3.79.13 \(\int 5 e^x \, dx\)

Optimal. Leaf size=28 \[ 5 \left (e^x+\frac {e^5}{\left (i \pi +\log \left (-4+\frac {e^{10}}{16}\right )\right )^2}\right ) \]

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Rubi [A]  time = 0.00, antiderivative size = 5, normalized size of antiderivative = 0.18, 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*} 5 e^x \end {gather*}

Antiderivative was successfully verified.

[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 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} &=5 \int e^x \, dx\\ &=5 e^x\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 5, normalized size = 0.18 \begin {gather*} 5 e^x \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[5*E^x,x]

[Out]

5*E^x

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fricas [A]  time = 0.62, size = 4, normalized size = 0.14 \begin {gather*} 5 \, e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

5*e^x

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giac [A]  time = 0.13, size = 4, normalized size = 0.14 \begin {gather*} 5 \, e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

5*e^x

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maple [A]  time = 0.01, size = 5, normalized size = 0.18

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

5*exp(x)

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maxima [A]  time = 0.36, size = 4, normalized size = 0.14 \begin {gather*} 5 \, e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

5*e^x

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mupad [B]  time = 0.01, size = 4, normalized size = 0.14 \begin {gather*} 5\,{\mathrm {e}}^x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(5*exp(x),x)

[Out]

5*exp(x)

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sympy [A]  time = 0.03, size = 3, normalized size = 0.11 \begin {gather*} 5 e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(5*exp(x),x)

[Out]

5*exp(x)

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