3.85.88 \(\int (-1-3 e^x) \, dx\)

Optimal. Leaf size=12 \[ 2 x-3 \left (5+e^x+x\right ) \]

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Rubi [A]  time = 0.00, antiderivative size = 9, normalized size of antiderivative = 0.75, 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*} -x-3 e^x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-1 - 3*E^x,x]

[Out]

-3*E^x - 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} &=-x-3 \int e^x \, dx\\ &=-3 e^x-x\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 9, normalized size = 0.75 \begin {gather*} -3 e^x-x \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-1 - 3*E^x,x]

[Out]

-3*E^x - x

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fricas [A]  time = 0.91, size = 8, normalized size = 0.67 \begin {gather*} -x - 3 \, e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-3*exp(x)-1,x, algorithm="fricas")

[Out]

-x - 3*e^x

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giac [A]  time = 0.20, size = 8, normalized size = 0.67 \begin {gather*} -x - 3 \, e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-3*exp(x)-1,x, algorithm="giac")

[Out]

-x - 3*e^x

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maple [A]  time = 0.02, size = 9, normalized size = 0.75

method	result	size
default	\(-x -3 \,{\mathrm e}^{x}\)	\(9\)
norman	\(-x -3 \,{\mathrm e}^{x}\)	\(9\)
risch	\(-x -3 \,{\mathrm e}^{x}\)	\(9\)
derivativedivides	\(-3 \,{\mathrm e}^{x}-\ln \left ({\mathrm e}^{x}\right )\)	\(11\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-3*exp(x)-1,x,method=_RETURNVERBOSE)

[Out]

-x-3*exp(x)

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maxima [A]  time = 0.36, size = 8, normalized size = 0.67 \begin {gather*} -x - 3 \, e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-3*exp(x)-1,x, algorithm="maxima")

[Out]

-x - 3*e^x

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mupad [B]  time = 0.03, size = 8, normalized size = 0.67 \begin {gather*} -x-3\,{\mathrm {e}}^x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(- 3*exp(x) - 1,x)

[Out]

- x - 3*exp(x)

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sympy [A]  time = 0.10, size = 7, normalized size = 0.58 \begin {gather*} - x - 3 e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-3*exp(x)-1,x)

[Out]

-x - 3*exp(x)

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