\(\int -\frac {4}{x \log (2)} \, dx\) [1719]

Optimal result

Integrand size = 9, antiderivative size = 12 \[ \int -\frac {4}{x \log (2)} \, dx=\frac {4 (5-\log (x))}{\log (2)} \]

[Out]

4*(5-ln(x))/ln(2)

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.67, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.222, Rules used = {12, 29} \[ \int -\frac {4}{x \log (2)} \, dx=-\frac {4 \log (x)}{\log (2)} \]

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

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.67 \[ \int -\frac {4}{x \log (2)} \, dx=-\frac {4 \log (x)}{\log (2)} \]

[In]

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

[Out]

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

Maple [A] (verified)

Time = 0.04 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.75

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

[In]

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

[Out]

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

Fricas [A] (verification not implemented)

none

Time = 0.24 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.67 \[ \int -\frac {4}{x \log (2)} \, dx=-\frac {4 \, \log \left (x\right )}{\log \left (2\right )} \]

[In]

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

[Out]

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

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.67 \[ \int -\frac {4}{x \log (2)} \, dx=- \frac {4 \log {\left (x \right )}}{\log {\left (2 \right )}} \]

[In]

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

[Out]

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

Maxima [A] (verification not implemented)

none

Time = 0.19 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.67 \[ \int -\frac {4}{x \log (2)} \, dx=-\frac {4 \, \log \left (x\right )}{\log \left (2\right )} \]

[In]

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

[Out]

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

Giac [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.75 \[ \int -\frac {4}{x \log (2)} \, dx=-\frac {4 \, \log \left ({\left | x \right |}\right )}{\log \left (2\right )} \]

[In]

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

[Out]

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

Mupad [B] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.67 \[ \int -\frac {4}{x \log (2)} \, dx=-\frac {4\,\ln \left (x\right )}{\ln \left (2\right )} \]

[In]

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

[Out]

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