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

Optimal. Leaf size=12 $$2x-3(5+e^x+x)$$

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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} $$\begin{array}{c}-x-3e^x\end{array}$$

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

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =-x-3\int e^{x}dx\\ & =-3e^x-x\end{array}\end{array}$$

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

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 $$\begin{array}{c}-x-3e^x\end{array}$$

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 $$\begin{array}{c}-x-3e^x\end{array}$$

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 $$\begin{array}{c}-x-3e^x\end{array}$$

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 $$\begin{array}{c}-x-3{\mathrm{e}}^x\end{array}$$

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 $$\begin{array}{c}-x-3e^x\end{array}$$

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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