\(\int 5 e^x \, dx\) [7813]

Optimal result

Integrand size = 5, antiderivative size = 28 \[ \int 5 e^x \, dx=5 \left (e^x+\frac {e^5}{\left (i \pi +\log \left (-4+\frac {e^{10}}{16}\right )\right )^2}\right ) \]

[Out]

5*exp(x)+5*exp(5)/ln(4-1/16*exp(5)^2)^2

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.18, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.400, Rules used = {12, 2225} \[ \int 5 e^x \, dx=5 e^x \]

[In]

Int[5*E^x,x]

[Out]

5*E^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 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}& = 5 \int e^x \, dx \\ & = 5 e^x \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.18 \[ \int 5 e^x \, dx=5 e^x \]

[In]

Integrate[5*E^x,x]

[Out]

5*E^x

Maple [A] (verified)

Time = 0.03 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.18

method	result	size
gosper	\(5 \,{\mathrm e}^{x}\)	\(5\)
lookup	\(5 \,{\mathrm e}^{x}\)	\(5\)
derivativedivides	\(5 \,{\mathrm e}^{x}\)	\(5\)
default	\(5 \,{\mathrm e}^{x}\)	\(5\)
norman	\(5 \,{\mathrm e}^{x}\)	\(5\)
risch	\(5 \,{\mathrm e}^{x}\)	\(5\)
parallelrisch	\(5 \,{\mathrm e}^{x}\)	\(5\)
parts	\(5 \,{\mathrm e}^{x}\)	\(5\)
meijerg	\(-5+5 \,{\mathrm e}^{x}\)	\(7\)

[In]

int(5*exp(x),x,method=_RETURNVERBOSE)

[Out]

5*exp(x)

Fricas [A] (verification not implemented)

none

Time = 0.24 (sec) , antiderivative size = 4, normalized size of antiderivative = 0.14 \[ \int 5 e^x \, dx=5 \, e^{x} \]

[In]

integrate(5*exp(x),x, algorithm="fricas")

[Out]

5*e^x

Sympy [A] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 3, normalized size of antiderivative = 0.11 \[ \int 5 e^x \, dx=5 e^{x} \]

[In]

integrate(5*exp(x),x)

[Out]

5*exp(x)

Maxima [A] (verification not implemented)

none

Time = 0.19 (sec) , antiderivative size = 4, normalized size of antiderivative = 0.14 \[ \int 5 e^x \, dx=5 \, e^{x} \]

[In]

integrate(5*exp(x),x, algorithm="maxima")

[Out]

5*e^x

Giac [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 4, normalized size of antiderivative = 0.14 \[ \int 5 e^x \, dx=5 \, e^{x} \]

[In]

integrate(5*exp(x),x, algorithm="giac")

[Out]

5*e^x

Mupad [B] (verification not implemented)

Time = 0.01 (sec) , antiderivative size = 4, normalized size of antiderivative = 0.14 \[ \int 5 e^x \, dx=5\,{\mathrm {e}}^x \]

[In]

int(5*exp(x),x)

[Out]

5*exp(x)