3.18.81 \(\int -\frac {e^{2 e^5}}{480 x^2} \, dx\)

Optimal. Leaf size=14 \[ \frac {e^{2 e^5}}{480 x} \]

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Rubi [A]  time = 0.00, antiderivative size = 14, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {12, 30} \begin {gather*} \frac {e^{2 e^5}}{480 x} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-1/480*E^(2*E^5)/x^2,x]

[Out]

E^(2*E^5)/(480*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 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 (\frac {1}{480} e^{2 e^5} \int \frac {1}{x^2} \, dx\right )\\ &=\frac {e^{2 e^5}}{480 x}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 14, normalized size = 1.00 \begin {gather*} \frac {e^{2 e^5}}{480 x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-1/480*E^(2*E^5)/x^2,x]

[Out]

E^(2*E^5)/(480*x)

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fricas [A]  time = 0.66, size = 10, normalized size = 0.71 \begin {gather*} \frac {e^{\left (2 \, e^{5}\right )}}{480 \, x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-1/480*exp(exp(5))^2/x^2,x, algorithm="fricas")

[Out]

1/480*e^(2*e^5)/x

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giac [A]  time = 0.21, size = 10, normalized size = 0.71 \begin {gather*} \frac {e^{\left (2 \, e^{5}\right )}}{480 \, x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-1/480*exp(exp(5))^2/x^2,x, algorithm="giac")

[Out]

1/480*e^(2*e^5)/x

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maple [A]  time = 0.02, size = 11, normalized size = 0.79

method	result	size
gosper	\(\frac {{\mathrm e}^{2 \,{\mathrm e}^{5}}}{480 x}\)	\(11\)
default	\(\frac {{\mathrm e}^{2 \,{\mathrm e}^{5}}}{480 x}\)	\(11\)
norman	\(\frac {{\mathrm e}^{2 \,{\mathrm e}^{5}}}{480 x}\)	\(11\)
risch	\(\frac {{\mathrm e}^{2 \,{\mathrm e}^{5}}}{480 x}\)	\(11\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-1/480*exp(exp(5))^2/x^2,x,method=_RETURNVERBOSE)

[Out]

1/480*exp(exp(5))^2/x

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maxima [A]  time = 0.79, size = 10, normalized size = 0.71 \begin {gather*} \frac {e^{\left (2 \, e^{5}\right )}}{480 \, x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-1/480*exp(exp(5))^2/x^2,x, algorithm="maxima")

[Out]

1/480*e^(2*e^5)/x

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mupad [B]  time = 0.03, size = 10, normalized size = 0.71 \begin {gather*} \frac {{\mathrm {e}}^{2\,{\mathrm {e}}^5}}{480\,x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-exp(2*exp(5))/(480*x^2),x)

[Out]

exp(2*exp(5))/(480*x)

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sympy [A]  time = 0.06, size = 8, normalized size = 0.57 \begin {gather*} \frac {e^{2 e^{5}}}{480 x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-1/480*exp(exp(5))**2/x**2,x)

[Out]

exp(2*exp(5))/(480*x)

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