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

Optimal. Leaf size=24 \[ \frac {\frac {2 e^2}{x}+e^{4 e^{e^2}} x}{x} \]

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Rubi [A]  time = 0.00, antiderivative size = 8, normalized size of antiderivative = 0.33, number of steps used = 2, number of rules used = 2, integrand size = 8, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.250, Rules used = {12, 30} \begin {gather*} \frac {2 e^2}{x^2} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

(2*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\right ) \int \frac {1}{x^3} \, dx\right )\\ &=\frac {2 e^2}{x^2}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 8, normalized size = 0.33 \begin {gather*} \frac {2 e^2}{x^2} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

(2*E^2)/x^2

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fricas [A]  time = 0.46, size = 7, normalized size = 0.29 \begin {gather*} \frac {2 \, e^{2}}{x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-4*exp(2)/x^3,x, algorithm="fricas")

[Out]

2*e^2/x^2

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giac [A]  time = 0.12, size = 7, normalized size = 0.29 \begin {gather*} \frac {2 \, e^{2}}{x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-4*exp(2)/x^3,x, algorithm="giac")

[Out]

2*e^2/x^2

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maple [A]  time = 0.02, size = 8, normalized size = 0.33

method	result	size
gosper	\(\frac {2 \,{\mathrm e}^{2}}{x^{2}}\)	\(8\)
default	\(\frac {2 \,{\mathrm e}^{2}}{x^{2}}\)	\(8\)
norman	\(\frac {2 \,{\mathrm e}^{2}}{x^{2}}\)	\(8\)
risch	\(\frac {2 \,{\mathrm e}^{2}}{x^{2}}\)	\(8\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-4*exp(2)/x^3,x,method=_RETURNVERBOSE)

[Out]

2*exp(2)/x^2

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maxima [A]  time = 0.36, size = 7, normalized size = 0.29 \begin {gather*} \frac {2 \, e^{2}}{x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-4*exp(2)/x^3,x, algorithm="maxima")

[Out]

2*e^2/x^2

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mupad [B]  time = 0.04, size = 7, normalized size = 0.29 \begin {gather*} \frac {2\,{\mathrm {e}}^2}{x^2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(4*exp(2))/x^3,x)

[Out]

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

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sympy [A]  time = 0.05, size = 7, normalized size = 0.29 \begin {gather*} \frac {2 e^{2}}{x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-4*exp(2)/x**3,x)

[Out]

2*exp(2)/x**2

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