3.42.43 \(\int \frac {\log (3)}{x^2} \, dx\) [4143]

Optimal. Leaf size=12 \[ \log \left (\frac {3^{-1/x}}{5}\right ) \]

[Out]

ln(1/5*exp(-ln(3)/x))

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Rubi [A]
time = 0.00, antiderivative size = 7, normalized size of antiderivative = 0.58, 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 {\log (3)}{x} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[Log[3]/x^2,x]

[Out]

-(Log[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} &=\log (3) \int \frac {1}{x^2} \, dx\\ &=-\frac {\log (3)}{x}\\ \end {aligned} \end {gather*}

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Mathematica [A]
time = 0.00, size = 7, normalized size = 0.58 \begin {gather*} -\frac {\log (3)}{x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[Log[3]/x^2,x]

[Out]

-(Log[3]/x)

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Maple [A]
time = 0.07, size = 8, normalized size = 0.67

method	result	size
gosper	\(-\frac {\ln \left (3\right )}{x}\)	\(8\)
default	\(-\frac {\ln \left (3\right )}{x}\)	\(8\)
norman	\(-\frac {\ln \left (3\right )}{x}\)	\(8\)
risch	\(-\frac {\ln \left (3\right )}{x}\)	\(8\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-ln(3)/x

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Maxima [A]
time = 0.27, size = 7, normalized size = 0.58 \begin {gather*} -\frac {\log \left (3\right )}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-log(3)/x

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Fricas [A]
time = 0.39, size = 7, normalized size = 0.58 \begin {gather*} -\frac {\log \left (3\right )}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-log(3)/x

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Sympy [A]
time = 0.01, size = 5, normalized size = 0.42 \begin {gather*} - \frac {\log {\left (3 \right )}}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-log(3)/x

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Giac [A]
time = 0.41, size = 7, normalized size = 0.58 \begin {gather*} -\frac {\log \left (3\right )}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-log(3)/x

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Mupad [B]
time = 0.02, size = 7, normalized size = 0.58 \begin {gather*} -\frac {\ln \left (3\right )}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(log(3)/x^2,x)

[Out]

-log(3)/x

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