3.3.34 \(\int \frac {1}{9} (17-9 e^x) \, dx\)

Optimal. Leaf size=18 \[ -e^x+\frac {1}{9} (-3-x)+2 x \]

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Rubi [A]  time = 0.00, antiderivative size = 11, normalized size of antiderivative = 0.61, number of steps used = 3, number of rules used = 2, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.182, Rules used = {12, 2194} \begin {gather*} \frac {17 x}{9}-e^x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(17 - 9*E^x)/9,x]

[Out]

-E^x + (17*x)/9

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}{9} \int \left (17-9 e^x\right ) \, dx\\ &=\frac {17 x}{9}-\int e^x \, dx\\ &=-e^x+\frac {17 x}{9}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 11, normalized size = 0.61 \begin {gather*} -e^x+\frac {17 x}{9} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(17 - 9*E^x)/9,x]

[Out]

-E^x + (17*x)/9

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fricas [A]  time = 0.83, size = 8, normalized size = 0.44 \begin {gather*} \frac {17}{9} \, x - e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-exp(x)+17/9,x, algorithm="fricas")

[Out]

17/9*x - e^x

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giac [A]  time = 0.31, size = 8, normalized size = 0.44 \begin {gather*} \frac {17}{9} \, x - e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-exp(x)+17/9,x, algorithm="giac")

[Out]

17/9*x - e^x

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maple [A]  time = 0.02, size = 9, normalized size = 0.50

method	result	size
default	\(\frac {17 x}{9}-{\mathrm e}^{x}\)	\(9\)
norman	\(\frac {17 x}{9}-{\mathrm e}^{x}\)	\(9\)
risch	\(\frac {17 x}{9}-{\mathrm e}^{x}\)	\(9\)
derivativedivides	\(-{\mathrm e}^{x}+\frac {17 \ln \left ({\mathrm e}^{x}\right )}{9}\)	\(11\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-exp(x)+17/9,x,method=_RETURNVERBOSE)

[Out]

17/9*x-exp(x)

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maxima [A]  time = 0.38, size = 8, normalized size = 0.44 \begin {gather*} \frac {17}{9} \, x - e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-exp(x)+17/9,x, algorithm="maxima")

[Out]

17/9*x - e^x

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mupad [B]  time = 0.27, size = 8, normalized size = 0.44 \begin {gather*} \frac {17\,x}{9}-{\mathrm {e}}^x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(17/9 - exp(x),x)

[Out]

(17*x)/9 - exp(x)

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sympy [A]  time = 0.06, size = 7, normalized size = 0.39 \begin {gather*} \frac {17 x}{9} - e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-exp(x)+17/9,x)

[Out]

17*x/9 - exp(x)

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