3.18.99 \(\int (4-2 e^x) \, dx\)

Optimal. Leaf size=11 \[ 1-2 \left (e^x-2 x\right ) \]

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Rubi [A]  time = 0.01, antiderivative size = 9, normalized size of antiderivative = 0.82, number of steps used = 2, number of rules used = 1, integrand size = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {2194} \begin {gather*} 4 x-2 e^x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[4 - 2*E^x,x]

[Out]

-2*E^x + 4*x

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} &=4 x-2 \int e^x \, dx\\ &=-2 e^x+4 x\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 9, normalized size = 0.82 \begin {gather*} -2 e^x+4 x \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[4 - 2*E^x,x]

[Out]

-2*E^x + 4*x

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fricas [A]  time = 0.59, size = 8, normalized size = 0.73 \begin {gather*} 4 \, x - 2 \, e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

4*x - 2*e^x

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giac [A]  time = 0.27, size = 8, normalized size = 0.73 \begin {gather*} 4 \, x - 2 \, e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

4*x - 2*e^x

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maple [A]  time = 0.02, size = 9, normalized size = 0.82

method	result	size
default	\(4 x -2 \,{\mathrm e}^{x}\)	\(9\)
norman	\(4 x -2 \,{\mathrm e}^{x}\)	\(9\)
risch	\(4 x -2 \,{\mathrm e}^{x}\)	\(9\)
derivativedivides	\(-2 \,{\mathrm e}^{x}+4 \ln \left ({\mathrm e}^{x}\right )\)	\(11\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

4*x-2*exp(x)

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maxima [A]  time = 0.35, size = 8, normalized size = 0.73 \begin {gather*} 4 \, x - 2 \, e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

4*x - 2*e^x

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mupad [B]  time = 1.07, size = 8, normalized size = 0.73 \begin {gather*} 4\,x-2\,{\mathrm {e}}^x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(4 - 2*exp(x),x)

[Out]

4*x - 2*exp(x)

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sympy [A]  time = 0.06, size = 7, normalized size = 0.64 \begin {gather*} 4 x - 2 e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

4*x - 2*exp(x)

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