3.60.37 \(\int -\frac {44}{25} e^{\frac {1}{5} (10-11 x)} \, dx\)

Optimal. Leaf size=13 \[ \frac {4}{5} e^{2-\frac {11 x}{5}} \]

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Rubi [A]  time = 0.00, antiderivative size = 15, normalized size of antiderivative = 1.15, number of steps used = 2, number of rules used = 2, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.133, Rules used = {12, 2194} \begin {gather*} \frac {4}{5} e^{\frac {1}{5} (10-11 x)} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-44*E^((10 - 11*x)/5))/25,x]

[Out]

(4*E^((10 - 11*x)/5))/5

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} &=-\left (\frac {44}{25} \int e^{\frac {1}{5} (10-11 x)} \, dx\right )\\ &=\frac {4}{5} e^{\frac {1}{5} (10-11 x)}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 13, normalized size = 1.00 \begin {gather*} \frac {4}{5} e^{2-\frac {11 x}{5}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-44*E^((10 - 11*x)/5))/25,x]

[Out]

(4*E^(2 - (11*x)/5))/5

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fricas [A]  time = 0.67, size = 8, normalized size = 0.62 \begin {gather*} \frac {4}{5} \, e^{\left (-\frac {11}{5} \, x + 2\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-44/25*exp(-11/5*x+2),x, algorithm="fricas")

[Out]

4/5*e^(-11/5*x + 2)

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giac [A]  time = 0.14, size = 8, normalized size = 0.62 \begin {gather*} \frac {4}{5} \, e^{\left (-\frac {11}{5} \, x + 2\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-44/25*exp(-11/5*x+2),x, algorithm="giac")

[Out]

4/5*e^(-11/5*x + 2)

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maple [A]  time = 0.04, size = 9, normalized size = 0.69

method	result	size
gosper	\(\frac {4 \,{\mathrm e}^{-\frac {11 x}{5}+2}}{5}\)	\(9\)
derivativedivides	\(\frac {4 \,{\mathrm e}^{-\frac {11 x}{5}+2}}{5}\)	\(9\)
default	\(\frac {4 \,{\mathrm e}^{-\frac {11 x}{5}+2}}{5}\)	\(9\)
norman	\(\frac {4 \,{\mathrm e}^{-\frac {11 x}{5}+2}}{5}\)	\(9\)
risch	\(\frac {4 \,{\mathrm e}^{-\frac {11 x}{5}+2}}{5}\)	\(9\)
meijerg	\(-\frac {4 \,{\mathrm e}^{2} \left (1-{\mathrm e}^{-\frac {11 x}{5}}\right )}{5}\)	\(13\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-44/25*exp(-11/5*x+2),x,method=_RETURNVERBOSE)

[Out]

4/5*exp(-11/5*x+2)

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maxima [A]  time = 0.36, size = 8, normalized size = 0.62 \begin {gather*} \frac {4}{5} \, e^{\left (-\frac {11}{5} \, x + 2\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-44/25*exp(-11/5*x+2),x, algorithm="maxima")

[Out]

4/5*e^(-11/5*x + 2)

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mupad [B]  time = 0.04, size = 8, normalized size = 0.62 \begin {gather*} \frac {4\,{\mathrm {e}}^{-\frac {11\,x}{5}}\,{\mathrm {e}}^2}{5} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(44*exp(2 - (11*x)/5))/25,x)

[Out]

(4*exp(-(11*x)/5)*exp(2))/5

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sympy [A]  time = 0.07, size = 10, normalized size = 0.77 \begin {gather*} \frac {4 e^{2 - \frac {11 x}{5}}}{5} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-44/25*exp(-11/5*x+2),x)

[Out]

4*exp(2 - 11*x/5)/5

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