3.104.10 \(\int 90 e^{2 e^2+x} \, dx\)

Optimal. Leaf size=16 \[ 45 e^{2 e^2} \left (3+2 e^x\right ) \]

________________________________________________________________________________________

Rubi [A]  time = 0.00, antiderivative size = 11, normalized size of antiderivative = 0.69, number of steps used = 2, number of rules used = 2, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.182, Rules used = {12, 2194} \begin {gather*} 90 e^{x+2 e^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[90*E^(2*E^2 + x),x]

[Out]

90*E^(2*E^2 + 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} &=90 \int e^{2 e^2+x} \, dx\\ &=90 e^{2 e^2+x}\\ \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [A]  time = 0.00, size = 11, normalized size = 0.69 \begin {gather*} 90 e^{2 e^2+x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[90*E^(2*E^2 + x),x]

[Out]

90*E^(2*E^2 + x)

________________________________________________________________________________________

fricas [A]  time = 0.58, size = 9, normalized size = 0.56 \begin {gather*} 90 \, e^{\left (x + 2 \, e^{2}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(90*exp(x)*exp(exp(1)^2)^2,x, algorithm="fricas")

[Out]

90*e^(x + 2*e^2)

________________________________________________________________________________________

giac [A]  time = 0.13, size = 9, normalized size = 0.56 \begin {gather*} 90 \, e^{\left (x + 2 \, e^{2}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(90*exp(x)*exp(exp(1)^2)^2,x, algorithm="giac")

[Out]

90*e^(x + 2*e^2)

________________________________________________________________________________________

maple [A]  time = 0.02, size = 10, normalized size = 0.62

method	result	size
risch	\(90 \,{\mathrm e}^{x +2 \,{\mathrm e}^{2}}\)	\(10\)
gosper	\(90 \,{\mathrm e}^{x} {\mathrm e}^{2 \,{\mathrm e}^{2}}\)	\(12\)
derivativedivides	\(90 \,{\mathrm e}^{x} {\mathrm e}^{2 \,{\mathrm e}^{2}}\)	\(12\)
default	\(90 \,{\mathrm e}^{x} {\mathrm e}^{2 \,{\mathrm e}^{2}}\)	\(12\)
norman	\(90 \,{\mathrm e}^{x} {\mathrm e}^{2 \,{\mathrm e}^{2}}\)	\(12\)
meijerg	\(-90 \,{\mathrm e}^{2 \,{\mathrm e}^{2}} \left (1-{\mathrm e}^{x}\right )\)	\(14\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(90*exp(x)*exp(exp(1)^2)^2,x,method=_RETURNVERBOSE)

[Out]

90*exp(x+2*exp(2))

________________________________________________________________________________________

maxima [A]  time = 0.35, size = 9, normalized size = 0.56 \begin {gather*} 90 \, e^{\left (x + 2 \, e^{2}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(90*exp(x)*exp(exp(1)^2)^2,x, algorithm="maxima")

[Out]

90*e^(x + 2*e^2)

________________________________________________________________________________________

mupad [B]  time = 0.02, size = 9, normalized size = 0.56 \begin {gather*} 90\,{\mathrm {e}}^{2\,{\mathrm {e}}^2}\,{\mathrm {e}}^x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(90*exp(2*exp(2))*exp(x),x)

[Out]

90*exp(2*exp(2))*exp(x)

________________________________________________________________________________________

sympy [A]  time = 0.08, size = 10, normalized size = 0.62 \begin {gather*} 90 e^{x} e^{2 e^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(90*exp(x)*exp(exp(1)**2)**2,x)

[Out]

90*exp(x)*exp(2*exp(2))

________________________________________________________________________________________