3.36.28 \(\int \frac {1}{3} (1-3 e^{5+x}) \, dx\)

Optimal. Leaf size=33 \[ -e^{5+x}+x+\frac {1}{3} \left (-1-2 x-\frac {1}{i \pi +\log \left (\log \left (\frac {5}{4}\right )\right )}\right ) \]

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Rubi [A]  time = 0.00, antiderivative size = 13, normalized size of antiderivative = 0.39, number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {12, 2194} \begin {gather*} \frac {x}{3}-e^{x+5} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(1 - 3*E^(5 + x))/3,x]

[Out]

-E^(5 + x) + x/3

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, 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} &=\frac {1}{3} \int \left (1-3 e^{5+x}\right ) \, dx\\ &=\frac {x}{3}-\int e^{5+x} \, dx\\ &=-e^{5+x}+\frac {x}{3}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 13, normalized size = 0.39 \begin {gather*} -e^{5+x}+\frac {x}{3} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(1 - 3*E^(5 + x))/3,x]

[Out]

-E^(5 + x) + x/3

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fricas [A]  time = 0.54, size = 10, normalized size = 0.30 \begin {gather*} \frac {1}{3} \, x - e^{\left (x + 5\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-exp(5+x)+1/3,x, algorithm="fricas")

[Out]

1/3*x - e^(x + 5)

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giac [A]  time = 0.21, size = 10, normalized size = 0.30 \begin {gather*} \frac {1}{3} \, x - e^{\left (x + 5\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-exp(5+x)+1/3,x, algorithm="giac")

[Out]

1/3*x - e^(x + 5)

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maple [A]  time = 0.02, size = 11, normalized size = 0.33

method	result	size
default	\(\frac {x}{3}-{\mathrm e}^{5+x}\)	\(11\)
norman	\(\frac {x}{3}-{\mathrm e}^{5+x}\)	\(11\)
risch	\(\frac {x}{3}-{\mathrm e}^{5+x}\)	\(11\)
derivativedivides	\(-{\mathrm e}^{5+x}+\frac {\ln \left ({\mathrm e}^{5+x}\right )}{3}\)	\(15\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-exp(5+x)+1/3,x,method=_RETURNVERBOSE)

[Out]

1/3*x-exp(5+x)

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maxima [A]  time = 0.36, size = 10, normalized size = 0.30 \begin {gather*} \frac {1}{3} \, x - e^{\left (x + 5\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-exp(5+x)+1/3,x, algorithm="maxima")

[Out]

1/3*x - e^(x + 5)

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mupad [B]  time = 0.06, size = 10, normalized size = 0.30 \begin {gather*} \frac {x}{3}-{\mathrm {e}}^{x+5} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/3 - exp(x + 5),x)

[Out]

x/3 - exp(x + 5)

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sympy [A]  time = 0.07, size = 7, normalized size = 0.21 \begin {gather*} \frac {x}{3} - e^{x + 5} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-exp(5+x)+1/3,x)

[Out]

x/3 - exp(x + 5)

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