-2 e^2\right ) x \]

[In]

Int[-2 + 4*E^2 - 12*x,x]

[Out]

-2*(1 - 2*E^2)*x - 6*x^2

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

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.15 \[ \int \left (-2+4 e^2-12 x\right ) \, dx=-2 x+4 e^2 x-6 x^2 \]

[In]

Integrate[-2 + 4*E^2 - 12*x,x]

[Out]

-2*x + 4*E^2*x - 6*x^2

Maple [A] (verified)

Time = 0.03 (sec) , antiderivative size = 13, normalized size of antiderivative = 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	\(4 \,{\mathrm e}^{2} x -6 x^{2}-2 x\)	\(15\)
parallelrisch	\(\left (4 \,{\mathrm e}^{2}-2\right ) x -6 x^{2}\)	\(15\)
parts	\(4 \,{\mathrm e}^{2} x -6 x^{2}-2 x\)	\(15\)

[In]

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

[Out]

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

Fricas [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.08 \[ \int \left (-2+4 e^2-12 x\right ) \, dx=-6 \, x^{2} + 4 \, x e^{2} - 2 \, x \]

[In]

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

[Out]

-6*x^2 + 4*x*e^2 - 2*x

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.92 \[ \int \left (-2+4 e^2-12 x\right ) \, dx=- 6 x^{2} + x \left (-2 + 4 e^{2}\right ) \]

[In]

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

[Out]

-6*x**2 + x*(-2 + 4*exp(2))

Maxima [A] (verification not implemented)

none

Time = 0.18 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.08 \[ \int \left (-2+4 e^2-12 x\right ) \, dx=-6 \, x^{2} + 4 \, x e^{2} - 2 \, x \]

[In]

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

[Out]

-6*x^2 + 4*x*e^2 - 2*x

Giac [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.08 \[ \int \left (-2+4 e^2-12 x\right ) \, dx=-6 \, x^{2} + 4 \, x e^{2} - 2 \, x \]

[In]

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

[Out]

-6*x^2 + 4*x*e^2 - 2*x

Mupad [B] (verification not implemented)

Time = 14.68 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.92 \[ \int \left (-2+4 e^2-12 x\right ) \, dx=-2\,x\,\left (3\,x-2\,{\mathrm {e}}^2+1\right ) \]

[In]

int(4*exp(2) - 12*x - 2,x)

[Out]

-2*x*(3*x - 2*exp(2) + 1)