3.5.53 \(\int e^{5+10 e^{18}+5 e^{36}} \, dx\)

Optimal. Leaf size=13 \[ e^{5 \left (1+e^{18}\right )^2} x \]

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Rubi [A]  time = 0.01, antiderivative size = 13, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.071, Rules used = {8} \begin {gather*} e^{5 \left (1+e^{18}\right )^2} x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[E^(5 + 10*E^18 + 5*E^36),x]

[Out]

E^(5*(1 + E^18)^2)*x

Rule 8

Int[a_, x_Symbol] :> Simp[a*x, x] /; FreeQ[a, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=e^{5 \left (1+e^{18}\right )^2} x\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 16, normalized size = 1.23 \begin {gather*} e^{5+10 e^{18}+5 e^{36}} x \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[E^(5 + 10*E^18 + 5*E^36),x]

[Out]

E^(5 + 10*E^18 + 5*E^36)*x

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fricas [A]  time = 0.72, size = 13, normalized size = 1.00 \begin {gather*} x e^{\left (5 \, e^{36} + 10 \, e^{18} + 5\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(5*exp(9)^4+10*exp(9)^2+5),x, algorithm="fricas")

[Out]

x*e^(5*e^36 + 10*e^18 + 5)

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giac [A]  time = 0.24, size = 13, normalized size = 1.00 \begin {gather*} x e^{\left (5 \, e^{36} + 10 \, e^{18} + 5\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(5*exp(9)^4+10*exp(9)^2+5),x, algorithm="giac")

[Out]

x*e^(5*e^36 + 10*e^18 + 5)

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maple [A]  time = 0.02, size = 14, normalized size = 1.08

method	result	size
risch	\(x \,{\mathrm e}^{5 \,{\mathrm e}^{36}+10 \,{\mathrm e}^{18}+5}\)	\(14\)
default	\(x \,{\mathrm e}^{5 \,{\mathrm e}^{36}+10 \,{\mathrm e}^{18}+5}\)	\(18\)
norman	\({\mathrm e}^{5 \,{\mathrm e}^{36}} {\mathrm e}^{10 \,{\mathrm e}^{18}} {\mathrm e}^{5} x\)	\(19\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(5*exp(9)^4+10*exp(9)^2+5),x,method=_RETURNVERBOSE)

[Out]

x*exp(5*exp(36)+10*exp(18)+5)

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maxima [A]  time = 0.39, size = 13, normalized size = 1.00 \begin {gather*} x e^{\left (5 \, e^{36} + 10 \, e^{18} + 5\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(5*exp(9)^4+10*exp(9)^2+5),x, algorithm="maxima")

[Out]

x*e^(5*e^36 + 10*e^18 + 5)

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mupad [B]  time = 0.00, size = 13, normalized size = 1.00 \begin {gather*} x\,{\mathrm {e}}^{10\,{\mathrm {e}}^{18}+5\,{\mathrm {e}}^{36}+5} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(10*exp(18) + 5*exp(36) + 5),x)

[Out]

x*exp(10*exp(18) + 5*exp(36) + 5)

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sympy [A]  time = 0.05, size = 14, normalized size = 1.08 \begin {gather*} x e^{5 + 10 e^{18} + 5 e^{36}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(5*exp(9)**4+10*exp(9)**2+5),x)

[Out]

x*exp(5 + 10*exp(18) + 5*exp(36))

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