\(\int (12+2 e^x-192 x) \, dx\) [3213]

Optimal result

Integrand size = 10, antiderivative size = 23 \[ \int \left (12+2 e^x-192 x\right ) \, dx=4 \left (-25+\frac {e^x}{2}-3 \left (3-x+8 x^2\right )\right ) \]

[Out]

2*exp(x)-136-96*x^2+12*x

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.61, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {2225} \[ \int \left (12+2 e^x-192 x\right ) \, dx=-96 x^2+12 x+2 e^x \]

[In]

Int[12 + 2*E^x - 192*x,x]

[Out]

2*E^x + 12*x - 96*x^2

Rule 2225

Int[((F_)^((c_.)*((a_.) + (b_.)*(x_))))^(n_.), x_Symbol] :> Simp[(F^(c*(a + b*x)))^n/(b*c*n*Log[F]), x] /; Fre
eQ[{F, a, b, c, n}, x]

Rubi steps \begin{align*} \text {integral}& = 12 x-96 x^2+2 \int e^x \, dx \\ & = 2 e^x+12 x-96 x^2 \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.61 \[ \int \left (12+2 e^x-192 x\right ) \, dx=2 \left (e^x+6 x-48 x^2\right ) \]

[In]

Integrate[12 + 2*E^x - 192*x,x]

[Out]

2*(E^x + 6*x - 48*x^2)

Maple [A] (verified)

Time = 0.12 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.61

method	result	size
default	\(-96 x^{2}+12 x +2 \,{\mathrm e}^{x}\)	\(14\)
norman	\(-96 x^{2}+12 x +2 \,{\mathrm e}^{x}\)	\(14\)
risch	\(-96 x^{2}+12 x +2 \,{\mathrm e}^{x}\)	\(14\)
parallelrisch	\(-96 x^{2}+12 x +2 \,{\mathrm e}^{x}\)	\(14\)
parts	\(-96 x^{2}+12 x +2 \,{\mathrm e}^{x}\)	\(14\)

[In]

int(2*exp(x)-192*x+12,x,method=_RETURNVERBOSE)

[Out]

-96*x^2+12*x+2*exp(x)

Fricas [A] (verification not implemented)

none

Time = 0.24 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.57 \[ \int \left (12+2 e^x-192 x\right ) \, dx=-96 \, x^{2} + 12 \, x + 2 \, e^{x} \]

[In]

integrate(2*exp(x)-192*x+12,x, algorithm="fricas")

[Out]

-96*x^2 + 12*x + 2*e^x

Sympy [A] (verification not implemented)

Time = 0.05 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.52 \[ \int \left (12+2 e^x-192 x\right ) \, dx=- 96 x^{2} + 12 x + 2 e^{x} \]

[In]

integrate(2*exp(x)-192*x+12,x)

[Out]

-96*x**2 + 12*x + 2*exp(x)

Maxima [A] (verification not implemented)

none

Time = 0.19 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.57 \[ \int \left (12+2 e^x-192 x\right ) \, dx=-96 \, x^{2} + 12 \, x + 2 \, e^{x} \]

[In]

integrate(2*exp(x)-192*x+12,x, algorithm="maxima")

[Out]

-96*x^2 + 12*x + 2*e^x

Giac [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.57 \[ \int \left (12+2 e^x-192 x\right ) \, dx=-96 \, x^{2} + 12 \, x + 2 \, e^{x} \]

[In]

integrate(2*exp(x)-192*x+12,x, algorithm="giac")

[Out]

-96*x^2 + 12*x + 2*e^x

Mupad [B] (verification not implemented)

Time = 0.04 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.57 \[ \int \left (12+2 e^x-192 x\right ) \, dx=12\,x+2\,{\mathrm {e}}^x-96\,x^2 \]

[In]

int(2*exp(x) - 192*x + 12,x)

[Out]

12*x + 2*exp(x) - 96*x^2