3.46.58 \(\int (-1-5 e^x) \, dx\)

Optimal. Leaf size=10 \[ 4-5 e^x-x \]

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Rubi [A]  time = 0.00, antiderivative size = 9, normalized size of antiderivative = 0.90, 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-5 e^x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-1 - 5*E^x,x]

[Out]

-5*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-5 \int e^x \, dx\\ &=-5 e^x-x\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 9, normalized size = 0.90 \begin {gather*} -5 e^x-x \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-1 - 5*E^x,x]

[Out]

-5*E^x - x

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fricas [A]  time = 0.59, size = 8, normalized size = 0.80 \begin {gather*} -x - 5 \, e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-5*exp(x)-1,x, algorithm="fricas")

[Out]

-x - 5*e^x

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giac [A]  time = 0.14, size = 8, normalized size = 0.80 \begin {gather*} -x - 5 \, e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-5*exp(x)-1,x, algorithm="giac")

[Out]

-x - 5*e^x

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maple [A]  time = 0.01, size = 9, normalized size = 0.90

method	result	size
default	\(-x -5 \,{\mathrm e}^{x}\)	\(9\)
norman	\(-x -5 \,{\mathrm e}^{x}\)	\(9\)
risch	\(-x -5 \,{\mathrm e}^{x}\)	\(9\)
derivativedivides	\(-5 \,{\mathrm e}^{x}-\ln \left ({\mathrm e}^{x}\right )\)	\(11\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-5*exp(x)-1,x,method=_RETURNVERBOSE)

[Out]

-x-5*exp(x)

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maxima [A]  time = 0.36, size = 8, normalized size = 0.80 \begin {gather*} -x - 5 \, e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-5*exp(x)-1,x, algorithm="maxima")

[Out]

-x - 5*e^x

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mupad [B]  time = 3.02, size = 8, normalized size = 0.80 \begin {gather*} -x-5\,{\mathrm {e}}^x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(- 5*exp(x) - 1,x)

[Out]

- x - 5*exp(x)

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sympy [A]  time = 0.07, size = 7, normalized size = 0.70 \begin {gather*} - x - 5 e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-5*exp(x)-1,x)

[Out]

-x - 5*exp(x)

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