3.18.19 \(\int -\frac {4}{x \log (2)} \, dx\)

Optimal. Leaf size=12 \[ \frac {4 (5-\log (x))}{\log (2)} \]

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Rubi [A]  time = 0.00, antiderivative size = 8, normalized size of antiderivative = 0.67, number of steps used = 2, number of rules used = 2, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.222, Rules used = {12, 29} \begin {gather*} -\frac {4 \log (x)}{\log (2)} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-4/(x*Log[2]),x]

[Out]

(-4*Log[x])/Log[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 29

Int[(x_)^(-1), x_Symbol] :> Simp[Log[x], x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=-\frac {4 \int \frac {1}{x} \, dx}{\log (2)}\\ &=-\frac {4 \log (x)}{\log (2)}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 8, normalized size = 0.67 \begin {gather*} -\frac {4 \log (x)}{\log (2)} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-4/(x*Log[2]),x]

[Out]

(-4*Log[x])/Log[2]

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fricas [A]  time = 0.81, size = 8, normalized size = 0.67 \begin {gather*} -\frac {4 \, \log \relax (x)}{\log \relax (2)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-4/x/log(2),x, algorithm="fricas")

[Out]

-4*log(x)/log(2)

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giac [A]  time = 0.30, size = 9, normalized size = 0.75 \begin {gather*} -\frac {4 \, \log \left ({\left | x \right |}\right )}{\log \relax (2)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-4/x/log(2),x, algorithm="giac")

[Out]

-4*log(abs(x))/log(2)

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maple [A]  time = 0.02, size = 9, normalized size = 0.75

method	result	size
default	\(-\frac {4 \ln \relax (x )}{\ln \relax (2)}\)	\(9\)
norman	\(-\frac {4 \ln \relax (x )}{\ln \relax (2)}\)	\(9\)
risch	\(-\frac {4 \ln \relax (x )}{\ln \relax (2)}\)	\(9\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-4/x/ln(2),x,method=_RETURNVERBOSE)

[Out]

-4*ln(x)/ln(2)

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maxima [A]  time = 0.38, size = 8, normalized size = 0.67 \begin {gather*} -\frac {4 \, \log \relax (x)}{\log \relax (2)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-4/x/log(2),x, algorithm="maxima")

[Out]

-4*log(x)/log(2)

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mupad [B]  time = 0.02, size = 8, normalized size = 0.67 \begin {gather*} -\frac {4\,\ln \relax (x)}{\ln \relax (2)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-4/(x*log(2)),x)

[Out]

-(4*log(x))/log(2)

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sympy [A]  time = 0.06, size = 8, normalized size = 0.67 \begin {gather*} - \frac {4 \log {\relax (x )}}{\log {\relax (2 )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-4/x/ln(2),x)

[Out]

-4*log(x)/log(2)

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