3.81.25 \(\int \frac {32}{3} e^{3+\sqrt [4]{e}} \, dx\)

Optimal. Leaf size=14 \[ \frac {32}{3} e^{3+\sqrt [4]{e}} x \]

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Rubi [A]  time = 0.00, antiderivative size = 14, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {8} \begin {gather*} \frac {32}{3} e^{3+\sqrt [4]{e}} x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(32*E^(3 + E^(1/4)))/3,x]

[Out]

(32*E^(3 + E^(1/4))*x)/3

Rule 8

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

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {32}{3} e^{3+\sqrt [4]{e}} x\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 14, normalized size = 1.00 \begin {gather*} \frac {32}{3} e^{3+\sqrt [4]{e}} x \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(32*E^(3 + E^(1/4)))/3,x]

[Out]

(32*E^(3 + E^(1/4))*x)/3

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fricas [A]  time = 0.92, size = 8, normalized size = 0.57 \begin {gather*} \frac {32}{3} \, x e^{\left (e^{\frac {1}{4}} + 3\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(32/3*exp(exp(1/4)+3),x, algorithm="fricas")

[Out]

32/3*x*e^(e^(1/4) + 3)

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giac [A]  time = 0.18, size = 8, normalized size = 0.57 \begin {gather*} \frac {32}{3} \, x e^{\left (e^{\frac {1}{4}} + 3\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(32/3*exp(exp(1/4)+3),x, algorithm="giac")

[Out]

32/3*x*e^(e^(1/4) + 3)

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maple [A]  time = 0.01, size = 9, normalized size = 0.64

method	result	size
default	\(\frac {32 \,{\mathrm e}^{{\mathrm e}^{\frac {1}{4}}+3} x}{3}\)	\(9\)
norman	\(\frac {32 \,{\mathrm e}^{{\mathrm e}^{\frac {1}{4}}} {\mathrm e}^{3} x}{3}\)	\(9\)
risch	\(\frac {32 \,{\mathrm e}^{{\mathrm e}^{\frac {1}{4}}+3} x}{3}\)	\(9\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(32/3*exp(exp(1/4)+3),x,method=_RETURNVERBOSE)

[Out]

32/3*exp(exp(1/4)+3)*x

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maxima [A]  time = 0.36, size = 8, normalized size = 0.57 \begin {gather*} \frac {32}{3} \, x e^{\left (e^{\frac {1}{4}} + 3\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(32/3*exp(exp(1/4)+3),x, algorithm="maxima")

[Out]

32/3*x*e^(e^(1/4) + 3)

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mupad [B]  time = 0.00, size = 8, normalized size = 0.57 \begin {gather*} \frac {32\,x\,{\mathrm {e}}^{{\mathrm {e}}^{1/4}+3}}{3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((32*exp(exp(1/4) + 3))/3,x)

[Out]

(32*x*exp(exp(1/4) + 3))/3

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sympy [A]  time = 0.04, size = 12, normalized size = 0.86 \begin {gather*} \frac {32 x e^{e^{\frac {1}{4}} + 3}}{3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(32/3*exp(exp(1/4)+3),x)

[Out]

32*x*exp(exp(1/4) + 3)/3

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