3.36.62 \(\int \frac {4 e}{x^3} \, dx\)

Optimal. Leaf size=6 \[ -\frac {2 e}{x^2} \]

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Rubi [A]  time = 0.00, antiderivative size = 6, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 6, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.333, Rules used = {12, 30} \begin {gather*} -\frac {2 e}{x^2} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

(-2*E)/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} &=(4 e) \int \frac {1}{x^3} \, dx\\ &=-\frac {2 e}{x^2}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 6, normalized size = 1.00 \begin {gather*} -\frac {2 e}{x^2} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

(-2*E)/x^2

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fricas [A]  time = 0.59, size = 10, normalized size = 1.67 \begin {gather*} -\frac {e^{\left (\log \relax (2) + 1\right )}}{x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*exp(1+log(2))/x^3,x, algorithm="fricas")

[Out]

-e^(log(2) + 1)/x^2

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giac [A]  time = 0.21, size = 10, normalized size = 1.67 \begin {gather*} -\frac {e^{\left (\log \relax (2) + 1\right )}}{x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*exp(1+log(2))/x^3,x, algorithm="giac")

[Out]

-e^(log(2) + 1)/x^2

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maple [A]  time = 0.03, size = 8, normalized size = 1.33

method	result	size
norman	\(-\frac {2 \,{\mathrm e}}{x^{2}}\)	\(8\)
risch	\(-\frac {2 \,{\mathrm e}}{x^{2}}\)	\(8\)
gosper	\(-\frac {{\mathrm e}^{1+\ln \relax (2)}}{x^{2}}\)	\(11\)
default	\(-\frac {{\mathrm e}^{1+\ln \relax (2)}}{x^{2}}\)	\(11\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(2*exp(1+ln(2))/x^3,x,method=_RETURNVERBOSE)

[Out]

-2*exp(1)/x^2

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maxima [A]  time = 0.35, size = 7, normalized size = 1.17 \begin {gather*} -\frac {2 \, e}{x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*exp(1+log(2))/x^3,x, algorithm="maxima")

[Out]

-2*e/x^2

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mupad [B]  time = 0.04, size = 7, normalized size = 1.17 \begin {gather*} -\frac {2\,\mathrm {e}}{x^2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((2*exp(log(2) + 1))/x^3,x)

[Out]

-(2*exp(1))/x^2

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sympy [A]  time = 0.05, size = 8, normalized size = 1.33 \begin {gather*} - \frac {2 e}{x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*exp(1+ln(2))/x**3,x)

[Out]

-2*E/x**2

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