3.100.92 \(\int 3 e^x \, dx\)

Optimal. Leaf size=10 \[ 8+e^3+3 e^x \]

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Rubi [A]  time = 0.00, antiderivative size = 5, normalized size of antiderivative = 0.50, number of steps used = 2, number of rules used = 2, integrand size = 5, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.400, Rules used = {12, 2194} \begin {gather*} 3 e^x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[3*E^x,x]

[Out]

3*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 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} &=3 \int e^x \, dx\\ &=3 e^x\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 5, normalized size = 0.50 \begin {gather*} 3 e^x \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[3*E^x,x]

[Out]

3*E^x

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fricas [A]  time = 1.08, size = 4, normalized size = 0.40 \begin {gather*} 3 \, e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(3*exp(x),x, algorithm="fricas")

[Out]

3*e^x

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giac [A]  time = 0.16, size = 4, normalized size = 0.40 \begin {gather*} 3 \, e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(3*exp(x),x, algorithm="giac")

[Out]

3*e^x

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maple [A]  time = 0.02, size = 5, normalized size = 0.50




method result size



gosper \(3 \,{\mathrm e}^{x}\) \(5\)
derivativedivides \(3 \,{\mathrm e}^{x}\) \(5\)
default \(3 \,{\mathrm e}^{x}\) \(5\)
norman \(3 \,{\mathrm e}^{x}\) \(5\)
risch \(3 \,{\mathrm e}^{x}\) \(5\)
meijerg \(-3+3 \,{\mathrm e}^{x}\) \(7\)



Verification of antiderivative is not currently implemented for this CAS.

[In]

int(3*exp(x),x,method=_RETURNVERBOSE)

[Out]

3*exp(x)

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maxima [A]  time = 0.38, size = 4, normalized size = 0.40 \begin {gather*} 3 \, e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(3*exp(x),x, algorithm="maxima")

[Out]

3*e^x

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mupad [B]  time = 0.01, size = 4, normalized size = 0.40 \begin {gather*} 3\,{\mathrm {e}}^x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(3*exp(x),x)

[Out]

3*exp(x)

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sympy [A]  time = 0.03, size = 3, normalized size = 0.30 \begin {gather*} 3 e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(3*exp(x),x)

[Out]

3*exp(x)

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