3.34.4 \(\int 4 e^{4 x} \, dx\)

Optimal. Leaf size=9 \[ -\frac {13}{4}+e^{4 x} \]

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Rubi [A]  time = 0.00, antiderivative size = 5, normalized size of antiderivative = 0.56, number of steps used = 2, number of rules used = 2, integrand size = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.286, Rules used = {12, 2194} \begin {gather*} e^{4 x} \end {gather*}

Antiderivative was successfully verified.

[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 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} &=4 \int e^{4 x} \, dx\\ &=e^{4 x}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 5, normalized size = 0.56 \begin {gather*} e^{4 x} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

E^(4*x)

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fricas [A]  time = 0.61, size = 4, normalized size = 0.44 \begin {gather*} e^{\left (4 \, x\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

e^(4*x)

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giac [A]  time = 0.19, size = 4, normalized size = 0.44 \begin {gather*} e^{\left (4 \, x\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

e^(4*x)

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maple [A]  time = 0.01, size = 5, normalized size = 0.56

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	\({\mathrm e}^{4 x}\)	\(5\)
meijerg	\({\mathrm e}^{4 x}-1\)	\(7\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

exp(4*x)

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maxima [A]  time = 0.34, size = 4, normalized size = 0.44 \begin {gather*} e^{\left (4 \, x\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

e^(4*x)

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mupad [B]  time = 0.01, size = 4, normalized size = 0.44 \begin {gather*} {\mathrm {e}}^{4\,x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

exp(4*x)

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sympy [A]  time = 0.04, size = 3, normalized size = 0.33 \begin {gather*} e^{4 x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

exp(4*x)

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