3.33.13 \(\int (12+2 e^x-192 x) \, dx\)

Optimal. Leaf size=23 \[ 4 \left (-25+\frac {e^x}{2}-3 \left (3-x+8 x^2\right )\right ) \]

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Rubi [A]  time = 0.00, antiderivative size = 14, normalized size of antiderivative = 0.61, number of steps used = 2, number of rules used = 1, integrand size = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {2194} \begin {gather*} -96 x^2+12 x+2 e^x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[12 + 2*E^x - 192*x,x]

[Out]

2*E^x + 12*x - 96*x^2

Rule 2194

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

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Mathematica [A]  time = 0.00, size = 14, normalized size = 0.61 \begin {gather*} 2 \left (e^x+6 x-48 x^2\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[12 + 2*E^x - 192*x,x]

[Out]

2*(E^x + 6*x - 48*x^2)

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fricas [A]  time = 0.48, size = 13, normalized size = 0.57 \begin {gather*} -96 \, x^{2} + 12 \, x + 2 \, e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-96*x^2 + 12*x + 2*e^x

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giac [A]  time = 0.18, size = 13, normalized size = 0.57 \begin {gather*} -96 \, x^{2} + 12 \, x + 2 \, e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-96*x^2 + 12*x + 2*e^x

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maple [A]  time = 0.01, size = 14, normalized size = 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	\(-96 x^{2}+12 x +2 \,{\mathrm e}^{x}\)	\(14\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maxima [A]  time = 0.36, size = 13, normalized size = 0.57 \begin {gather*} -96 \, x^{2} + 12 \, x + 2 \, e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-96*x^2 + 12*x + 2*e^x

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mupad [B]  time = 0.04, size = 13, normalized size = 0.57 \begin {gather*} 12\,x+2\,{\mathrm {e}}^x-96\,x^2 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(2*exp(x) - 192*x + 12,x)

[Out]

12*x + 2*exp(x) - 96*x^2

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sympy [A]  time = 0.09, size = 12, normalized size = 0.52 \begin {gather*} - 96 x^{2} + 12 x + 2 e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-96*x**2 + 12*x + 2*exp(x)

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