3.10.89 \(\int -\frac {3}{4} e^{\frac {1}{4} (4-3 x)} \, dx\)

Optimal. Leaf size=9 \[ e^{1-\frac {3 x}{4}} \]

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Rubi [A]  time = 0.01, antiderivative size = 11, normalized size of antiderivative = 1.22, 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*} e^{\frac {1}{4} (4-3 x)} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-3*E^((4 - 3*x)/4))/4,x]

[Out]

E^((4 - 3*x)/4)

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 {3}{4} \int e^{\frac {1}{4} (4-3 x)} \, dx\right )\\ &=e^{\frac {1}{4} (4-3 x)}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 9, normalized size = 1.00 \begin {gather*} e^{1-\frac {3 x}{4}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-3*E^((4 - 3*x)/4))/4,x]

[Out]

E^(1 - (3*x)/4)

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fricas [A]  time = 0.67, size = 6, normalized size = 0.67 \begin {gather*} e^{\left (-\frac {3}{4} \, x + 1\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-3/4*exp(1-3/4*x),x, algorithm="fricas")

[Out]

e^(-3/4*x + 1)

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giac [A]  time = 0.31, size = 6, normalized size = 0.67 \begin {gather*} e^{\left (-\frac {3}{4} \, x + 1\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-3/4*exp(1-3/4*x),x, algorithm="giac")

[Out]

e^(-3/4*x + 1)

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maple [A]  time = 0.02, size = 7, normalized size = 0.78

method	result	size
gosper	\({\mathrm e}^{1-\frac {3 x}{4}}\)	\(7\)
derivativedivides	\({\mathrm e}^{1-\frac {3 x}{4}}\)	\(7\)
default	\({\mathrm e}^{1-\frac {3 x}{4}}\)	\(7\)
norman	\({\mathrm e}^{1-\frac {3 x}{4}}\)	\(7\)
risch	\({\mathrm e}^{1-\frac {3 x}{4}}\)	\(7\)
meijerg	\(-{\mathrm e} \left (1-{\mathrm e}^{-\frac {3 x}{4}}\right )\)	\(13\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-3/4*exp(1-3/4*x),x,method=_RETURNVERBOSE)

[Out]

exp(1-3/4*x)

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maxima [A]  time = 0.71, size = 6, normalized size = 0.67 \begin {gather*} e^{\left (-\frac {3}{4} \, x + 1\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-3/4*exp(1-3/4*x),x, algorithm="maxima")

[Out]

e^(-3/4*x + 1)

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mupad [B]  time = 0.68, size = 7, normalized size = 0.78 \begin {gather*} {\mathrm {e}}^{-\frac {3\,x}{4}}\,\mathrm {e} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(3*exp(1 - (3*x)/4))/4,x)

[Out]

exp(-(3*x)/4)*exp(1)

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sympy [A]  time = 0.07, size = 7, normalized size = 0.78 \begin {gather*} e^{1 - \frac {3 x}{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-3/4*exp(1-3/4*x),x)

[Out]

exp(1 - 3*x/4)

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