3.16.31 \(\int e^x (1+e^5) \, dx\)

Optimal. Leaf size=9 \[ e^x \left (1+e^5\right ) \]

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Rubi [A]  time = 0.00, antiderivative size = 9, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.222, Rules used = {12, 2194} \begin {gather*} \left (1+e^5\right ) e^x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[E^x*(1 + E^5),x]

[Out]

E^x*(1 + E^5)

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} &=\left (1+e^5\right ) \int e^x \, dx\\ &=e^x \left (1+e^5\right )\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 9, normalized size = 1.00 \begin {gather*} e^x \left (1+e^5\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[E^x*(1 + E^5),x]

[Out]

E^x*(1 + E^5)

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fricas [A]  time = 0.75, size = 7, normalized size = 0.78 \begin {gather*} {\left (e^{5} + 1\right )} e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((exp(5)+1)*exp(x),x, algorithm="fricas")

[Out]

(e^5 + 1)*e^x

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giac [A]  time = 1.00, size = 7, normalized size = 0.78 \begin {gather*} {\left (e^{5} + 1\right )} e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((exp(5)+1)*exp(x),x, algorithm="giac")

[Out]

(e^5 + 1)*e^x

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maple [A]  time = 0.02, size = 8, normalized size = 0.89

method	result	size
gosper	\(\left ({\mathrm e}^{5}+1\right ) {\mathrm e}^{x}\)	\(8\)
derivativedivides	\(\left ({\mathrm e}^{5}+1\right ) {\mathrm e}^{x}\)	\(8\)
default	\(\left ({\mathrm e}^{5}+1\right ) {\mathrm e}^{x}\)	\(8\)
norman	\(\left ({\mathrm e}^{5}+1\right ) {\mathrm e}^{x}\)	\(8\)
risch	\({\mathrm e}^{5} {\mathrm e}^{x}+{\mathrm e}^{x}\)	\(9\)
meijerg	\(-{\mathrm e}^{5} \left (1-{\mathrm e}^{x}\right )-1+{\mathrm e}^{x}\)	\(15\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(5)+1)*exp(x),x,method=_RETURNVERBOSE)

[Out]

(exp(5)+1)*exp(x)

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maxima [A]  time = 0.51, size = 7, normalized size = 0.78 \begin {gather*} {\left (e^{5} + 1\right )} e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((exp(5)+1)*exp(x),x, algorithm="maxima")

[Out]

(e^5 + 1)*e^x

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mupad [B]  time = 0.02, size = 7, normalized size = 0.78 \begin {gather*} {\mathrm {e}}^x\,\left ({\mathrm {e}}^5+1\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(x)*(exp(5) + 1),x)

[Out]

exp(x)*(exp(5) + 1)

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sympy [A]  time = 0.08, size = 7, normalized size = 0.78 \begin {gather*} \left (1 + e^{5}\right ) e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((exp(5)+1)*exp(x),x)

[Out]

(1 + exp(5))*exp(x)

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