3.81.56 \(\int 14 e^{9+14 x} \, dx\)

Optimal. Leaf size=21 \[ e^{1+2 \left (-12-x-x^2+(4+x)^2\right )} \]

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Rubi [A]  time = 0.00, antiderivative size = 7, normalized size of antiderivative = 0.33, 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*} e^{14 x+9} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[14*E^(9 + 14*x),x]

[Out]

E^(9 + 14*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} &=14 \int e^{9+14 x} \, dx\\ &=e^{9+14 x}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 7, normalized size = 0.33 \begin {gather*} e^{9+14 x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[14*E^(9 + 14*x),x]

[Out]

E^(9 + 14*x)

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fricas [A]  time = 0.80, size = 6, normalized size = 0.29 \begin {gather*} e^{\left (14 \, x + 9\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(14*exp(14*x+9),x, algorithm="fricas")

[Out]

e^(14*x + 9)

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giac [A]  time = 0.12, size = 6, normalized size = 0.29 \begin {gather*} e^{\left (14 \, x + 9\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(14*exp(14*x+9),x, algorithm="giac")

[Out]

e^(14*x + 9)

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maple [A]  time = 0.01, size = 7, normalized size = 0.33

method	result	size
gosper	\({\mathrm e}^{14 x +9}\)	\(7\)
derivativedivides	\({\mathrm e}^{14 x +9}\)	\(7\)
default	\({\mathrm e}^{14 x +9}\)	\(7\)
norman	\({\mathrm e}^{14 x +9}\)	\(7\)
risch	\({\mathrm e}^{14 x +9}\)	\(7\)
meijerg	\(-{\mathrm e}^{9} \left (1-{\mathrm e}^{14 x}\right )\)	\(13\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(14*exp(14*x+9),x,method=_RETURNVERBOSE)

[Out]

exp(14*x+9)

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maxima [A]  time = 0.36, size = 6, normalized size = 0.29 \begin {gather*} e^{\left (14 \, x + 9\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(14*exp(14*x+9),x, algorithm="maxima")

[Out]

e^(14*x + 9)

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mupad [B]  time = 0.06, size = 7, normalized size = 0.33 \begin {gather*} {\mathrm {e}}^{14\,x}\,{\mathrm {e}}^9 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(14*exp(14*x + 9),x)

[Out]

exp(14*x)*exp(9)

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sympy [A]  time = 0.07, size = 5, normalized size = 0.24 \begin {gather*} e^{14 x + 9} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(14*exp(14*x+9),x)

[Out]

exp(14*x + 9)

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