3.1.43 \(\int 90 e^{9 e^{10 x}+10 x} \, dx\)

Optimal. Leaf size=9 \[ e^{9 e^{10 x}} \]

________________________________________________________________________________________

Rubi [A]  time = 0.01, antiderivative size = 9, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 3, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {12, 2282, 2194} \begin {gather*} e^{9 e^{10 x}} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[90*E^(9*E^(10*x) + 10*x),x]

[Out]

E^(9*E^(10*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]

Rule 2282

Int[u_, x_Symbol] :> With[{v = FunctionOfExponential[u, x]}, Dist[v/D[v, x], Subst[Int[FunctionOfExponentialFu
nction[u, x]/x, x], x, v], x]] /; FunctionOfExponentialQ[u, x] &&  !MatchQ[u, (w_)*((a_.)*(v_)^(n_))^(m_) /; F
reeQ[{a, m, n}, x] && IntegerQ[m*n]] &&  !MatchQ[u, E^((c_.)*((a_.) + (b_.)*x))*(F_)[v_] /; FreeQ[{a, b, c}, x
] && InverseFunctionQ[F[x]]]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=90 \int e^{9 e^{10 x}+10 x} \, dx\\ &=9 \operatorname {Subst}\left (\int e^{9 x} \, dx,x,e^{10 x}\right )\\ &=e^{9 e^{10 x}}\\ \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [A]  time = 0.01, size = 9, normalized size = 1.00 \begin {gather*} e^{9 e^{10 x}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[90*E^(9*E^(10*x) + 10*x),x]

[Out]

E^(9*E^(10*x))

________________________________________________________________________________________

fricas [A]  time = 0.69, size = 7, normalized size = 0.78 \begin {gather*} e^{\left (9 \, e^{\left (10 \, x\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(90*exp(10*x)*exp(9*exp(10*x)),x, algorithm="fricas")

[Out]

e^(9*e^(10*x))

________________________________________________________________________________________

giac [A]  time = 0.43, size = 7, normalized size = 0.78 \begin {gather*} e^{\left (9 \, e^{\left (10 \, x\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(90*exp(10*x)*exp(9*exp(10*x)),x, algorithm="giac")

[Out]

e^(9*e^(10*x))

________________________________________________________________________________________

maple [A]  time = 0.01, size = 8, normalized size = 0.89

method	result	size
derivativedivides	\({\mathrm e}^{9 \,{\mathrm e}^{10 x}}\)	\(8\)
default	\({\mathrm e}^{9 \,{\mathrm e}^{10 x}}\)	\(8\)
norman	\({\mathrm e}^{9 \,{\mathrm e}^{10 x}}\)	\(8\)
risch	\({\mathrm e}^{9 \,{\mathrm e}^{10 x}}\)	\(8\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(90*exp(10*x)*exp(9*exp(10*x)),x,method=_RETURNVERBOSE)

[Out]

exp(9*exp(10*x))

________________________________________________________________________________________

maxima [A]  time = 0.38, size = 7, normalized size = 0.78 \begin {gather*} e^{\left (9 \, e^{\left (10 \, x\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(90*exp(10*x)*exp(9*exp(10*x)),x, algorithm="maxima")

[Out]

e^(9*e^(10*x))

________________________________________________________________________________________

mupad [B]  time = 0.05, size = 7, normalized size = 0.78 \begin {gather*} {\mathrm {e}}^{9\,{\mathrm {e}}^{10\,x}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(90*exp(9*exp(10*x))*exp(10*x),x)

[Out]

exp(9*exp(10*x))

________________________________________________________________________________________

sympy [A]  time = 0.09, size = 7, normalized size = 0.78 \begin {gather*} e^{9 e^{10 x}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(90*exp(10*x)*exp(9*exp(10*x)),x)

[Out]

exp(9*exp(10*x))

________________________________________________________________________________________