\(\int 4 e^{4 x} \, dx\) [5204]

Optimal result

Integrand size = 7, antiderivative size = 14 \[ \int 4 e^{4 x} \, dx=-e^3+e^5+e^{4 x} \]

[Out]

exp(5)+exp(x)^4-exp(3)

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.36, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.286, Rules used = {12, 2225} \[ \int 4 e^{4 x} \, dx=e^{4 x} \]

[In]

Int[4*E^(4*x),x]

[Out]

E^(4*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}& = 4 \int e^{4 x} \, dx \\ & = e^{4 x} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.36 \[ \int 4 e^{4 x} \, dx=e^{4 x} \]

[In]

Integrate[4*E^(4*x),x]

[Out]

E^(4*x)

Maple [A] (verified)

Time = 0.06 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.36

method	result	size
gosper	\({\mathrm e}^{4 x}\)	\(5\)
derivativedivides	\({\mathrm e}^{4 x}\)	\(5\)
default	\({\mathrm e}^{4 x}\)	\(5\)
norman	\({\mathrm e}^{4 x}\)	\(5\)
risch	\({\mathrm e}^{4 x}\)	\(5\)
parallelrisch	\({\mathrm e}^{4 x}\)	\(5\)
meijerg	\({\mathrm e}^{4 x}-1\)	\(7\)

[In]

int(4*exp(x)^4,x,method=_RETURNVERBOSE)

[Out]

exp(x)^4

Fricas [A] (verification not implemented)

none

Time = 0.24 (sec) , antiderivative size = 4, normalized size of antiderivative = 0.29 \[ \int 4 e^{4 x} \, dx=e^{\left (4 \, x\right )} \]

[In]

integrate(4*exp(x)^4,x, algorithm="fricas")

[Out]

e^(4*x)

Sympy [A] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 3, normalized size of antiderivative = 0.21 \[ \int 4 e^{4 x} \, dx=e^{4 x} \]

[In]

integrate(4*exp(x)**4,x)

[Out]

exp(4*x)

Maxima [A] (verification not implemented)

none

Time = 0.19 (sec) , antiderivative size = 4, normalized size of antiderivative = 0.29 \[ \int 4 e^{4 x} \, dx=e^{\left (4 \, x\right )} \]

[In]

integrate(4*exp(x)^4,x, algorithm="maxima")

[Out]

e^(4*x)

Giac [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 4, normalized size of antiderivative = 0.29 \[ \int 4 e^{4 x} \, dx=e^{\left (4 \, x\right )} \]

[In]

integrate(4*exp(x)^4,x, algorithm="giac")

[Out]

e^(4*x)

Mupad [B] (verification not implemented)

Time = 0.01 (sec) , antiderivative size = 4, normalized size of antiderivative = 0.29 \[ \int 4 e^{4 x} \, dx={\mathrm {e}}^{4\,x} \]

[In]

int(4*exp(4*x),x)

[Out]

exp(4*x)