\(\int -\frac {3}{4} e^{\frac {1}{4} (4-3 x)} \, dx\) [989]

Optimal result

Integrand size = 15, antiderivative size = 9 \[ \int -\frac {3}{4} e^{\frac {1}{4} (4-3 x)} \, dx=e^{1-\frac {3 x}{4}} \]

[Out]

exp(1-3/4*x)

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.22, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.133, Rules used = {12, 2225} \[ \int -\frac {3}{4} e^{\frac {1}{4} (4-3 x)} \, dx=e^{\frac {1}{4} (4-3 x)} \]

[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 2225

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{align*} \text {integral}& = -\left (\frac {3}{4} \int e^{\frac {1}{4} (4-3 x)} \, dx\right ) \\ & = e^{\frac {1}{4} (4-3 x)} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.02 (sec) , antiderivative size = 9, normalized size of antiderivative = 1.00 \[ \int -\frac {3}{4} e^{\frac {1}{4} (4-3 x)} \, dx=e^{1-\frac {3 x}{4}} \]

[In]

Integrate[(-3*E^((4 - 3*x)/4))/4,x]

[Out]

E^(1 - (3*x)/4)

Maple [A] (verified)

Time = 0.02 (sec) , antiderivative size = 7, normalized size of antiderivative = 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	\({\mathrm e}^{1-\frac {3 x}{4}}\)	\(7\)
parallelrisch	\({\mathrm e}^{1-\frac {3 x}{4}}\)	\(7\)
parts	\({\mathrm e}^{1-\frac {3 x}{4}}\)	\(7\)
meijerg	\(-{\mathrm e} \left (1-{\mathrm e}^{-\frac {3 x}{4}}\right )\)	\(13\)

[In]

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

[Out]

exp(1-3/4*x)

Fricas [A] (verification not implemented)

none

Time = 0.23 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.67 \[ \int -\frac {3}{4} e^{\frac {1}{4} (4-3 x)} \, dx=e^{\left (-\frac {3}{4} \, x + 1\right )} \]

[In]

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

[Out]

e^(-3/4*x + 1)

Sympy [A] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.78 \[ \int -\frac {3}{4} e^{\frac {1}{4} (4-3 x)} \, dx=e^{1 - \frac {3 x}{4}} \]

[In]

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

[Out]

exp(1 - 3*x/4)

Maxima [A] (verification not implemented)

none

Time = 0.19 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.67 \[ \int -\frac {3}{4} e^{\frac {1}{4} (4-3 x)} \, dx=e^{\left (-\frac {3}{4} \, x + 1\right )} \]

[In]

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

[Out]

e^(-3/4*x + 1)

Giac [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.67 \[ \int -\frac {3}{4} e^{\frac {1}{4} (4-3 x)} \, dx=e^{\left (-\frac {3}{4} \, x + 1\right )} \]

[In]

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

[Out]

e^(-3/4*x + 1)

Mupad [B] (verification not implemented)

Time = 0.04 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.78 \[ \int -\frac {3}{4} e^{\frac {1}{4} (4-3 x)} \, dx={\mathrm {e}}^{-\frac {3\,x}{4}}\,\mathrm {e} \]

[In]

int(-(3*exp(1 - (3*x)/4))/4,x)

[Out]

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