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

Optimal. Leaf size=10 \[ \frac {2 \left (e^3+x\right )}{x} \]

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Rubi [A]  time = 0.00, antiderivative size = 8, normalized size of antiderivative = 0.80, 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^3}{x} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

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

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Mathematica [A]  time = 0.00, size = 8, normalized size = 0.80 \begin {gather*} \frac {2 e^3}{x} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

(2*E^3)/x

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fricas [A]  time = 0.65, size = 7, normalized size = 0.70 \begin {gather*} \frac {2 \, e^{3}}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

2*e^3/x

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giac [A]  time = 0.25, size = 7, normalized size = 0.70 \begin {gather*} \frac {2 \, e^{3}}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

2*e^3/x

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maple [A]  time = 0.02, size = 8, normalized size = 0.80

method	result	size
gosper	\(\frac {2 \,{\mathrm e}^{3}}{x}\)	\(8\)
default	\(\frac {2 \,{\mathrm e}^{3}}{x}\)	\(8\)
norman	\(\frac {2 \,{\mathrm e}^{3}}{x}\)	\(8\)
risch	\(\frac {2 \,{\mathrm e}^{3}}{x}\)	\(8\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

2*exp(3)/x

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maxima [A]  time = 0.36, size = 7, normalized size = 0.70 \begin {gather*} \frac {2 \, e^{3}}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

2*e^3/x

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mupad [B]  time = 0.02, size = 7, normalized size = 0.70 \begin {gather*} \frac {2\,{\mathrm {e}}^3}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

(2*exp(3))/x

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sympy [A]  time = 0.05, size = 5, normalized size = 0.50 \begin {gather*} \frac {2 e^{3}}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

2*exp(3)/x

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