3.72.25 \(\int \frac {1}{3} (3-7 e^{\frac {1}{3} (10-3 e^9+7 x)}) \, dx\)

Optimal. Leaf size=23 \[ -e^{2-e^9+2 x+\frac {4+x}{3}}+x \]

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Rubi [A]  time = 0.01, antiderivative size = 20, normalized size of antiderivative = 0.87, number of steps used = 3, number of rules used = 2, integrand size = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.083, Rules used = {12, 2194} \begin {gather*} x-e^{\frac {1}{3} \left (7 x-3 e^9+10\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(3 - 7*E^((10 - 3*E^9 + 7*x)/3))/3,x]

[Out]

-E^((10 - 3*E^9 + 7*x)/3) + x

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 (3-7 e^{\frac {1}{3} \left (10-3 e^9+7 x\right )}\right ) \, dx\\ &=x-\frac {7}{3} \int e^{\frac {1}{3} \left (10-3 e^9+7 x\right )} \, dx\\ &=-e^{\frac {1}{3} \left (10-3 e^9+7 x\right )}+x\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.02, size = 20, normalized size = 0.87 \begin {gather*} -e^{\frac {10}{3}-e^9+\frac {7 x}{3}}+x \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(3 - 7*E^((10 - 3*E^9 + 7*x)/3))/3,x]

[Out]

-E^(10/3 - E^9 + (7*x)/3) + x

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fricas [A]  time = 0.96, size = 14, normalized size = 0.61 \begin {gather*} x - e^{\left (\frac {7}{3} \, x - e^{9} + \frac {10}{3}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-7/3*exp(-exp(9)+7/3*x+10/3)+1,x, algorithm="fricas")

[Out]

x - e^(7/3*x - e^9 + 10/3)

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giac [A]  time = 0.21, size = 14, normalized size = 0.61 \begin {gather*} x - e^{\left (\frac {7}{3} \, x - e^{9} + \frac {10}{3}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-7/3*exp(-exp(9)+7/3*x+10/3)+1,x, algorithm="giac")

[Out]

x - e^(7/3*x - e^9 + 10/3)

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maple [A]  time = 0.02, size = 15, normalized size = 0.65

method	result	size
default	\(x -{\mathrm e}^{-{\mathrm e}^{9}+\frac {7 x}{3}+\frac {10}{3}}\)	\(15\)
norman	\(x -{\mathrm e}^{-{\mathrm e}^{9}+\frac {7 x}{3}+\frac {10}{3}}\)	\(15\)
risch	\(x -{\mathrm e}^{-{\mathrm e}^{9}+\frac {7 x}{3}+\frac {10}{3}}\)	\(15\)
derivativedivides	\(-{\mathrm e}^{-{\mathrm e}^{9}+\frac {7 x}{3}+\frac {10}{3}}+\frac {3 \ln \left ({\mathrm e}^{-{\mathrm e}^{9}+\frac {7 x}{3}+\frac {10}{3}}\right )}{7}\)	\(27\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-7/3*exp(-exp(9)+7/3*x+10/3)+1,x,method=_RETURNVERBOSE)

[Out]

x-exp(-exp(9)+7/3*x+10/3)

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maxima [A]  time = 0.35, size = 14, normalized size = 0.61 \begin {gather*} x - e^{\left (\frac {7}{3} \, x - e^{9} + \frac {10}{3}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-7/3*exp(-exp(9)+7/3*x+10/3)+1,x, algorithm="maxima")

[Out]

x - e^(7/3*x - e^9 + 10/3)

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mupad [B]  time = 0.08, size = 15, normalized size = 0.65 \begin {gather*} x-{\mathrm {e}}^{-{\mathrm {e}}^9}\,{\mathrm {e}}^{\frac {7\,x}{3}}\,{\mathrm {e}}^{10/3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1 - (7*exp((7*x)/3 - exp(9) + 10/3))/3,x)

[Out]

x - exp(-exp(9))*exp((7*x)/3)*exp(10/3)

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sympy [A]  time = 0.09, size = 14, normalized size = 0.61 \begin {gather*} x - e^{\frac {7 x}{3} - e^{9} + \frac {10}{3}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-7/3*exp(-exp(9)+7/3*x+10/3)+1,x)

[Out]

x - exp(7*x/3 - exp(9) + 10/3)

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