3.98.78 \(\int -\frac {4 e^{2 e^{4 e^2}}}{x^3} \, dx\)

Optimal. Leaf size=16 \[ \frac {2 e^{2 e^{4 e^2}}}{x^2} \]

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Rubi [A]  time = 0.00, antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {12, 30} \begin {gather*} \frac {2 e^{2 e^{4 e^2}}}{x^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-4*E^(2*E^(4*E^2)))/x^3,x]

[Out]

(2*E^(2*E^(4*E^2)))/x^2

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

Rule 30

Int[(x_)^(m_.), x_Symbol] :> Simp[x^(m + 1)/(m + 1), x] /; FreeQ[m, x] && NeQ[m, -1]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=-\left (\left (4 e^{2 e^{4 e^2}}\right ) \int \frac {1}{x^3} \, dx\right )\\ &=\frac {2 e^{2 e^{4 e^2}}}{x^2}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 16, normalized size = 1.00 \begin {gather*} \frac {2 e^{2 e^{4 e^2}}}{x^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-4*E^(2*E^(4*E^2)))/x^3,x]

[Out]

(2*E^(2*E^(4*E^2)))/x^2

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fricas [A]  time = 0.54, size = 13, normalized size = 0.81 \begin {gather*} \frac {2 \, e^{\left (2 \, e^{\left (4 \, e^{2}\right )}\right )}}{x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-4*exp(-log(x)+exp(exp(2))^4)^2/x,x, algorithm="fricas")

[Out]

2*e^(2*e^(4*e^2))/x^2

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giac [A]  time = 0.25, size = 13, normalized size = 0.81 \begin {gather*} \frac {2 \, e^{\left (2 \, e^{\left (4 \, e^{2}\right )}\right )}}{x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-4*exp(-log(x)+exp(exp(2))^4)^2/x,x, algorithm="giac")

[Out]

2*e^(2*e^(4*e^2))/x^2

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maple [A]  time = 0.08, size = 14, normalized size = 0.88

method	result	size
norman	\(\frac {2 \,{\mathrm e}^{2 \,{\mathrm e}^{4 \,{\mathrm e}^{2}}}}{x^{2}}\)	\(14\)
risch	\(\frac {2 \,{\mathrm e}^{2 \,{\mathrm e}^{4 \,{\mathrm e}^{2}}}}{x^{2}}\)	\(14\)
gosper	\(\frac {2 \,{\mathrm e}^{2 \,{\mathrm e}^{4 \,{\mathrm e}^{2}}}}{x^{2}}\)	\(16\)
derivativedivides	\(\frac {2 \,{\mathrm e}^{2 \,{\mathrm e}^{4 \,{\mathrm e}^{2}}}}{x^{2}}\)	\(16\)
default	\(\frac {2 \,{\mathrm e}^{2 \,{\mathrm e}^{4 \,{\mathrm e}^{2}}}}{x^{2}}\)	\(16\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-4*exp(-ln(x)+exp(exp(2))^4)^2/x,x,method=_RETURNVERBOSE)

[Out]

2*exp(exp(exp(2))^4)^2/x^2

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maxima [A]  time = 0.37, size = 13, normalized size = 0.81 \begin {gather*} \frac {2 \, e^{\left (2 \, e^{\left (4 \, e^{2}\right )}\right )}}{x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-4*exp(-log(x)+exp(exp(2))^4)^2/x,x, algorithm="maxima")

[Out]

2*e^(2*e^(4*e^2))/x^2

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mupad [B]  time = 5.68, size = 13, normalized size = 0.81 \begin {gather*} \frac {2\,{\mathrm {e}}^{2\,{\mathrm {e}}^{4\,{\mathrm {e}}^2}}}{x^2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(4*exp(2*exp(4*exp(2)) - 2*log(x)))/x,x)

[Out]

(2*exp(2*exp(4*exp(2))))/x^2

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sympy [A]  time = 0.07, size = 14, normalized size = 0.88 \begin {gather*} \frac {2 e^{2 e^{4 e^{2}}}}{x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-4*exp(-ln(x)+exp(exp(2))**4)**2/x,x)

[Out]

2*exp(2*exp(4*exp(2)))/x**2

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